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Istanbul, Turkey, known before 330 as Byzantium and between 330 and 1930 as Constantinople, is a transcontinental city of Europe and Asia, straddling the Bosporus strait between the Sea of Marmara and the Black Sea. Its commercial and historical center lies on the European side; about a third of its residents live on the Asian side. The population of the city has increased tenfold since the 1950s to around 15 million, making Istanbul one of the world's most populous cities and the fourth-largest city proper. Founded on the Sarayburnu promontory around 660 BCE, the city grew in size and influence. It was an imperial capital for almost 16 centuries, during the Roman and Byzantine (330–1204), Latin (1204–1261), Palaiologos Byzantine (1261–1453) and Ottoman (1453–1922) empires. Although Ankara was chosen as the new capital after the Turkish War of Independence, Istanbul remains Turkey's economic and cultural center. (Full article...)

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Roman Empire Senatus Populusque Romanus (Latin) Imperium Romanum[n 1] (Latin) Βασιλεία Ῥωμαίων (Ancient Greek) Basileía Rhōmaíōn 27 BC – 395 AD 395 – 476/480 (Western) 395 – 1453 (Eastern) Flag of Roman Empire Aureus of Augustus {{{coat_alt}}} Vexillum The Roman Empire in AD 117, at its greatest extent at the time of Trajan's death (with its vassals in pink).[1] The Roman Empire in AD 117, at its greatest extent at the time of Trajan's death (with its vassals in pink).[1] Capital Rome (27 BC–330 AD) Mediolanum (286–402, Western) Ravenna (402–476, Western) Nicomedia (286–330, Eastern) Constantinople (330–1453, Eastern)[n 2] Common languages Latin (official until 610) Greek (official after 610) Regional / local languages Religion Imperial cult-driven polytheism (Before AD 380) Nicene Christianity (State Church of the Roman Empire) (From AD 380) Government Semi-elective, functionally absolute monarchy Emperor • 27 BC  – AD 14 Augustus (first) • 98–117 Trajan • 284–305 Diocletian • 306–337 Constantine I • 379–395 Theodosius I[n 3] • 474–480 Julius Nepos[n 4] • 527–565 Justinian I • 976–1025 Basil II • 1449–1453 Constantine XI[n 5] Legislature Senate Historical era Classical era to Late Middle Ages • Final War of the Roman Republic 32–30 BC • Empire established 30–2 BC • Constantinople becomes capital 11 May 330 • Final East-West divide 17 Jan 395 • Fall of the Western Roman Empire 4 Sep 476 • Fourth Crusade 12 Apr 1204 • Reconquest of Constantinople 25 Jul 1261 • Fall of Constantinople 29 May 1453 • Fall of Trebizond 15 August 1461 Area 25 BC[2][3] 2,750,000 km2 (1,060,000 sq mi) AD 117[2][4] 5,000,000 km2 (1,900,000 sq mi) AD 390[2] 4,400,000 km2 (1,700,000 sq mi) Population • 25 BC[2][3] 56,800,000 Currency Sestertius,[n 6] Aureus, Solidus, Nomisma Preceded by Succeeded by Q. Servilius Caepio (M. Junius) Brutus, denarius, 54 BC, RRC 433-1 reverse.jpg Roman Republic Western Roman Empire Julius Nepos Tremissis.jpg Eastern Roman Empire Constantine multiple CdM Beistegui 233.jpg The Roman Empire (Latin: Imperium Rōmānum, Classical Latin: [ɪmˈpɛ.ri.ũː roːˈmaː.nũː]; Koine and Medieval Greek: Βασιλεία τῶν Ῥωμαίων, tr. Basileia tōn Rhōmaiōn; Italian: Impero romano) was the post-Roman Republic period of the ancient Roman civilization. It had a government headed by emperors and large territorial holdings around the Mediterranean Sea in Europe, North Africa, and West Asia. From the constitutional reforms of Augustus to the military anarchy of the third century, the Empire was a principate ruled from the city of Rome (27 BC - 285 AD). The Roman Empire was then divided between a Western Roman Empire, based in Milan and later Ravenna, and an Eastern Roman Empire, based in Nicomedia and later Constantinople, and it was ruled by multiple emperors (with the exception of the sole rule of Constantine I between 324 and 337, and Theodosius I between 392 and 395).

The previous Republic, which had replaced Rome's monarchy in the 6th century BC, became severely destabilized in a series of civil wars and political conflict. In the mid-1st century BC Julius Caesar was appointed as perpetual dictator and then assassinated in 44 BC. Civil wars and executions continued, culminating in the victory of Octavian, Caesar's adopted son, over Mark Antony and Cleopatra at the Battle of Actium in 31 BC. The following year Octavian conquered Ptolemaic Egypt, ending the Hellenistic period that had begun with the conquests of Alexander the Great of Macedon in the 4th century BC. Octavian's power was then unassailable and in 27 BC the Roman Senate formally granted him overarching power and the new title Augustus, effectively making him the first emperor.

The first two centuries of the Empire were a period of unprecedented stability and prosperity known as the Pax Romana ("Roman Peace"). It reached its greatest territorial expanse during the reign of Trajan (98–117 AD). A period of increasing trouble and decline began with the reign of Commodus. In the 3rd century, the Empire underwent a crisis that threatened its existence, but was reunified under Aurelian. In an effort to stabilize the Empire, Diocletian set up two different imperial courts in the Greek East and Latin West. Christians rose to power in the 4th century following the Edict of Milan in 313 and the Edict of Thessalonica in 380. Shortly after, the Migration Period involving large invasions by Germanic peoples and the Huns of Attila led to the decline of the Western Roman Empire. With the Fall of Ravenna to the Germanic Herulians and deposition of Romulus Augustulus in 476 AD by Odoacer, who proclaimed himself King of Italy, the Western Roman Empire finally collapsed and it was formally abolished by emperor Zeno in 480 AD. The Eastern Roman Empire, known in the post-Roman West as the Byzantine Empire, collapsed when Constantinople fell to the Ottoman Turks of Mehmed II in 1453.

Due to the Roman Empire's vast extent and long endurance, the institutions and culture of Rome had a profound and lasting influence on the development of language, religion, architecture, philosophy, law, and forms of government in the territory it governed, particularly Europe. The Latin language of the Romans evolved into the Romance languages of the medieval and modern world, while Medieval Greek became the language of the Eastern Roman Empire. Its adoption of Christianity led to the formation of Christendom during the Middle Ages. Greek and Roman art had a profound impact on the late medieval Italian Renaissance, while Rome's republican institutions influenced the political development of later republics such as the United States and France. The corpus of Roman law has its descendants in many legal systems of the world today, such as the Napoleonic Code. Rome's architectural tradition served as the basis for Neoclassical architecture.

Contents 1 History 2 Legacy 3 Geography and demography 4 Languages 4.1 Local languages and linguistic legacy 5 Society 5.1 Legal status 5.1.1 Women in Roman law 5.1.2 Slaves and the law 5.1.3 Freedmen 5.2 Census rank 5.2.1 Unequal justice 6 Government and military 6.1 Central government 6.2 Military 6.3 Provincial government 6.4 Roman law 6.5 Taxation 7 Economy 7.1 Currency and banking 7.2 Mining and metallurgy 7.3 Transportation and communication 7.4 Trade and commodities 7.5 Labour and occupations 7.6 GDP and income distribution 8 Architecture and engineering 9 Daily life 9.1 City and country 9.2 Food and dining 9.3 Recreation and spectacles 9.3.1 Personal training and play 9.4 Clothing 10 The arts 10.1 Portraiture 10.2 Sculpture 10.2.1 Sarcophagi 10.3 Painting 10.4 Mosaic 10.5 Decorative arts 10.6 Performing arts 11 Literacy, books, and education 11.1 Primary education 11.2 Secondary education 11.3 Educated women 11.4 The shape of literacy 12 Literature 13 Religion 14 Political legacy 15 See also 16 Notes 17 References 17.1 Citations 17.2 Cited sources 18 External links History Main article: History of the Roman Empire See also: Campaign history of the Roman military and Roman Kingdom Rome had begun expanding shortly after the founding of the republic in the 6th century BC, though it did not expand outside the Italian peninsula until the 3rd century BC. Then, it was an "empire" long before it had an emperor.[5][6][7][8] The Roman Republic was not a nation-state in the modern sense, but a network of towns left to rule themselves (though with varying degrees of independence from the Roman Senate) and provinces administered by military commanders. It was ruled, not by emperors, but by annually elected magistrates (Roman Consuls above all) in conjunction with the senate.[9] For various reasons, the 1st century BC was a time of political and military upheaval, which ultimately led to rule by emperors.[6][10][11][12] The consuls' military power rested in the Roman legal concept of imperium, which literally means "command" (though typically in a military sense).[13] Occasionally, successful consuls were given the honorary title imperator (commander), and this is the origin of the word emperor (and empire) since this title (among others) was always bestowed to the early emperors upon their accession.[14]

The Augustus of Prima Porta (early 1st century AD) Rome suffered a long series of internal conflicts, conspiracies and civil wars from the late second century BC onward, while greatly extending its power beyond Italy. This was the period of the Crisis of the Roman Republic. Towards the end of this era, in 44 BC, Julius Caesar was briefly perpetual dictator before being assassinated. The faction of his assassins was driven from Rome and defeated at the Battle of Philippi in 42 BC by an army led by Mark Antony and Caesar's adopted son Octavian. Antony and Octavian's division of the Roman world between themselves did not last and Octavian's forces defeated those of Mark Antony and Cleopatra at the Battle of Actium in 31 BC, ending the Final War of the Roman Republic. In 27 BC the Senate and People of Rome made Octavian princeps ("first citizen") with proconsular imperium, thus beginning the Principate (the first epoch of Roman imperial history, usually dated from 27 BC to AD 284), and gave him the name "Augustus" ("the venerated").

Though the old constitutional machinery remained in place, Augustus came to predominate it. Although the republic stood in name, contemporaries of Augustus knew it was just a veil and that Augustus had all meaningful authority in Rome.[15] Since his rule ended a century of civil wars and began an unprecedented period of peace and prosperity, he was so loved that he came to hold the power of a monarch de facto if not de jure. During the years of his rule, a new constitutional order emerged (in part organically and in part by design), so that, upon his death, this new constitutional order operated as before when Tiberius was accepted as the new emperor. The 200 years that began with Augustus's rule is traditionally regarded as the Pax Romana ("Roman Peace"). During this period, the cohesion of the empire was furthered by a degree of social stability and economic prosperity that Rome had never before experienced. Uprisings in the provinces were infrequent, but put down "mercilessly and swiftly" when they occurred.[16]

The success of Augustus in establishing principles of dynastic succession was limited by his outliving a number of talented potential heirs. The Julio-Claudian dynasty lasted for four more emperors—Tiberius, Caligula, Claudius and Nero—before it yielded in 69 AD to the strife-torn Year of Four Emperors, from which Vespasian emerged as victor. Vespasian became the founder of the brief Flavian dynasty, to be followed by the Nerva–Antonine dynasty which produced the "Five Good Emperors": Nerva, Trajan, Hadrian, Antoninus Pius and the philosophically-inclined Marcus Aurelius.

The so-called Five Good Emperors (from left to right): Nerva, Trajan, Hadrian, Antoninus Pius and Marcus Aurelius. In the view of the Greek historian Dio Cassius, a contemporary observer, the accession of the emperor Commodus in 180 AD marked the descent "from a kingdom of gold to one of rust and iron"[17]—a famous comment which has led some historians, notably Edward Gibbon, to take Commodus' reign as the beginning of the decline of the Roman Empire.[18][19]

In 212, during the reign of Caracalla, Roman citizenship was granted to all freeborn inhabitants of the empire. But despite this gesture of universality, the Severan dynasty was tumultuous—an emperor's reign was ended routinely by his murder or execution—and, following its collapse, the Roman Empire was engulfed by the Crisis of the Third Century, a period of invasions, civil strife, economic disorder, and plague.[20] In defining historical epochs, this crisis is sometimes viewed as marking the transition from Classical Antiquity to Late Antiquity. Aurelian (reigned 270–275) brought the empire back from the brink and stabilized it. Diocletian completed the work of fully restoring the empire, but declined the role of princeps and became the first emperor to be addressed regularly as domine, "master" or "lord".[21] This marked the end of the Principate, and the beginning of the Dominate. Diocletian's reign also brought the empire's most concerted effort against the perceived threat of Christianity, the "Great Persecution". The state of absolute monarchy that began with Diocletian endured until the fall of the Eastern Roman Empire in 1453.[citation needed]

The Barbarian Invasions consisted of the movement of (mainly) ancient Germanic peoples into Roman territory. Even though northern invasions took place throughout the life of the Empire, this period officially began in the IV century and lasted for many centuries during which the western territory was under the dominion of foreign northern rulers, a notable one being Charlemagne. Historically, this event marked the transition between the ancient world and the medieval ages. Diocletian divided the empire into four regions, each ruled by a separate emperor, the Tetrarchy.[22] Confident that he fixed the disorders that were plaguing Rome, he abdicated along with his co-emperor, and the Tetrarchy soon collapsed. Order was eventually restored by Constantine the Great, who became the first emperor to convert to Christianity, and who established Constantinople as the new capital of the eastern empire. During the decades of the Constantinian and Valentinian dynasties, the empire was divided along an east–west axis, with dual power centres in Constantinople and Rome. The reign of Julian, who under the influence of his adviser Mardonius attempted to restore Classical Roman and Hellenistic religion, only briefly interrupted the succession of Christian emperors. Theodosius I, the last emperor to rule over both East and West, died in 395 AD after making Christianity the official religion of the empire.[23]

The Roman Empire by 476 The Western Roman Empire began to disintegrate in the early 5th century as Germanic migrations and invasions overwhelmed the capacity of the Empire to assimilate the migrants and fight off the invaders.[citation needed] The Romans were successful in fighting off all invaders, most famously Attila,[citation needed] though the empire had assimilated so many Germanic peoples of dubious loyalty to Rome that the empire started to dismember itself.[citation needed] Most chronologies place the end of the Western Roman Empire in 476, when Romulus Augustulus was forced to abdicate to the Germanic warlord Odoacer.[24][better source needed] By placing himself under the rule of the Eastern Emperor, rather than naming himself Emperor (as other Germanic chiefs had done after deposing past emperors), Odoacer ended the Western Empire by ending the line of Western emperors.[citation needed]

The empire in the East—often known as the Byzantine Empire, but referred to in its time as the Roman Empire or by various other names—had a different fate. It survived for almost a millennium after the fall of its Western counterpart and became the most stable Christian realm during the Middle Ages. During the 6th century, Justinian I reconquered the Italian peninsula from the Ostrogoths, North Africa from the Vandals, and southern Spain from the Visigoths. But within a few years of Justinian's death, Byzantine possessions in Italy were greatly reduced by the Lombards who settled in the peninsula.[25] In the east, partially resulting from the destructive Plague of Justinian, the Romans were threatened by the rise of Islam, whose followers rapidly conquered the territories of Syria, Armenia and Egypt during the Byzantine-Arab Wars, and soon presented a direct threat to Constantinople.[26][27] In the following century, the Arabs also captured southern Italy and Sicily.[28] Slavic populations were also able to penetrate deep into the Balkans.[citation needed]

The Roman (Byzantine) Empire c. 1263. The Romans, however, managed to stop further Islamic expansion into their lands during the 8th century and, beginning in the 9th century, reclaimed parts of the conquered lands.[29] In 1000 AD, the Eastern Empire was at its height: Basil II reconquered Bulgaria and Armenia, culture and trade flourished.[30] However, soon after, the expansion was abruptly stopped in 1071 with the Byzantine defeat in the Battle of Manzikert. The aftermath of this battle sent the empire into a short period of decline. Two decades of internal strife and Turkic invasions ultimately paved the way for Emperor Alexios I Komnenos to send a call for help to the Western European kingdoms in 1095.[26] Under the Komnenian restoration the state regained its strength.

In 1204, participants in the Fourth Crusade took part in the Sack of Constantinople. The conquest of Constantinople in 1204 fragmented what remained of the Empire into successor states, the ultimate victor being that of Nicaea.[31] After the recapture of Constantinople by Imperial forces, the Empire was little more than a Greek state confined to the Aegean Sea coast. The Eastern Roman Empire finally collapsed when Mehmed the Conqueror conquered Constantinople on 29 May 1453.[32]

Legacy The Roman Empire was among the most powerful economic, cultural, political and military forces in the world of its time. It was one of the largest empires in world history. At its height under Trajan, it covered 5 million square kilometres.[2][4] It held sway over an estimated 70 million people, at that time 21% of the world's entire population. The longevity and vast extent of the empire ensured the lasting influence of Latin and Greek language, culture, religion, inventions, architecture, philosophy, law and forms of government over the empire's descendants. Throughout the European medieval period, attempts were even made to establish successors to the Roman Empire, including the Empire of Romania, a Crusader state; and the Holy Roman Empire. By means of European colonialism following the Renaissance, and their descendant states, Greco-Roman and Judaeo-Christian culture was exported on a worldwide scale, playing a crucial role in the development of the modern world.

Geography and demography Main articles: Demography of the Roman Empire and Borders of the Roman Empire Further information: Classical demography

Italy organized by Augustus. As the homeland of the Romans and metropole of the empire, Italy was the Domina (ruler) of the provinces,[33] and was referred as the "rectrix mundi" (queen of the world) and "omnium terrarum parens" (motherland of all lands).[34] The Roman Empire was one of the largest in history, with contiguous territories throughout Europe, North Africa, and the Middle East.[35] The Latin phrase imperium sine fine ("empire without end"[36][n 7]) expressed the ideology that neither time nor space limited the Empire. In Vergil's epic poem the Aeneid, limitless empire is said to be granted to the Romans by their supreme deity Jupiter.[36][37][38][39][40] This claim of universal dominion was renewed and perpetuated when the Empire came under Christian rule in the 4th century.[n 8] In addition to annexing large regions in their quest for empire-building, the Romans were also very large sculptors of their environment who directly altered their geography. For instance, entire forests were cut down to provide enough wood resources for an expanding empire. In his book Critias, Plato described that deforestation: where there was once "an abundance of wood in the mountains," he could now only see "the mere skeleton of the land."[41]

In reality, Roman expansion was mostly accomplished under the Republic, though parts of northern Europe were conquered in the 1st century AD, when Roman control in Europe, Africa and Asia was strengthened. During the reign of Augustus, a "global map of the known world" was displayed for the first time in public at Rome, coinciding with the composition of the most comprehensive work on political geography that survives from antiquity, the Geography of the Pontic Greek writer Strabo.[42] When Augustus died, the commemorative account of his achievements (Res Gestae) prominently featured the geographical cataloguing of peoples and places within the Empire.[43] Geography, the census, and the meticulous keeping of written records were central concerns of Roman Imperial administration.[44]

The cities of the Roman world in the Imperial Period. Data source: Hanson, J. W. (2016), Cities database, (OXREP databases). Version 1.0. (link).

A segment of the ruins of Hadrian's Wall in northern England The Empire reached its largest expanse under Trajan (reigned 98–117),[40] encompassing an area of 5 million square kilometres. The traditional population estimate of 55–60 million inhabitants[45] accounted for between one-sixth and one-fourth of the world's total population[46] and made it the largest population of any unified political entity in the West until the mid-19th century.[47] Recent demographic studies have argued for a population peak ranging from 70 million to more than 100 million.[48][49] Each of the three largest cities in the Empire—Rome, Alexandria, and Antioch—was almost twice the size of any European city at the beginning of the 17th century.[50]

As the historian Christopher Kelly has described it:

Then the empire stretched from Hadrian's Wall in drizzle-soaked northern England to the sun-baked banks of the Euphrates in Syria; from the great Rhine–Danube river system, which snaked across the fertile, flat lands of Europe from the Low Countries to the Black Sea, to the rich plains of the North African coast and the luxuriant gash of the Nile Valley in Egypt. The empire completely circled the Mediterranean ... referred to by its conquerors as mare nostrum—'our sea'.[45]

Trajan's successor Hadrian adopted a policy of maintaining rather than expanding the empire. Borders (fines) were marked, and the frontiers (limites) patrolled.[40] The most heavily fortified borders were the most unstable.[10] Hadrian's Wall, which separated the Roman world from what was perceived as an ever-present barbarian threat, is the primary surviving monument of this effort.[51][52][53]

Languages

This section may contain misleading parts. Please help clarify this article according to any suggestions provided on the talk page. (September 2016) Main article: Languages of the Roman Empire The language of the Romans was Latin, which Virgil emphasizes as a source of Roman unity and tradition.[54][55][56] Until the time of Alexander Severus (reigned 222–235), the birth certificates and wills of Roman citizens had to be written in Latin.[57] Latin was the language of the law courts in the West and of the military throughout the Empire,[58] but was not imposed officially on peoples brought under Roman rule.[59][60] This policy contrasts with that of Alexander the Great, who aimed to impose Greek throughout his empire as the official language.[61] As a consequence of Alexander's conquests, koine Greek had become the shared language around the eastern Mediterranean and into Asia Minor.[62][63] The "linguistic frontier" dividing the Latin West and the Greek East passed through the Balkan peninsula.[64]

A 5th-century papyrus showing a parallel Latin-Greek text of a speech by Cicero[65] Romans who received an elite education studied Greek as a literary language, and most men of the governing classes could speak Greek.[66] The Julio-Claudian emperors encouraged high standards of correct Latin (Latinitas), a linguistic movement identified in modern terms as Classical Latin, and favoured Latin for conducting official business.[67] Claudius tried to limit the use of Greek, and on occasion revoked the citizenship of those who lacked Latin, but even in the Senate he drew on his own bilingualism in communicating with Greek-speaking ambassadors.[67] Suetonius quotes him as referring to "our two languages".[68]

In the Eastern empire, laws and official documents were regularly translated into Greek from Latin.[69] The everyday interpenetration of the two languages is indicated by bilingual inscriptions, which sometimes even switch back and forth between Greek and Latin.[70][71] After all freeborn inhabitants of the empire were universally enfranchised in AD 212, a great number of Roman citizens would have lacked Latin, though Latin remained a marker of "Romanness."[72]

Among other reforms, the emperor Diocletian (reigned 284–305) sought to renew the authority of Latin, and the Greek expression hē kratousa dialektos attests to the continuing status of Latin as "the language of power."[73] In the early 6th century, the emperor Justinian engaged in a quixotic effort to reassert the status of Latin as the language of law, even though in his time Latin no longer held any currency as a living language in the East.[74]

Local languages and linguistic legacy

Bilingual Latin-Punic inscription at the theatre in Leptis Magna, Roman Africa (present-day Libya) References to interpreters indicate the continuing use of local languages other than Greek and Latin, particularly in Egypt, where Coptic predominated, and in military settings along the Rhine and Danube. Roman jurists also show a concern for local languages such as Punic, Gaulish, and Aramaic in assuring the correct understanding and application of laws and oaths.[75] In the province of Africa, Libyco-Berber and Punic were used in inscriptions and for legends on coins during the time of Tiberius (1st century AD). Libyco-Berber and Punic inscriptions appear on public buildings into the 2nd century, some bilingual with Latin.[76] In Syria, Palmyrene soldiers even used their dialect of Aramaic for inscriptions, in a striking exception to the rule that Latin was the language of the military.[77]

The Babatha Archive is a suggestive example of multilingualism in the Empire. These papyri, named for a Jewish woman in the province of Arabia and dating from 93 to 132 AD, mostly employ Aramaic, the local language, written in Greek characters with Semitic and Latin influences; a petition to the Roman governor, however, was written in Greek.[78]

The dominance of Latin among the literate elite may obscure the continuity of spoken languages, since all cultures within the Roman Empire were predominantly oral.[76] In the West, Latin, referred to in its spoken form as Vulgar Latin, gradually replaced Celtic and Italic languages that were related to it by a shared Indo-European origin. Commonalities in syntax and vocabulary facilitated the adoption of Latin.[79][80][81]

After the decentralization of political power in late antiquity, Latin developed locally into branches that became the Romance languages, such as Spanish, Portuguese, French, Italian and Romanian, and a large number of minor languages and dialects. Today, more than 900 million people are native speakers worldwide.

As an international language of learning and literature, Latin itself continued as an active medium of expression for diplomacy and for intellectual developments identified with Renaissance humanism up to the 17th century, and for law and the Roman Catholic Church to the present.[82][83]

Although Greek continued as the language of the Byzantine Empire, linguistic distribution in the East was more complex. A Greek-speaking majority lived in the Greek peninsula and islands, western Anatolia, major cities, and some coastal areas.[63] Like Greek and Latin, the Thracian language was of Indo-European origin, as were several now-extinct languages in Anatolia attested by Imperial-era inscriptions.[63][76] Albanian is often seen as the descendant of Illyrian, although this hypothesis has been challenged by some linguists, who maintain that it derives from Dacian or Thracian.[84] (Illyrian, Dacian, and Thracian, however, may have formed a subgroup or a Sprachbund; see Thraco-Illyrian.) Various Afroasiatic languages—primarily Coptic in Egypt, and Aramaic in Syria and Mesopotamia—were never replaced by Greek. The international use of Greek, however, was one factor enabling the spread of Christianity, as indicated for example by the use of Greek for the Epistles of Paul.[63]

Society Further information: Ancient Roman society

A multigenerational banquet depicted on a wall painting from Pompeii (1st century AD)

Spread of Seuso at Lacus Pelso (Lake Balaton) The Roman Empire was remarkably multicultural, with "a rather astonishing cohesive capacity" to create a sense of shared identity while encompassing diverse peoples within its political system over a long span of time.[85] The Roman attention to creating public monuments and communal spaces open to all—such as forums, amphitheatres, racetracks and baths—helped foster a sense of "Romanness".[86]

Roman society had multiple, overlapping social hierarchies that modern concepts of "class" in English may not represent accurately.[87] The two decades of civil war from which Augustus rose to sole power left traditional society in Rome in a state of confusion and upheaval,[88] but did not effect an immediate redistribution of wealth and social power. From the perspective of the lower classes, a peak was merely added to the social pyramid.[89] Personal relationships—patronage, friendship (amicitia), family, marriage—continued to influence the workings of politics and government, as they had in the Republic.[90] By the time of Nero, however, it was not unusual to find a former slave who was richer than a freeborn citizen, or an equestrian who exercised greater power than a senator.[91]

The blurring or diffusion of the Republic's more rigid hierarchies led to increased social mobility under the Empire,[92][93] both upward and downward, to an extent that exceeded that of all other well-documented ancient societies.[94] Women, freedmen, and slaves had opportunities to profit and exercise influence in ways previously less available to them.[95] Social life in the Empire, particularly for those whose personal resources were limited, was further fostered by a proliferation of voluntary associations and confraternities (collegia and sodalitates) formed for various purposes: professional and trade guilds, veterans' groups, religious sodalities, drinking and dining clubs,[96] performing arts troupes,[97] and burial societies.[98]

Citizen of Roman Egypt (Fayum mummy portrait) Legal status Main articles: Status in Roman legal system and Roman citizenship According to the jurist Gaius, the essential distinction in the Roman "law of persons" was that all human beings were either free (liberi) or slaves (servi).[99][100] The legal status of free persons might be further defined by their citizenship. Most citizens held limited rights (such as the ius Latinum, "Latin right"), but were entitled to legal protections and privileges not enjoyed by those who lacked citizenship. Free people not considered citizens, but living within the Roman world, held status as peregrini, non-Romans.[101] In 212 AD, by means of the edict known as the Constitutio Antoniniana, the emperor Caracalla extended citizenship to all freeborn inhabitants of the empire. This legal egalitarianism would have required a far-reaching revision of existing laws that had distinguished between citizens and non-citizens.[102]

Women in Roman law Main article: Women in ancient Rome Freeborn Roman women were considered citizens throughout the Republic and Empire, but did not vote, hold political office, or serve in the military. A mother's citizen status determined that of her children, as indicated by the phrase ex duobus civibus Romanis natos ("children born of two Roman citizens").[n 9] A Roman woman kept her own family name (nomen) for life. Children most often took the father's name, but in the Imperial period sometimes made their mother's name part of theirs, or even used it instead.[103]

Left image: Roman fresco of a blond maiden reading a text, Pompeian Fourth Style (60–79 AD), Pompeii, Italy Right image: Bronze statuette (1st century AD) of a young woman reading, based on a Hellenistic original The archaic form of manus marriage in which the woman had been subject to her husband's authority was largely abandoned by the Imperial era, and a married woman retained ownership of any property she brought into the marriage. Technically she remained under her father's legal authority, even though she moved into her husband's home, but when her father died she became legally emancipated.[104] This arrangement was one of the factors in the degree of independence Roman women enjoyed relative to those of many other ancient cultures and up to the modern period:[105][106] although she had to answer to her father in legal matters, she was free of his direct scrutiny in her daily life,[107] and her husband had no legal power over her.[108] Although it was a point of pride to be a "one-man woman" (univira) who had married only once, there was little stigma attached to divorce, nor to speedy remarriage after the loss of a husband through death or divorce.[109]

Girls had equal inheritance rights with boys if their father died without leaving a will.[110][111][112] A Roman mother's right to own property and to dispose of it as she saw fit, including setting the terms of her own will, gave her enormous influence over her sons even when they were adults.[113]

As part of the Augustan programme to restore traditional morality and social order, moral legislation attempted to regulate the conduct of men and women as a means of promoting "family values". Adultery, which had been a private family matter under the Republic, was criminalized,[114] and defined broadly as an illicit sex act (stuprum) that occurred between a male citizen and a married woman, or between a married woman and any man other than her husband.[n 10] Childbearing was encouraged by the state: a woman who had given birth to three children was granted symbolic honours and greater legal freedom (the ius trium liberorum).

Because of their legal status as citizens and the degree to which they could become emancipated, women could own property, enter contracts, and engage in business,[115][116] including shipping, manufacturing, and lending money. Inscriptions throughout the Empire honour women as benefactors in funding public works, an indication they could acquire and dispose of considerable fortunes; for instance, the Arch of the Sergii was funded by Salvia Postuma, a female member of the family honoured, and the largest building in the forum at Pompeii was funded by Eumachia, a priestess of Venus.[117]

Slaves and the law Main article: Slavery in ancient Rome At the time of Augustus, as many as 35% of the people in Italy were slaves,[118] making Rome one of five historical "slave societies" in which slaves constituted at least a fifth of the population and played a major role in the economy.[119] Slavery was a complex institution that supported traditional Roman social structures as well as contributing economic utility.[120] In urban settings, slaves might be professionals such as teachers, physicians, chefs, and accountants, in addition to the majority of slaves who provided trained or unskilled labour in households or workplaces. Agriculture and industry, such as milling and mining, relied on the exploitation of slaves. Outside Italy, slaves made up on average an estimated 10 to 20% of the population, sparse in Roman Egypt but more concentrated in some Greek areas. Expanding Roman ownership of arable land and industries would have affected preexisting practices of slavery in the provinces.[121][122] Although the institution of slavery has often been regarded as waning in the 3rd and 4th centuries, it remained an integral part of Roman society until the 5th century. Slavery ceased gradually in the 6th and 7th centuries along with the decline of urban centres in the West and the disintegration of the complex Imperial economy that had created the demand for it.[123]

Slave holding writing tablets for his master (relief from a 4th-century sarcophagus) Laws pertaining to slavery were "extremely intricate".[124] Under Roman law, slaves were considered property and had no legal personhood. They could be subjected to forms of corporal punishment not normally exercised on citizens, sexual exploitation, torture, and summary execution. A slave could not as a matter of law be raped, since rape could be committed only against people who were free; a slave's rapist had to be prosecuted by the owner for property damage under the Aquilian Law.[125][126] Slaves had no right to the form of legal marriage called conubium, but their unions were sometimes recognized, and if both were freed they could marry.[127] Following the Servile Wars of the Republic, legislation under Augustus and his successors shows a driving concern for controlling the threat of rebellions through limiting the size of work groups, and for hunting down fugitive slaves.[128]

Technically, a slave could not own property,[129] but a slave who conducted business might be given access to an individual account or fund (peculium) that he could use as if it were his own. The terms of this account varied depending on the degree of trust and co-operation between owner and slave: a slave with an aptitude for business could be given considerable leeway to generate profit, and might be allowed to bequeath the peculium he managed to other slaves of his household.[130] Within a household or workplace, a hierarchy of slaves might exist, with one slave in effect acting as the master of other slaves.[131]

Over time slaves gained increased legal protection, including the right to file complaints against their masters. A bill of sale might contain a clause stipulating that the slave could not be employed for prostitution, as prostitutes in ancient Rome were often slaves.[132] The burgeoning trade in eunuch slaves in the late 1st century AD prompted legislation that prohibited the castration of a slave against his will "for lust or gain."[133][134]

Roman slavery was not based on race.[135][136] Slaves were drawn from all over Europe and the Mediterranean, including Gaul, Hispania, Germany, Britannia, the Balkans, Greece... Generally slaves in Italy were indigenous Italians,[137] with a minority of foreigners (including both slaves and freedmen) born outside of Italy estimated at 5% of the total in the capital at its peak, where their number was largest. Those from outside of Europe were predominantly of Greek descent, while the Jewish ones never fully assimilated into Roman society, remaining an identifiable minority. These slaves (especially the foreigners) had higher mortality rates and lower birth rates than natives, and were sometimes even subjected to mass expulsions.[138] The average recorded age at death for the slaves of the city of Rome was extraordinarily low: seventeen and a half years (17.2 for males; 17.9 for females).[139]

During the period of Republican expansionism when slavery had become pervasive, war captives were a main source of slaves. The range of ethnicities among slaves to some extent reflected that of the armies Rome defeated in war, and the conquest of Greece brought a number of highly skilled and educated slaves into Rome. Slaves were also traded in markets, and sometimes sold by pirates. Infant abandonment and self-enslavement among the poor were other sources.[121] Vernae, by contrast, were "homegrown" slaves born to female slaves within the urban household or on a country estate or farm. Although they had no special legal status, an owner who mistreated or failed to care for his vernae faced social disapproval, as they were considered part of his familia, the family household, and in some cases might actually be the children of free males in the family.[140][141]

Talented slaves with a knack for business might accumulate a large enough peculium to justify their freedom, or be manumitted for services rendered. Manumission had become frequent enough that in 2 BC a law (Lex Fufia Caninia) limited the number of slaves an owner was allowed to free in his will.[142]

Freedmen

Cinerary urn for the freedman Tiberius Claudius Chryseros and two women, probably his wife and daughter Rome differed from Greek city-states in allowing freed slaves to become citizens. After manumission, a slave who had belonged to a Roman citizen enjoyed not only passive freedom from ownership, but active political freedom (libertas), including the right to vote.[143] A slave who had acquired libertas was a libertus ("freed person," feminine liberta) in relation to his former master, who then became his patron (patronus): the two parties continued to have customary and legal obligations to each other. As a social class generally, freed slaves were libertini, though later writers used the terms libertus and libertinus interchangeably.[144][145]

A libertinus was not entitled to hold public office or the highest state priesthoods, but he could play a priestly role in the cult of the emperor. He could not marry a woman from a family of senatorial rank, nor achieve legitimate senatorial rank himself, but during the early Empire, freedmen held key positions in the government bureaucracy, so much so that Hadrian limited their participation by law.[145] Any future children of a freedman would be born free, with full rights of citizenship.

The rise of successful freedmen—through either political influence in imperial service, or wealth—is a characteristic of early Imperial society. The prosperity of a high-achieving group of freedmen is attested by inscriptions throughout the Empire, and by their ownership of some of the most lavish houses at Pompeii, such as the House of the Vettii. The excesses of nouveau riche freedmen were satirized in the character of Trimalchio in the Satyricon by Petronius, who wrote in the time of Nero. Such individuals, while exceptional, are indicative of the upward social mobility possible in the Empire.

Census rank See also: Senate of the Roman Empire, Equestrian order, and Decurion (administrative) The Latin word ordo (plural ordines) refers to a social distinction that is translated variously into English as "class, order, rank," none of which is exact. One purpose of the Roman census was to determine the ordo to which an individual belonged. The two highest ordines in Rome were the senatorial and equestrian. Outside Rome, the decurions, also known as curiales (Greek bouleutai), were the top governing ordo of an individual city.

Fragment of a sarcophagus depicting Gordian III and senators (3rd century) "Senator" was not itself an elected office in ancient Rome; an individual gained admission to the Senate after he had been elected to and served at least one term as an executive magistrate. A senator also had to meet a minimum property requirement of 1 million sestertii, as determined by the census.[146][147] Nero made large gifts of money to a number of senators from old families who had become too impoverished to qualify. Not all men who qualified for the ordo senatorius chose to take a Senate seat, which required legal domicile at Rome. Emperors often filled vacancies in the 600-member body by appointment.[148][149] A senator's son belonged to the ordo senatorius, but he had to qualify on his own merits for admission to the Senate itself. A senator could be removed for violating moral standards: he was prohibited, for instance, from marrying a freedwoman or fighting in the arena.[150]

In the time of Nero, senators were still primarily from Rome and other parts of Italy, with some from the Iberian peninsula and southern France; men from the Greek-speaking provinces of the East began to be added under Vespasian.[151] The first senator from the most eastern province, Cappadocia, was admitted under Marcus Aurelius.[152] By the time of the Severan dynasty (193–235), Italians made up less than half the Senate.[153] During the 3rd century, domicile at Rome became impractical, and inscriptions attest to senators who were active in politics and munificence in their homeland (patria).[150]

Senators had an aura of prestige and were the traditional governing class who rose through the cursus honorum, the political career track, but equestrians of the Empire often possessed greater wealth and political power. Membership in the equestrian order was based on property; in Rome's early days, equites or knights had been distinguished by their ability to serve as mounted warriors (the "public horse"), but cavalry service was a separate function in the Empire.[n 11] A census valuation of 400,000 sesterces and three generations of free birth qualified a man as an equestrian.[154] The census of 28 BC uncovered large numbers of men who qualified, and in 14 AD, a thousand equestrians were registered at Cadiz and Padua alone.[n 12][155] Equestrians rose through a military career track (tres militiae) to become highly placed prefects and procurators within the Imperial administration.[156][157]

The rise of provincial men to the senatorial and equestrian orders is an aspect of social mobility in the first three centuries of the Empire. Roman aristocracy was based on competition, and unlike later European nobility, a Roman family could not maintain its position merely through hereditary succession or having title to lands.[158][159] Admission to the higher ordines brought distinction and privileges, but also a number of responsibilities. In antiquity, a city depended on its leading citizens to fund public works, events, and services (munera), rather than on tax revenues, which primarily supported the military. Maintaining one's rank required massive personal expenditures.[160] Decurions were so vital for the functioning of cities that in the later Empire, as the ranks of the town councils became depleted, those who had risen to the Senate were encouraged by the central government to give up their seats and return to their hometowns, in an effort to sustain civic life.[161]

In the later Empire, the dignitas ("worth, esteem") that attended on senatorial or equestrian rank was refined further with titles such as vir illustris, "illustrious man".[162] The appellation clarissimus (Greek lamprotatos) was used to designate the dignitas of certain senators and their immediate family, including women.[163] "Grades" of equestrian status proliferated. Those in Imperial service were ranked by pay grade (sexagenarius, 60,000 sesterces per annum; centenarius, 100,000; ducenarius, 200,000). The title eminentissimus, "most eminent" (Greek exochôtatos) was reserved for equestrians who had been Praetorian prefects. The higher equestrian officials in general were perfectissimi, "most distinguished" (Greek diasêmotatoi), the lower merely egregii, "outstanding" (Greek kratistos).[164]

Unequal justice

Condemned man attacked by a leopard in the arena (3rd-century mosaic from Tunisia) As the republican principle of citizens' equality under the law faded, the symbolic and social privileges of the upper classes led to an informal division of Roman society into those who had acquired greater honours (honestiores) and those who were humbler folk (humiliores). In general, honestiores were the members of the three higher "orders," along with certain military officers.[165][166] The granting of universal citizenship in 212 seems to have increased the competitive urge among the upper classes to have their superiority over other citizens affirmed, particularly within the justice system.[166][167][168] Sentencing depended on the judgement of the presiding official as to the relative "worth" (dignitas) of the defendant: an honestior could pay a fine when convicted of a crime for which an humilior might receive a scourging.[166]

Execution, which had been an infrequent legal penalty for free men under the Republic even in a capital case,[169][170] could be quick and relatively painless for the Imperial citizen considered "more honourable", while those deemed inferior might suffer the kinds of torture and prolonged death previously reserved for slaves, such as crucifixion and condemnation to the beasts as a spectacle in the arena.[171] In the early Empire, those who converted to Christianity could lose their standing as honestiores, especially if they declined to fulfil the religious aspects of their civic responsibilities, and thus became subject to punishments that created the conditions of martyrdom.[166][172]

Government and military Main article: Constitution of the Roman Empire

Reconstructed statue of Augustus as Jove, holding scepter and orb (first half of 1st century AD).[173] The Imperial cult of ancient Rome identified emperors and some members of their families with the divinely sanctioned authority (auctoritas) of the Roman State. The official offer of cultus to a living emperor acknowledged his office and rule as divinely approved and constitutional: his Principate should therefore demonstrate pious respect for traditional Republican deities and mores[citation needed]

Forum of Gerasa (Jerash in present-day Jordan), with columns marking a covered walkway (stoa) for vendor stalls, and a semicircular space for public speaking The three major elements of the Imperial Roman state were the central government, the military, and provincial government.[174] The military established control of a territory through war, but after a city or people was brought under treaty, the military mission turned to policing: protecting Roman citizens (after 212 AD, all freeborn inhabitants of the Empire), the agricultural fields that fed them, and religious sites.[175] Without modern instruments of either mass communication or mass destruction, the Romans lacked sufficient manpower or resources to impose their rule through force alone. Cooperation with local power elites was necessary to maintain order, collect information, and extract revenue. The Romans often exploited internal political divisions by supporting one faction over another: in the view of Plutarch, "it was discord between factions within cities that led to the loss of self-governance".[176][177][178]

Communities with demonstrated loyalty to Rome retained their own laws, could collect their own taxes locally, and in exceptional cases were exempt from Roman taxation. Legal privileges and relative independence were an incentive to remain in good standing with Rome.[179] Roman government was thus limited, but efficient in its use of the resources available to it.[180]

Central government See also: Roman emperor and Senate of the Roman Empire The dominance of the emperor was based on the consolidation of certain powers from several republican offices, including the inviolability of the tribunes of the people and the authority of the censors to manipulate the hierarchy of Roman society.[181] The emperor also made himself the central religious authority as Pontifex Maximus, and centralized the right to declare war, ratify treaties, and negotiate with foreign leaders.[182] While these functions were clearly defined during the Principate, the emperor's powers over time became less constitutional and more monarchical, culminating in the Dominate.[183]

Antoninus Pius (reigned 138–161), wearing a toga (Hermitage Museum) The emperor was the ultimate authority in policy- and decision-making, but in the early Principate he was expected to be accessible to individuals from all walks of life, and to deal personally with official business and petitions. A bureaucracy formed around him only gradually.[184] The Julio-Claudian emperors relied on an informal body of advisors that included not only senators and equestrians, but trusted slaves and freedmen.[185] After Nero, the unofficial influence of the latter was regarded with suspicion, and the emperor's council (consilium) became subject to official appointment for the sake of greater transparency.[186] Though the senate took a lead in policy discussions until the end of the Antonine dynasty, equestrians played an increasingly important role in the consilium.[187] The women of the emperor's family often intervened directly in his decisions. Plotina exercised influence on both her husband Trajan and his successor Hadrian. Her influence was advertised by having her letters on official matters published, as a sign that the emperor was reasonable in his exercise of authority and listened to his people.[188]

Access to the emperor by others might be gained at the daily reception (salutatio), a development of the traditional homage a client paid to his patron; public banquets hosted at the palace; and religious ceremonies. The common people who lacked this access could manifest their general approval or displeasure as a group at the games held in large venues.[189] By the 4th century, as urban centres decayed, the Christian emperors became remote figureheads who issued general rulings, no longer responding to individual petitions.[190]

Although the senate could do little short of assassination and open rebellion to contravene the will of the emperor, it survived the Augustan restoration and the turbulent Year of Four Emperors to retain its symbolic political centrality during the Principate.[191] The senate legitimated the emperor's rule, and the emperor needed the experience of senators as legates (legati) to serve as generals, diplomats, and administrators.[192][193] A successful career required competence as an administrator and remaining in favour with the emperor, or over time perhaps multiple emperors.[194]

The practical source of an emperor's power and authority was the military. The legionaries were paid by the Imperial treasury, and swore an annual military oath of loyalty to the emperor (sacramentum).[195] The death of an emperor led to a crucial period of uncertainty and crisis. Most emperors indicated their choice of successor, usually a close family member or adopted heir. The new emperor had to seek a swift acknowledgement of his status and authority to stabilize the political landscape. No emperor could hope to survive, much less to reign, without the allegiance and loyalty of the Praetorian Guard and of the legions. To secure their loyalty, several emperors paid the donativum, a monetary reward. In theory, the Senate was entitled to choose the new emperor, but did so mindful of acclamation by the army or Praetorians.[193]

Military

The Roman empire under Hadrian (ruled 117–138) showing the location of the Roman legions deployed in AD 125 Main articles: Imperial Roman army and Structural history of the Roman military After the Punic Wars, the Imperial Roman army was composed of professional soldiers who volunteered for 20 years of active duty and five as reserves. The transition to a professional military had begun during the late Republic, and was one of the many profound shifts away from republicanism, under which an army of conscripts had exercised their responsibilities as citizens in defending the homeland in a campaign against a specific threat. For Imperial Rome, the military was a full-time career in itself.[196] The Romans expanded their war machine by "organizing the communities that they conquered in Italy into a system that generated huge reservoirs of manpower for their army... Their main demand of all defeated enemies was they provide men for the Roman army every year."[197]

The primary mission of the Roman military of the early empire was to preserve the Pax Romana.[198] The three major divisions of the military were:

the garrison at Rome, which includes both the Praetorians and the vigiles who functioned as police and firefighters; the provincial army, comprising the Roman legions and the auxiliaries provided by the provinces (auxilia); the navy. The pervasiveness of military garrisons throughout the Empire was a major influence in the process of cultural exchange and assimilation known as "Romanization," particularly in regard to politics, the economy, and religion.[199] Knowledge of the Roman military comes from a wide range of sources: Greek and Roman literary texts; coins with military themes; papyri preserving military documents; monuments such as Trajan's Column and triumphal arches, which feature artistic depictions of both fighting men and military machines; the archaeology of military burials, battle sites, and camps; and inscriptions, including military diplomas, epitaphs, and dedications.[200]

Through his military reforms, which included consolidating or disbanding units of questionable loyalty, Augustus changed and regularized the legion, down to the hobnail pattern on the soles of army boots. A legion was organized into ten cohorts, each of which comprised six centuries, with a century further made up of ten squads (contubernia); the exact size of the Imperial legion, which is most likely to have been determined by logistics, has been estimated to range from 4,800 to 5,280.[201]

Relief panel from Trajan's Column showing the building of a fort and the reception of a Dacian embassy In AD 9, Germanic tribes wiped out three full legions in the Battle of the Teutoburg Forest. This disastrous event reduced the number of the legions to 25. The total of the legions would later be increased again and for the next 300 years always be a little above or below 30.[202] The army had about 300,000 soldiers in the 1st century, and under 400,000 in the 2nd, "significantly smaller" than the collective armed forces of the territories it conquered. No more than 2% of adult males living in the Empire served in the Imperial army.[203]

Augustus also created the Praetorian Guard: nine cohorts, ostensibly to maintain the public peace, which were garrisoned in Italy. Better paid than the legionaries, the Praetorians served only sixteen years.[204]

The auxilia were recruited from among the non-citizens. Organized in smaller units of roughly cohort strength, they were paid less than the legionaries, and after 25 years of service were rewarded with Roman citizenship, also extended to their sons. According to Tacitus[205] there were roughly as many auxiliaries as there were legionaries. The auxilia thus amounted to around 125,000 men, implying approximately 250 auxiliary regiments.[206] The Roman cavalry of the earliest Empire were primarily from Celtic, Hispanic or Germanic areas. Several aspects of training and equipment, such as the four-horned saddle, derived from the Celts, as noted by Arrian and indicated by archaeology.[207][208]

The Roman navy (Latin: classis, "fleet") not only aided in the supply and transport of the legions, but also helped in the protection of the frontiers along the rivers Rhine and Danube. Another of its duties was the protection of the crucial maritime trade routes against the threat of pirates. It patrolled the whole of the Mediterranean, parts of the North Atlantic coasts, and the Black Sea. Nevertheless, the army was considered the senior and more prestigious branch.[209]

Provincial government

The Pula Arena in Croatia is one of the largest and most intact of the remaining Roman amphitheatres An annexed territory became a province in a three-step process: making a register of cities, taking a census of the population, and surveying the land.[210] Further government recordkeeping included births and deaths, real estate transactions, taxes, and juridical proceedings.[211] In the 1st and 2nd centuries, the central government sent out around 160 officials each year to govern outside Italy.[9] Among these officials were the "Roman governors", as they are called in English: either magistrates elected at Rome who in the name of the Roman people governed senatorial provinces; or governors, usually of equestrian rank, who held their imperium on behalf of the emperor in provinces excluded from senatorial control, most notably Roman Egypt.[212] A governor had to make himself accessible to the people he governed, but he could delegate various duties.[213] His staff, however, was minimal: his official attendants (apparitores), including lictors, heralds, messengers, scribes, and bodyguards; legates, both civil and military, usually of equestrian rank; and friends, ranging in age and experience, who accompanied him unofficially.[213]

Other officials were appointed as supervisors of government finances.[9] Separating fiscal responsibility from justice and administration was a reform of the Imperial era. Under the Republic, provincial governors and tax farmers could exploit local populations for personal gain more freely.[214] Equestrian procurators, whose authority was originally "extra-judicial and extra-constitutional," managed both state-owned property and the vast personal property of the emperor (res privata).[213] Because Roman government officials were few in number, a provincial who needed help with a legal dispute or criminal case might seek out any Roman perceived to have some official capacity, such as a procurator or a military officer, including centurions down to the lowly stationarii or military police.[215][216]

Roman law Main article: Roman law

Roman portraiture frescos from Pompeii, 1st century AD, depicting two different men wearing laurel wreaths, one holding the rotulus (blondish figure, left), the other a volumen (brunet figure, right), both made of papyrus Roman courts held original jurisdiction over cases involving Roman citizens throughout the empire, but there were too few judicial functionaries to impose Roman law uniformly in the provinces. Most parts of the Eastern empire already had well-established law codes and juridical procedures.[88] In general, it was Roman policy to respect the mos regionis ("regional tradition" or "law of the land") and to regard local laws as a source of legal precedent and social stability.[88][217] The compatibility of Roman and local law was thought to reflect an underlying ius gentium, the "law of nations" or international law regarded as common and customary among all human communities.[218] If the particulars of provincial law conflicted with Roman law or custom, Roman courts heard appeals, and the emperor held final authority to render a decision.[88][219][220]

In the West, law had been administered on a highly localized or tribal basis, and private property rights may have been a novelty of the Roman era, particularly among Celtic peoples. Roman law facilitated the acquisition of wealth by a pro-Roman elite who found their new privileges as citizens to be advantageous.[88] The extension of universal citizenship to all free inhabitants of the Empire in 212 required the uniform application of Roman law, replacing the local law codes that had applied to non-citizens. Diocletian's efforts to stabilize the Empire after the Crisis of the Third Century included two major compilations of law in four years, the Codex Gregorianus and the Codex Hermogenianus, to guide provincial administrators in setting consistent legal standards.[221]

The pervasive exercise of Roman law throughout Western Europe led to its enormous influence on the Western legal tradition, reflected by the continued use of Latin legal terminology in modern law.

Taxation Taxation under the Empire amounted to about 5% of the Empire's gross product.[222] The typical tax rate paid by individuals ranged from 2 to 5%.[223] The tax code was "bewildering" in its complicated system of direct and indirect taxes, some paid in cash and some in kind. Taxes might be specific to a province, or kinds of properties such as fisheries or salt evaporation ponds; they might be in effect for a limited time.[224] Tax collection was justified by the need to maintain the military,[46][225] and taxpayers sometimes got a refund if the army captured a surplus of booty.[226] In-kind taxes were accepted from less-monetized areas, particularly those who could supply grain or goods to army camps.[227]

Personification of the River Nile and his children, from the Temple of Serapis and Isis in Rome (1st century AD) The primary source of direct tax revenue was individuals, who paid a poll tax and a tax on their land, construed as a tax on its produce or productive capacity.[223] Supplemental forms could be filed by those eligible for certain exemptions; for example, Egyptian farmers could register fields as fallow and tax-exempt depending on flood patterns of the Nile.[228] Tax obligations were determined by the census, which required each head of household to appear before the presiding official and provide a head count of his household, as well as an accounting of property he owned that was suitable for agriculture or habitation.[228]

A major source of indirect-tax revenue was the portoria, customs and tolls on imports and exports, including among provinces.[223] Special taxes were levied on the slave trade. Towards the end of his reign, Augustus instituted a 4% tax on the sale of slaves,[229] which Nero shifted from the purchaser to the dealers, who responded by raising their prices.[230] An owner who manumitted a slave paid a "freedom tax", calculated at 5% of value.[231]

An inheritance tax of 5% was assessed when Roman citizens above a certain net worth left property to anyone but members of their immediate family. Revenues from the estate tax and from a 1% sales tax on auctions went towards the veterans' pension fund (aerarium militare).[223]

Low taxes helped the Roman aristocracy increase their wealth, which equalled or exceeded the revenues of the central government. An emperor sometimes replenished his treasury by confiscating the estates of the "super-rich", but in the later period, the resistance of the wealthy to paying taxes was one of the factors contributing to the collapse of the Empire.[46]

Economy Main article: Roman economy Moses Finley was the chief proponent of the primitivist view that the Roman economy was "underdeveloped and underachieving," characterized by subsistence agriculture; urban centres that consumed more than they produced in terms of trade and industry; low-status artisans; slowly developing technology; and a "lack of economic rationality."[232] Current views are more complex. Territorial conquests permitted a large-scale reorganization of land use that resulted in agricultural surplus and specialization, particularly in north Africa.[233] Some cities were known for particular industries or commercial activities, and the scale of building in urban areas indicates a significant construction industry.[233] Papyri preserve complex accounting methods that suggest elements of economic rationalism,[234] and the Empire was highly monetized.[235] Although the means of communication and transport were limited in antiquity, transportation in the 1st and 2nd centuries expanded greatly, and trade routes connected regional economies.[236] The supply contracts for the army, which pervaded every part of the Empire, drew on local suppliers near the base (castrum), throughout the province, and across provincial borders.[237] The Empire is perhaps best thought of as a network of regional economies, based on a form of "political capitalism" in which the state monitored and regulated commerce to assure its own revenues.[238] Economic growth, though not comparable to modern economies, was greater than that of most other societies prior to industrialization.[234]

Socially, economic dynamism opened up one of the avenues of social mobility in the Roman Empire. Social advancement was thus not dependent solely on birth, patronage, good luck, or even extraordinary ability. Although aristocratic values permeated traditional elite society, a strong tendency towards plutocracy is indicated by the wealth requirements for census rank. Prestige could be obtained through investing one's wealth in ways that advertised it appropriately: grand country estates or townhouses, durable luxury items such as jewels and silverware, public entertainments, funerary monuments for family members or coworkers, and religious dedications such as altars. Guilds (collegia) and corporations (corpora) provided support for individuals to succeed through networking, sharing sound business practices, and a willingness to work.[165]

Currency and banking See also: Roman currency and Roman finance Currency denominations[citation needed] 27 BC–AD 212: 1 gold aureus (1/40 lb. of gold, devalued to 1/50 lb. by 212) = 25 silver denarii = 100 bronze sestertii = 400 copper asses 294–312: 1 gold aureus solidus (1/60 lb. of gold) = 10 silver argentei = 40 bronze folles = 1,000 debased metal denarii 312 onwards: 1 gold solidus (1/72 lb.) = 24 silver siliquae = 180 bronze folles The early Empire was monetized to a near-universal extent, in the sense of using money as a way to express prices and debts.[239] The sestertius (plural sestertii, English "sesterces", symbolized as HS) was the basic unit of reckoning value into the 4th century,[240] though the silver denarius, worth four sesterces, was used also for accounting beginning in the Severan dynasty.[241] The smallest coin commonly circulated was the bronze as (plural asses), one-fourth sestertius.[242] Bullion and ingots seem not to have counted as pecunia, "money," and were used only on the frontiers for transacting business or buying property. Romans in the 1st and 2nd centuries counted coins, rather than weighing them—an indication that the coin was valued on its face, not for its metal content. This tendency towards fiat money led eventually to the debasement of Roman coinage, with consequences in the later Empire.[243] The standardization of money throughout the Empire promoted trade and market integration.[239] The high amount of metal coinage in circulation increased the money supply for trading or saving.[244]

Rome had no central bank, and regulation of the banking system was minimal. Banks of classical antiquity typically kept less in reserves than the full total of customers' deposits. A typical bank had fairly limited capital, and often only one principal, though a bank might have as many as six to fifteen principals. Seneca assumes that anyone involved in commerce needs access to credit.[243]

Solidus issued under Constantine II, and on the reverse Victoria, one of the last deities to appear on Roman coins, gradually transforming into an angel under Christian rule[245] A professional deposit banker (argentarius, coactor argentarius, or later nummularius) received and held deposits for a fixed or indefinite term, and lent money to third parties. The senatorial elite were involved heavily in private lending, both as creditors and borrowers, making loans from their personal fortunes on the basis of social connections.[243][246] The holder of a debt could use it as a means of payment by transferring it to another party, without cash changing hands. Although it has sometimes been thought that ancient Rome lacked "paper" or documentary transactions, the system of banks throughout the Empire also permitted the exchange of very large sums without the physical transfer of coins, in part because of the risks of moving large amounts of cash, particularly by sea. Only one serious credit shortage is known to have occurred in the early Empire, a credit crisis in 33 AD that put a number of senators at risk; the central government rescued the market through a loan of 100 million HS made by the emperor Tiberius to the banks (mensae).[247] Generally, available capital exceeded the amount needed by borrowers.[243] The central government itself did not borrow money, and without public debt had to fund deficits from cash reserves.[248]

Emperors of the Antonine and Severan dynasties overall debased the currency, particularly the denarius, under the pressures of meeting military payrolls.[240] Sudden inflation during the reign of Commodus damaged the credit market.[243] In the mid-200s, the supply of specie contracted sharply.[240] Conditions during the Crisis of the Third Century—such as reductions in long-distance trade, disruption of mining operations, and the physical transfer of gold coinage outside the empire by invading enemies—greatly diminished the money supply and the banking sector by the year 300.[240][243] Although Roman coinage had long been fiat money or fiduciary currency, general economic anxieties came to a head under Aurelian, and bankers lost confidence in coins legitimately issued by the central government. Despite Diocletian's introduction of the gold solidus and monetary reforms, the credit market of the Empire never recovered its former robustness.[243]

Mining and metallurgy Main article: Roman metallurgy See also: Mining in Roman Britain

Landscape resulting from the ruina montium mining technique at Las Médulas, Spain, one of the most important gold mines in the Roman Empire The main mining regions of the Empire were the Iberian Peninsula (gold, silver, copper, tin, lead); Gaul (gold, silver, iron); Britain (mainly iron, lead, tin), the Danubian provinces (gold, iron); Macedonia and Thrace (gold, silver); and Asia Minor (gold, silver, iron, tin). Intensive large-scale mining—of alluvial deposits, and by means of open-cast mining and underground mining—took place from the reign of Augustus up to the early 3rd century AD, when the instability of the Empire disrupted production. The gold mines of Dacia, for instance, were no longer available for Roman exploitation after the province was surrendered in 271. Mining seems to have resumed to some extent during the 4th century.[249]

Hydraulic mining, which Pliny referred to as ruina montium ("ruin of the mountains"), allowed base and precious metals to be extracted on a proto-industrial scale.[250] The total annual iron output is estimated at 82,500 tonnes.[251][252][253] Copper was produced at an annual rate of 15,000 t,[250][254] and lead at 80,000 t,[250][255][256] both production levels unmatched until the Industrial Revolution;[254][255][256][257] Hispania alone had a 40% share in world lead production.[255] The high lead output was a by-product of extensive silver mining which reached 200 t per annum. At its peak around the mid-2nd century AD, the Roman silver stock is estimated at 10,000 t, five to ten times larger than the combined silver mass of medieval Europe and the Caliphate around 800 AD.[256][258] As an indication of the scale of Roman metal production, lead pollution in the Greenland ice sheet quadrupled over its prehistoric levels during the Imperial era and dropped again thereafter.[259]

Transportation and communication See also: Roman roads

Gallo-Roman relief depicting a river boat transporting wine barrels, an invention of the Gauls that came into widespread use during the 2nd century; above, wine is stored in the traditional amphorae, some covered in wicker[260][261] The Roman Empire completely encircled the Mediterranean, which they called "our sea" (mare nostrum).[262] Roman sailing vessels navigated the Mediterranean as well as the major rivers of the Empire, including the Guadalquivir, Ebro, Rhône, Rhine, Tiber and Nile.[263] Transport by water was preferred where possible, and moving commodities by land was more difficult.[264] Vehicles, wheels, and ships indicate the existence of a great number of skilled woodworkers.[265]

Land transport utilized the advanced system of Roman roads, which were called "viae". These roads were primarily built for military purposes,[266] but also served commercial ends. The in-kind taxes paid by communities included the provision of personnel, animals, or vehicles for the cursus publicus, the state mail and transport service established by Augustus.[227] Relay stations were located along the roads every seven to twelve Roman miles, and tended to grow into a village or trading post.[267] A mansio (plural mansiones) was a privately run service station franchised by the imperial bureaucracy for the cursus publicus. The support staff at such a facility included muleteers, secretaries, blacksmiths, cartwrights, a veterinarian, and a few military police and couriers. The distance between mansiones was determined by how far a wagon could travel in a day.[267] Mules were the animal most often used for pulling carts, travelling about 4 mph.[268] As an example of the pace of communication, it took a messenger a minimum of nine days to travel to Rome from Mainz in the province of Germania Superior, even on a matter of urgency.[269] In addition to the mansiones, some taverns offered accommodations as well as food and drink; one recorded tab for a stay showed charges for wine, bread, mule feed, and the services of a prostitute.[270]

Trade and commodities See also: Roman commerce, Indo-Roman trade and relations, and Sino-Roman relations

A green Roman glass cup unearthed from an Eastern Han Dynasty (25–220 AD) tomb in Guangxi, southern China; the earliest Roman glassware found in China was discovered in a Western Han tomb in Guangzhou, dated to the early 1st century BC, and ostensibly came via the maritime route through the South China Sea[271] Roman provinces traded among themselves, but trade extended outside the frontiers to regions as far away as China and India.[263] The main commodity was grain.[272] Chinese trade was mostly conducted overland through middle men along the Silk Road; Indian trade, however, also occurred by sea from Egyptian ports on the Red Sea. Along these trade paths, the horse, upon which Roman expansion and commerce depended, was one of the main channels through which disease spread.[273] Also in transit for trade were olive oil, various foodstuffs, garum (fish sauce), slaves, ore and manufactured metal objects, fibres and textiles, timber, pottery, glassware, marble, papyrus, spices and materia medica, ivory, pearls, and gemstones.[274]

The Pompeii Lakshmi, an ivory statuette from the Indian subcontinent found in the ruins of Pompeii. Though most provinces were capable of producing wine, regional varietals were desirable and wine was a central item of trade. Shortages of vin ordinaire were rare.[275][276] The major suppliers for the city of Rome were the west coast of Italy, southern Gaul, the Tarraconensis region of Hispania, and Crete. Alexandria, the second-largest city, imported wine from Laodicea in Syria and the Aegean.[277] At the retail level, taverns or speciality wine shops (vinaria) sold wine by the jug for carryout and by the drink on premises, with price ranges reflecting quality.[278]

Labour and occupations

Workers at a cloth-processing shop, in a painting from the fullonica of Veranius Hypsaeus in Pompeii

Roman hunters during the preparations, set-up of traps, and in-action hunting near Tarraco Inscriptions record 268 different occupations in the city of Rome, and 85 in Pompeii.[203] Professional associations or trade guilds (collegia) are attested for a wide range of occupations, including fishermen (piscatores), salt merchants (salinatores), olive oil dealers (olivarii), entertainers (scaenici), cattle dealers (pecuarii), goldsmiths (aurifices), teamsters (asinarii or muliones), and stonecutters (lapidarii). These are sometimes quite specialized: one collegium at Rome was strictly limited to craftsmen who worked in ivory and citrus wood.[165]

Work performed by slaves falls into five general categories: domestic, with epitaphs recording at least 55 different household jobs; imperial or public service; urban crafts and services; agriculture; and mining. Convicts provided much of the labour in the mines or quarries, where conditions were notoriously brutal.[279] In practice, there was little division of labour between slave and free,[88] and most workers were illiterate and without special skills.[280] The greatest number of common labourers were employed in agriculture: in the Italian system of industrial farming (latifundia), these may have been mostly slaves, but throughout the Empire, slave farm labour was probably less important than other forms of dependent labour by people who were technically not enslaved.[88]

Textile and clothing production was a major source of employment. Both textiles and finished garments were traded among the peoples of the Empire, whose products were often named for them or a particular town, rather like a fashion "label".[281] Better ready-to-wear was exported by businessmen (negotiatores or mercatores) who were often well-to-do residents of the production centres.[282] Finished garments might be retailed by their sales agents, who travelled to potential customers, or by vestiarii, clothing dealers who were mostly freedmen; or they might be peddled by itinerant merchants.[282] In Egypt, textile producers could run prosperous small businesses employing apprentices, free workers earning wages, and slaves.[283] The fullers (fullones) and dye workers (coloratores) had their own guilds.[284] Centonarii were guild workers who specialized in textile production and the recycling of old clothes into pieced goods.[n 13]

GDP and income distribution Further information: Roman economy § Gross domestic product Economic historians vary in their calculations of the gross domestic product of the Roman economy during the Principate.[285] In the sample years of 14, 100, and 150 AD, estimates of per capita GDP range from 166 to 380 HS. The GDP per capita of Italy is estimated as 40[286] to 66%[287] higher than in the rest of the Empire, due to tax transfers from the provinces and the concentration of elite income in the heartland. In regard to Italy, "There can be little doubt that the lower classes of Pomepii, Herculaneum and other provincial towns of the Roman Empire enjoyed a high standard of living not equaled again in Western Europe until the 19th century after Christ, "Stephen L. Dyson, Community and Society in Roman Italy, 1992, p. 177, ISBN 0-8018-4175-5 quoting J.E. Packer, "Middle and Lower Class Housing in Pompeii and Herculaneum: A Preliminary Survey," In Neue Forschung in Pompeji, pp. 133–42.

In the Scheidel–Friesen economic model, the total annual income generated by the Empire is placed at nearly 20 billion HS, with about 5% extracted by central and local government. Households in the top 1.5% of income distribution captured about 20% of income. Another 20% went to about 10% of the population who can be characterized as a non-elite middle. The remaining "vast majority" produced more than half of the total income, but lived near subsistence.[288] The elite were 1.2-1.7% and the middling " who enjoyed modest, comfortable levels of existence but not extreme wealth amounted to 6-12%" ..."while the vast majority lived around subsistence," Kyle Harper, Slavery in the Late Roman World, 275-425, 2011, pp. 55–56 quoting Scheidel and Friesen, ISBN 978-0-521-19861-5.

Architecture and engineering Main articles: Ancient Roman architecture, Roman engineering, and Roman technology

Amphitheatres of the Roman Empire

Construction on the Flavian Amphitheatre, more commonly known as the Colosseum, began during the reign of Vespasian The chief Roman contributions to architecture were the arch, vault and the dome. Even after more than 2,000 years some Roman structures still stand, due in part to sophisticated methods of making cements and concrete.[289][290] Roman roads are considered the most advanced roads built until the early 19th century. The system of roadways facilitated military policing, communications, and trade. The roads were resistant to floods and other environmental hazards. Even after the collapse of the central government, some roads remained usable for more than a thousand years.

Roman bridges were among the first large and lasting bridges, built from stone with the arch as the basic structure. Most utilized concrete as well. The largest Roman bridge was Trajan's bridge over the lower Danube, constructed by Apollodorus of Damascus, which remained for over a millennium the longest bridge to have been built both in terms of overall span and length.[291][292][293]

The Romans built many dams and reservoirs for water collection, such as the Subiaco Dams, two of which fed the Anio Novus, one of the largest aqueducts of Rome.[294][295][296] They built 72 dams just on the Iberian peninsula, and many more are known across the Empire, some still in use. Several earthen dams are known from Roman Britain, including a well-preserved example from Longovicium (Lanchester).

The Pont du Gard aqueduct, which crosses the Gardon River in southern France, is on UNESCO's list of World Heritage Sites The Romans constructed numerous aqueducts. A surviving treatise by Frontinus, who served as curator aquarum (water commissioner) under Nerva, reflects the administrative importance placed on ensuring the water supply. Masonry channels carried water from distant springs and reservoirs along a precise gradient, using gravity alone. After the water passed through the aqueduct, it was collected in tanks and fed through pipes to public fountains, baths, toilets, or industrial sites.[297] The main aqueducts in the city of Rome were the Aqua Claudia and the Aqua Marcia.[298] The complex system built to supply Constantinople had its most distant supply drawn from over 120 km away along a sinuous route of more than 336 km.[299] Roman aqueducts were built to remarkably fine tolerance, and to a technological standard that was not to be equalled until modern times.[300] The Romans also made use of aqueducts in their extensive mining operations across the empire, at sites such as Las Medulas and Dolaucothi in South Wales.[301]

Insulated glazing (or "double glazing") was used in the construction of public baths. Elite housing in cooler climates might have hypocausts, a form of central heating. The Romans were the first culture to assemble all essential components of the much later steam engine, when Hero built the aeolipile. With the crank and connecting rod system, all elements for constructing a steam engine (invented in 1712)—Hero's aeolipile (generating steam power), the cylinder and piston (in metal force pumps), non-return valves (in water pumps), gearing (in water mills and clocks)—were known in Roman times.[302]

Daily life Main article: Culture of ancient Rome

Cityscape from the Villa Boscoreale (60s AD) City and country In the ancient world, a city was viewed as a place that fostered civilization by being "properly designed, ordered, and adorned."[303] Augustus undertook a vast building programme in Rome, supported public displays of art that expressed the new imperial ideology, and reorganized the city into neighbourhoods (vici) administered at the local level with police and firefighting services.[304] A focus of Augustan monumental architecture was the Campus Martius, an open area outside the city centre that in early times had been devoted to equestrian sports and physical training for youth. The Altar of Augustan Peace (Ara Pacis Augustae) was located there, as was an obelisk imported from Egypt that formed the pointer (gnomon) of a horologium. With its public gardens, the Campus became one of the most attractive places in the city to visit.[304]

City planning and urban lifestyles had been influenced by the Greeks from an early period,[305] and in the eastern Empire, Roman rule accelerated and shaped the local development of cities that already had a strong Hellenistic character. Cities such as Athens, Aphrodisias, Ephesus and Gerasa altered some aspects of city planning and architecture to conform to imperial ideals, while also expressing their individual identity and regional preeminence.[306][307] In the areas of the western Empire inhabited by Celtic-speaking peoples, Rome encouraged the development of urban centres with stone temples, forums, monumental fountains, and amphitheatres, often on or near the sites of the preexisting walled settlements known as oppida.[308][309][n 14] Urbanization in Roman Africa expanded on Greek and Punic cities along the coast.[267]

Aquae Sulis in Bath, England: architectural features above the level of the pillar bases are a later reconstruction The network of cities throughout the Empire (coloniae, municipia, civitates or in Greek terms poleis) was a primary cohesive force during the Pax Romana.[310] Romans of the 1st and 2nd centuries AD were encouraged by imperial propaganda to "inculcate the habits of peacetime".[303][311] As the classicist Clifford Ando has noted:

Most of the cultural appurtenances popularly associated with imperial culture—public cult and its games and civic banquets, competitions for artists, speakers, and athletes, as well as the funding of the great majority of public buildings and public display of art—were financed by private individuals, whose expenditures in this regard helped to justify their economic power and legal and provincial privileges.[312]

Even the Christian polemicist Tertullian declared that the world of the late 2nd century was more orderly and well-cultivated than in earlier times: "Everywhere there are houses, everywhere people, everywhere the res publica, the commonwealth, everywhere life."[313] The decline of cities and civic life in the 4th century, when the wealthy classes were unable or disinclined to support public works, was one sign of the Empire's imminent dissolution.[314]

Public toilets (latrinae) from Ostia Antica In the city of Rome, most people lived in multistory apartment buildings (insulae) that were often squalid firetraps. Public facilities—such as baths (thermae), toilets that were flushed with running water (latrinae), conveniently located basins or elaborate fountains (nymphea) delivering fresh water,[309] and large-scale entertainments such as chariot races and gladiator combat—were aimed primarily at the common people who lived in the insulae.[315] Similar facilities were constructed in cities throughout the Empire, and some of the best-preserved Roman structures are in Spain, southern France, and northern Africa.

The public baths served hygienic, social and cultural functions.[316] Bathing was the focus of daily socializing in the late afternoon before dinner.[317] Roman baths were distinguished by a series of rooms that offered communal bathing in three temperatures, with varying amenities that might include an exercise and weight-training room, sauna, exfoliation spa (where oils were massaged into the skin and scraped from the body with a strigil), ball court, or outdoor swimming pool. Baths had hypocaust heating: the floors were suspended over hot-air channels that circulated warmth.[318] Mixed nude bathing was not unusual in the early Empire, though some baths may have offered separate facilities or hours for men and women. Public baths were a part of urban culture throughout the provinces, but in the late 4th century, individual tubs began to replace communal bathing. Christians were advised to go to the baths for health and cleanliness, not pleasure, but to avoid the games (ludi), which were part of religious festivals they considered "pagan". Tertullian says that otherwise Christians not only availed themselves of the baths, but participated fully in commerce and society.[319]

Reconstructed peristyle garden based on the House of the Vettii Rich families from Rome usually had two or more houses, a townhouse (domus, plural domūs) and at least one luxury home (villa) outside the city. The domus was a privately owned single-family house, and might be furnished with a private bath (balneum),[318] but it was not a place to retreat from public life.[320] Although some neighbourhoods of Rome show a higher concentration of well-to-do houses, the rich did not live in segregated enclaves. Their houses were meant to be visible and accessible. The atrium served as a reception hall in which the paterfamilias (head of household) met with clients every morning, from wealthy friends to poorer dependents who received charity.[304] It was also a centre of family religious rites, containing a shrine and the images of family ancestors.[321] The houses were located on busy public roads, and ground-level spaces facing the street were often rented out as shops (tabernae).[322] In addition to a kitchen garden—windowboxes might substitute in the insulae—townhouses typically enclosed a peristyle garden that brought a tract of nature, made orderly, within walls.[323][324]

Birds and fountain within a garden setting, with oscilla (hanging masks)[325] above, in a painting from Pompeii The villa by contrast was an escape from the bustle of the city, and in literature represents a lifestyle that balances the civilized pursuit of intellectual and artistic interests (otium) with an appreciation of nature and the agricultural cycle.[326] Ideally a villa commanded a view or vista, carefully framed by the architectural design.[327] It might be located on a working estate, or in a "resort town" situated on the seacoast, such as Pompeii and Herculaneum.

The programme of urban renewal under Augustus, and the growth of Rome's population to as many as 1 million people, was accompanied by a nostalgia for rural life expressed in the arts. Poetry praised the idealized lives of farmers and shepherds. The interiors of houses were often decorated with painted gardens, fountains, landscapes, vegetative ornament,[327] and animals, especially birds and marine life, rendered accurately enough that modern scholars can sometimes identify them by species.[328] The Augustan poet Horace gently satirized the dichotomy of urban and rural values in his fable of the city mouse and the country mouse, which has often been retold as a children's story.[329][330][331]

On a more practical level, the central government took an active interest in supporting agriculture.[332] Producing food was the top priority of land use.[333] Larger farms (latifundia) achieved an economy of scale that sustained urban life and its more specialized division of labour.[332] Small farmers benefited from the development of local markets in towns and trade centres. Agricultural techniques such as crop rotation and selective breeding were disseminated throughout the Empire, and new crops were introduced from one province to another, such as peas and cabbage to Britain.[334]

Maintaining an affordable food supply to the city of Rome had become a major political issue in the late Republic, when the state began to provide a grain dole (annona) to citizens who registered for it.[332] About 200,000–250,000 adult males in Rome received the dole, amounting to about 33 kg. per month, for a per annum total of about 100,000 tons of wheat primarily from Sicily, north Africa, and Egypt.[335] The dole cost at least 15% of state revenues,[332] but improved living conditions and family life among the lower classes,[336] and subsidized the rich by allowing workers to spend more of their earnings on the wine and olive oil produced on the estates of the landowning class.[332]

Bread stall, from a Pompeiian wall painting The grain dole also had symbolic value: it affirmed both the emperor's position as universal benefactor, and the right of all citizens to share in "the fruits of conquest".[332] The annona, public facilities, and spectacular entertainments mitigated the otherwise dreary living conditions of lower-class Romans, and kept social unrest in check. The satirist Juvenal, however, saw "bread and circuses" (panem et circenses) as emblematic of the loss of republican political liberty:[337][338]

The public has long since cast off its cares: the people that once bestowed commands, consulships, legions and all else, now meddles no more and longs eagerly for just two things: bread and circuses.[339]

Food and dining Main article: Food and dining in the Roman Empire See also: Grain supply to the city of Rome and Ancient Rome and wine Most apartments in Rome lacked kitchens, though a charcoal brazier could be used for rudimentary cookery.[340][341] Prepared food was sold at pubs and bars, inns, and food stalls (tabernae, cauponae, popinae, thermopolia).[342] Carryout and restaurant dining were for the lower classes; fine dining could be sought only at private dinner parties in well-to-do houses with a chef (archimagirus) and trained kitchen staff,[343] or at banquets hosted by social clubs (collegia).[344]

Most people would have consumed at least 70% of their daily calories in the form of cereals and legumes.[345] Puls (pottage) was considered the aboriginal food of the Romans.[346][347] The basic grain pottage could be elaborated with chopped vegetables, bits of meat, cheese, or herbs to produce dishes similar to polenta or risotto.[348]

An Ostian taberna for eating and drinking; the faded painting over the counter pictured eggs, olives, fruit and radishes[349] Urban populations and the military preferred to consume their grain in the form of bread.[345] Mills and commercial ovens were usually combined in a bakery complex.[350] By the reign of Aurelian, the state had begun to distribute the annona as a daily ration of bread baked in state factories, and added olive oil, wine, and pork to the dole.[332][351][352]

The importance of a good diet to health was recognized by medical writers such as Galen (2nd century AD), whose treatises included one On Barley Soup. Views on nutrition were influenced by schools of thought such as humoral theory.[353]

Roman literature focuses on the dining habits of the upper classes,[354] for whom the evening meal (cena) had important social functions.[355] Guests were entertained in a finely decorated dining room (triclinium), often with a view of the peristyle garden. Diners lounged on couches, leaning on the left elbow. By the late Republic, if not earlier, women dined, reclined, and drank wine along with men.[356]

The most famous description of a Roman meal is probably Trimalchio's dinner party in the Satyricon, a fictional extravaganza that bears little resemblance to reality even among the most wealthy.[357] The poet Martial describes serving a more plausible dinner, beginning with the gustatio ("tasting" or "appetizer"), which was a composed salad of mallow leaves, lettuce, chopped leeks, mint, arugula, mackerel garnished with rue, sliced eggs, and marinated sow udder. The main course was succulent cuts of kid, beans, greens, a chicken, and leftover ham, followed by a dessert of fresh fruit and vintage wine.[358] The Latin expression for a full-course dinner was ab ovo usque mala, "from the egg to the apples," equivalent to the English "from soup to nuts."[359]

Still life on a 2nd-century Roman mosaic A book-length collection of Roman recipes is attributed to Apicius, a name for several figures in antiquity that became synonymous with "gourmet."[360] Roman "foodies" indulged in wild game, fowl such as peacock and flamingo, large fish (mullet was especially prized), and shellfish. Luxury ingredients were brought by the fleet from the far reaches of empire, from the Parthian frontier to the Straits of Gibraltar.[361]

Refined cuisine could be moralized as a sign of either civilized progress or decadent decline.[362] The early Imperial historian Tacitus contrasted the indulgent luxuries of the Roman table in his day with the simplicity of the Germanic diet of fresh wild meat, foraged fruit, and cheese, unadulterated by imported seasonings and elaborate sauces.[363] Most often, because of the importance of landowning in Roman culture, produce—cereals, legumes, vegetables, and fruit—was considered a more civilized form of food than meat. The Mediterranean staples of bread, wine, and oil were sacralized by Roman Christianity, while Germanic meat consumption became a mark of paganism,[364] as it might be the product of animal sacrifice.

Some philosophers and Christians resisted the demands of the body and the pleasures of food, and adopted fasting as an ideal.[365] Food became simpler in general as urban life in the West diminished, trade routes were disrupted,[364] and the rich retreated to the more limited self-sufficiency of their country estates. As an urban lifestyle came to be associated with decadence, the Church formally discouraged gluttony,[366] and hunting and pastoralism were seen as simple, virtuous ways of life.[364]

Recreation and spectacles See also: Ludi, Chariot racing, and Gladiator

Wall painting depicting a sports riot at the amphitheatre of Pompeii, which led to the banning of gladiator combat in the town[367][368] When Juvenal complained that the Roman people had exchanged their political liberty for "bread and circuses", he was referring to the state-provided grain dole and the circenses, events held in the entertainment venue called a circus in Latin. The largest such venue in Rome was the Circus Maximus, the setting of horse races, chariot races, the equestrian Troy Game, staged beast hunts (venationes), athletic contests, gladiator combat, and historical re-enactments. From earliest times, several religious festivals had featured games (ludi), primarily horse and chariot races (ludi circenses).[369] Although their entertainment value tended to overshadow ritual significance, the races remained part of archaic religious observances that pertained to agriculture, initiation, and the cycle of birth and death.[n 15]

Under Augustus, public entertainments were presented on 77 days of the year; by the reign of Marcus Aurelius, the number of days had expanded to 135.[370] Circus games were preceded by an elaborate parade (pompa circensis) that ended at the venue.[371] Competitive events were held also in smaller venues such as the amphitheatre, which became the characteristic Roman spectacle venue, and stadium. Greek-style athletics included footraces, boxing, wrestling, and the pancratium.[372] Aquatic displays, such as the mock sea battle (naumachia) and a form of "water ballet", were presented in engineered pools.[373] State-supported theatrical events (ludi scaenici) took place on temple steps or in grand stone theatres, or in the smaller enclosed theatre called an odeum.[374]

A victor in his four-horse chariot Circuses were the largest structure regularly built in the Roman world,[375] though the Greeks had their own architectural traditions for the similarly purposed hippodrome. The Flavian Amphitheatre, better known as the Colosseum, became the regular arena for blood sports in Rome after it opened in 80 AD.[376] The circus races continued to be held more frequently.[377] The Circus Maximus could seat around 150,000 spectators, and the Colosseum about 50,000 with standing room for about 10,000 more.[378] Many Roman amphitheatres, circuses and theatres built in cities outside Italy are visible as ruins today.[376] The local ruling elite were responsible for sponsoring spectacles and arena events, which both enhanced their status and drained their resources.[171]

The physical arrangement of the amphitheatre represented the order of Roman society: the emperor presiding in his opulent box; senators and equestrians watching from the advantageous seats reserved for them; women seated at a remove from the action; slaves given the worst places, and everybody else packed in-between.[379][380][381] The crowd could call for an outcome by booing or cheering, but the emperor had the final say. Spectacles could quickly become sites of social and political protest, and emperors sometimes had to deploy force to put down crowd unrest, most notoriously at the Nika riots in the year 532, when troops under Justinian slaughtered thousands.[382][383][384][385]

The Zliten mosaic, from a dining room in present-day Libya, depicts a series of arena scenes: from top, musicians playing a Roman tuba, a water pipe organ and two horns; six pairs of gladiators with two referees; four beast fighters; and three convicts condemned to the beasts[386] The chariot teams were known by the colours they wore, with the Blues and Greens the most popular. Fan loyalty was fierce and at times erupted into sports riots.[383][387][388] Racing was perilous, but charioteers were among the most celebrated and well-compensated athletes.[389] One star of the sport was Diocles, from Lusitania (present-day Portugal), who raced chariots for 24 years and had career earnings of 35 million sesterces.[390][391] Horses had their fans too, and were commemorated in art and inscriptions, sometimes by name.[392][393] The design of Roman circuses was developed to assure that no team had an unfair advantage and to minimize collisions (naufragia, "shipwrecks"),[394][395] which were nonetheless frequent and spectacularly satisfying to the crowd.[396][397] The races retained a magical aura through their early association with chthonic rituals: circus images were considered protective or lucky, curse tablets have been found buried at the site of racetracks, and charioteers were often suspected of sorcery.[391][398][399][400][401] Chariot racing continued into the Byzantine period under imperial sponsorship, but the decline of cities in the 6th and 7th centuries led to its eventual demise.[375]

The Romans thought gladiator contests had originated with funeral games and sacrifices in which select captive warriors were forced to fight to expiate the deaths of noble Romans. Some of the earliest styles of gladiator fighting had ethnic designations such as "Thracian" or "Gallic".[402][403][404] The staged combats were considered munera, "services, offerings, benefactions", initially distinct from the festival games (ludi).[403][404]

Throughout his 40-year reign, Augustus presented eight gladiator shows in which a total of 10,000 men fought, as well as 26 staged beast hunts that resulted in the deaths of 3,500 animals.[405][406][407] To mark the opening of the Colosseum, the emperor Titus presented 100 days of arena events, with 3,000 gladiators competing on a single day.[376][408][409] Roman fascination with gladiators is indicated by how widely they are depicted on mosaics, wall paintings, lamps, and even graffiti drawings.[410]

Gladiators were trained combatants who might be slaves, convicts, or free volunteers.[411] Death was not a necessary or even desirable outcome in matches between these highly skilled fighters, whose training represented a costly and time-consuming investment.[409][412][413] By contrast, noxii were convicts sentenced to the arena with little or no training, often unarmed, and with no expectation of survival. Physical suffering and humiliation were considered appropriate retributive justice for the crimes they had committed.[171] These executions were sometimes staged or ritualized as re-enactments of myths, and amphitheatres were equipped with elaborate stage machinery to create special effects.[171][414][415] Tertullian considered deaths in the arena to be nothing more than a dressed-up form of human sacrifice.[416][417][418]

Modern scholars have found the pleasure Romans took in the "theatre of life and death"[419] to be one of the more difficult aspects of their civilization to understand and explain.[420][421] The younger Pliny rationalized gladiator spectacles as good for the people, a way "to inspire them to face honourable wounds and despise death, by exhibiting love of glory and desire for victory even in the bodies of slaves and criminals".[422][423] Some Romans such as Seneca were critical of the brutal spectacles, but found virtue in the courage and dignity of the defeated fighter rather than in victory[424]—an attitude that finds its fullest expression with the Christians martyred in the arena. Even martyr literature, however, offers "detailed, indeed luxuriant, descriptions of bodily suffering",[425] and became a popular genre at times indistinguishable from fiction.[426][427][428][429][430][431]

Personal training and play

Boys and girls playing ball games (2nd century relief from the Louvre) In the plural, ludi almost always refers to the large-scale spectator games. The singular ludus, "play, game, sport, training," had a wide range of meanings such as "word play," "theatrical performance," "board game," "primary school," and even "gladiator training school" (as in Ludus Magnus, the largest such training camp at Rome).[432][433]

Activities for children and young people included hoop rolling and knucklebones (astragali or "jacks"). The sarcophagi of children often show them playing games. Girls had dolls, typically 15–16 cm tall with jointed limbs, made of materials such as wood, terracotta, and especially bone and ivory.[434] Ball games include trigon, which required dexterity, and harpastum, a rougher sport.[435] Pets appear often on children's memorials and in literature, including birds, dogs, cats, goats, sheep, rabbits and geese.[436]

So-called "bikini girls" mosaic from the Villa del Casale, Roman Sicily, 4th century After adolescence, most physical training for males was of a military nature. The Campus Martius originally was an exercise field where young men developed the skills of horsemanship and warfare. Hunting was also considered an appropriate pastime. According to Plutarch, conservative Romans disapproved of Greek-style athletics that promoted a fine body for its own sake, and condemned Nero's efforts to encourage gymnastic games in the Greek manner.[437]

Some women trained as gymnasts and dancers, and a rare few as female gladiators. The famous "bikini girls" mosaic shows young women engaging in apparatus routines that might be compared to rhythmic gymnastics.[n 16][438] Women in general were encouraged to maintain their health through activities such as playing ball, swimming, walking, reading aloud (as a breathing exercise), riding in vehicles, and travel.[439]

Stone game board from Aphrodisias: boards could also be made of wood, with deluxe versions in costly materials such as ivory; game pieces or counters were bone, glass, or polished stone, and might be coloured or have markings or images[440] People of all ages played board games pitting two players against each other, including latrunculi ("Raiders"), a game of strategy in which opponents coordinated the movements and capture of multiple game pieces, and XII scripta ("Twelve Marks"), involving dice and arranging pieces on a grid of letters or words.[441] A game referred to as alea (dice) or tabula (the board), to which the emperor Claudius was notoriously addicted, may have been similar to backgammon, using a dice-cup (pyrgus).[440] Playing with dice as a form of gambling was disapproved of, but was a popular pastime during the December festival of the Saturnalia with its carnival, norms-overturned atmosphere.

Clothing Main article: Clothing in ancient Rome In a status-conscious society like that of the Romans, clothing and personal adornment gave immediate visual clues about the etiquette of interacting with the wearer.[442] Wearing the correct clothing was supposed to reflect a society in good order.[443] The toga was the distinctive national garment of the Roman male citizen, but it was heavy and impractical, worn mainly for conducting political business and religious rites, and for going to court.[444][445] The clothing Romans wore ordinarily was dark or colourful, and the most common male attire seen daily throughout the provinces would have been tunics, cloaks, and in some regions trousers.[446] The study of how Romans dressed in daily life is complicated by a lack of direct evidence, since portraiture may show the subject in clothing with symbolic value, and surviving textiles from the period are rare.[445][447][448]

Women from the wall painting at the Villa of the Mysteries, Pompeii The basic garment for all Romans, regardless of gender or wealth, was the simple sleeved tunic. The length differed by wearer: a man's reached mid-calf, but a soldier's was somewhat shorter; a woman's fell to her feet, and a child's to its knees.[449] The tunics of poor people and labouring slaves were made from coarse wool in natural, dull shades, with the length determined by the type of work they did. Finer tunics were made of lightweight wool or linen. A man who belonged to the senatorial or equestrian order wore a tunic with two purple stripes (clavi) woven vertically into the fabric: the wider the stripe, the higher the wearer's status.[449] Other garments could be layered over the tunic.

The Imperial toga was a "vast expanse" of semi-circular white wool that could not be put on and draped correctly without assistance.[444] In his work on oratory, Quintilian describes in detail how the public speaker ought to orchestrate his gestures in relation to his toga.[443][445][450] In art, the toga is shown with the long end dipping between the feet, a deep curved fold in front, and a bulbous flap at the midsection.[445] The drapery became more intricate and structured over time, with the cloth forming a tight roll across the chest in later periods.[451] The toga praetexta, with a purple or purplish-red stripe representing inviolability, was worn by children who had not come of age, curule magistrates, and state priests. Only the emperor could wear an all-purple toga (toga picta).[452]

Claudius wearing an early Imperial toga (see a later, more structured toga above), and the pallium as worn by a priest of Serapis,[453] sometimes identified as the emperor Julian In the 2nd century, emperors and men of status are often portrayed wearing the pallium, an originally Greek mantle (himation) folded tightly around the body. Women are also portrayed in the pallium. Tertullian considered the pallium an appropriate garment both for Christians, in contrast to the toga, and for educated people, since it was associated with philosophers.[443][445][454] By the 4th century, the toga had been more or less replaced by the pallium as a garment that embodied social unity.[455]

Roman clothing styles changed over time, though not as rapidly as fashions today.[456] In the Dominate, clothing worn by both soldiers and government bureaucrats became highly decorated, with woven or embroidered stripes (clavi) and circular roundels (orbiculi) applied to tunics and cloaks. These decorative elements consisted of geometrical patterns, stylized plant motifs, and in more elaborate examples, human or animal figures.[457] The use of silk increased, and courtiers of the later Empire wore elaborate silk robes. The militarization of Roman society, and the waning of cultural life based on urban ideals, affected habits of dress: heavy military-style belts were worn by bureaucrats as well as soldiers, and the toga was abandoned.[458]

The arts Main article: Roman art

The Wedding of Zephyrus and Chloris (54–68 AD, Pompeian Fourth Style) within painted architectural panels from the Casa del Naviglio People visiting or living in Rome or the cities throughout the Empire would have seen art in a range of styles and media on a daily basis. Public or official art—including sculpture, monuments such as victory columns or triumphal arches, and the iconography on coins—is often analysed for its historical significance or as an expression of imperial ideology.[459][460] At Imperial public baths, a person of humble means could view wall paintings, mosaics, statues, and interior decoration often of high quality.[461] In the private sphere, objects made for religious dedications, funerary commemoration, domestic use, and commerce can show varying degrees of aesthetic quality and artistic skill.[462] A wealthy person might advertise his appreciation of culture through painting, sculpture, and decorative arts at his home—though some efforts strike modern viewers and some ancient connoisseurs as strenuous rather than tasteful.[463] Greek art had a profound influence on the Roman tradition, and some of the most famous examples of Greek statues are known only from Roman Imperial versions and the occasional description in a Greek or Latin literary source.[464]

Despite the high value placed on works of art, even famous artists were of low social status among the Greeks and Romans, who regarded artists, artisans, and craftsmen alike as manual labourers. At the same time, the level of skill required to produce quality work was recognized, and even considered a divine gift.[465]

Portraiture Main article: Roman portraiture

Two portraits circa 130 AD: the empress Vibia Sabina (left); and the Antinous Mondragone, one of the abundant likenesses of Hadrian's famously beautiful male companion Antinous Portraiture, which survives mainly in the medium of sculpture, was the most copious form of imperial art. Portraits during the Augustan period utilize youthful and classical proportions, evolving later into a mixture of realism and idealism.[466] Republican portraits had been characterized by a "warts and all" verism, but as early as the 2nd century BC, the Greek convention of heroic nudity was adopted sometimes for portraying conquering generals.[467] Imperial portrait sculptures may model the head as mature, even craggy, atop a nude or seminude body that is smooth and youthful with perfect musculature; a portrait head might even be added to a body created for another purpose.[468] Clothed in the toga or military regalia, the body communicates rank or sphere of activity, not the characteristics of the individual.[469]

Women of the emperor's family were often depicted dressed as goddesses or divine personifications such as Pax ("Peace"). Portraiture in painting is represented primarily by the Fayum mummy portraits, which evoke Egyptian and Roman traditions of commemorating the dead with the realistic painting techniques of the Empire. Marble portrait sculpture would have been painted, and while traces of paint have only rarely survived the centuries, the Fayum portraits indicate why ancient literary sources marvelled at how lifelike artistic representations could be.[470]

The bronze Drunken Satyr, excavated at Herculaneum and exhibited in the 18th century, inspired an interest among later sculptors in similar "carefree" subjects[471] Sculpture Main article: Roman sculpture Examples of Roman sculpture survive abundantly, though often in damaged or fragmentary condition, including freestanding statues and statuettes in marble, bronze and terracotta, and reliefs from public buildings, temples, and monuments such as the Ara Pacis, Trajan's Column, and the Arch of Titus. Niches in amphitheatres such as the Colosseum were originally filled with statues,[472][473] and no formal garden was complete without statuary.[474]

Temples housed the cult images of deities, often by famed sculptors.[475] The religiosity of the Romans encouraged the production of decorated altars, small representations of deities for the household shrine or votive offerings, and other pieces for dedicating at temples. Divine and mythological figures were also given secular, humorous, and even obscene depictions.[citation needed]

On the Ludovisi sarcophagus, an example of the battle scenes favoured during the Crisis of the Third Century, the "writhing and highly emotive" Romans and Goths fill the surface in a packed, anti-classical composition[476] Sarcophagi Main article: Ancient Roman sarcophagi Elaborately carved marble and limestone sarcophagi are characteristic of the 2nd to the 4th centuries[477] with at least 10,000 examples surviving.[478] Although mythological scenes have been most widely studied,[479] sarcophagus relief has been called the "richest single source of Roman iconography,"[480] and may also depict the deceased's occupation or life course, military scenes, and other subject matter. The same workshops produced sarcophagi with Jewish or Christian imagery.[481]

The Primavera of Stabiae, perhaps the goddess Flora Painting Much of what is known of Roman painting is based on the interior decoration of private homes, particularly as preserved at Pompeii and Herculaneum by the eruption of Vesuvius in 79 AD. In addition to decorative borders and panels with geometric or vegetative motifs, wall painting depicts scenes from mythology and the theatre, landscapes and gardens, recreation and spectacles, work and everyday life, and frank pornography. Birds, animals, and marine life are often depicted with careful attention to realistic detail.[citation needed]

A unique source for Jewish figurative painting under the Empire is the Dura-Europos synagogue, dubbed "the Pompeii of the Syrian Desert,"[n 17] buried and preserved in the mid-3rd century after the city was destroyed by Persians.[482][483]

Mosaic Main article: Roman mosaic

The Triumph of Neptune floor mosaic from Africa Proconsularis (present-day Tunisia), celebrating agricultural success with allegories of the Seasons, vegetation, workers and animals viewable from multiple perspectives in the room (latter 2nd century)[484] Mosaics are among the most enduring of Roman decorative arts, and are found on the surfaces of floors and other architectural features such as walls, vaulted ceilings, and columns. The most common form is the tessellated mosaic, formed from uniform pieces (tesserae) of materials such as stone and glass.[485] Mosaics were usually crafted on site, but sometimes assembled and shipped as ready-made panels. A mosaic workshop was led by the master artist (pictor) who worked with two grades of assistants.[486]

Figurative mosaics share many themes with painting, and in some cases portray subject matter in almost identical compositions. Although geometric patterns and mythological scenes occur throughout the Empire, regional preferences also find expression. In North Africa, a particularly rich source of mosaics, homeowners often chose scenes of life on their estates, hunting, agriculture, and local wildlife.[484] Plentiful and major examples of Roman mosaics come also from present-day Turkey, Italy, southern France, Spain, and Portugal. More than 300 Antioch mosaics from the 3rd century are known.[citation needed]

Opus sectile is a related technique in which flat stone, usually coloured marble, is cut precisely into shapes from which geometric or figurative patterns are formed. This more difficult technique was highly prized, and became especially popular for luxury surfaces in the 4th century, an abundant example of which is the Basilica of Junius Bassus.[487]

Decorative arts See also: Ancient Roman pottery and Roman glass Decorative arts for luxury consumers included fine pottery, silver and bronze vessels and implements, and glassware. The manufacture of pottery in a wide range of quality was important to trade and employment, as were the glass and metalworking industries. Imports stimulated new regional centres of production. Southern Gaul became a leading producer of the finer red-gloss pottery (terra sigillata) that was a major item of trade in 1st-century Europe.[488] Glassblowing was regarded by the Romans as originating in Syria in the 1st century BC, and by the 3rd century Egypt and the Rhineland had become noted for fine glass.[489][490]

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Silver cup, from the Boscoreale Treasure (early 1st century AD)

Figural bronze oil lamps from Nova Zagora in Roman-era Bulgaria (1st–2nd century)

Finely decorated Gallo-Roman terra sigillata bowl

Gold earrings with gemstones, 3rd century

Glass cage cup from the Rhineland, latter 4th century

Seuso plate (detail)

Performing arts Main articles: Theatre of ancient Rome and Music of ancient Rome In Roman tradition, borrowed from the Greeks, literary theatre was performed by all-male troupes that used face masks with exaggerated facial expressions that allowed audiences to "see" how a character was feeling. Such masks were occasionally also specific to a particular role, and an actor could then play multiple roles merely by switching masks. Female roles were played by men in drag (travesti). Roman literary theatre tradition is particularly well represented in Latin literature by the tragedies of Seneca. The circumstances under which Seneca's tragedies were performed are however unclear; scholarly conjectures range from minimally staged readings to full production pageants. More popular than literary theatre was the genre-defying mimus theatre, which featured scripted scenarios with free improvisation, risqué language and jokes, sex scenes, action sequences, and political satire, along with dance numbers, juggling, acrobatics, tightrope walking, striptease, and dancing bears.[491][492][493] Unlike literary theatre, mimus was played without masks, and encouraged stylistic realism in acting. Female roles were performed by women, not by men.[494] Mimus was related to the genre called pantomimus, an early form of story ballet that contained no spoken dialogue. Pantomimus combined expressive dancing, instrumental music and a sung libretto, often mythological, that could be either tragic or comic.[495][496]

All-male theatrical troupe preparing for a masked performance, on a mosaic from the House of the Tragic Poet Although sometimes regarded as foreign elements in Roman culture, music and dance had existed in Rome from earliest times.[497] Music was customary at funerals, and the tibia (Greek aulos), a woodwind instrument, was played at sacrifices to ward off ill influences.[498] Song (carmen) was an integral part of almost every social occasion. The Secular Ode of Horace, commissioned by Augustus, was performed publicly in 17 BC by a mixed children's choir. Music was thought to reflect the orderliness of the cosmos, and was associated particularly with mathematics and knowledge.[499]

Various woodwinds and "brass" instruments were played, as were stringed instruments such as the cithara, and percussion.[498] The cornu, a long tubular metal wind instrument that curved around the musician's body, was used for military signals and on parade.[498] These instruments are found in parts of the Empire where they did not originate, and indicate that music was among the aspects of Roman culture that spread throughout the provinces. Instruments are widely depicted in Roman art.[citation needed]

The hydraulic pipe organ (hydraulis) was "one of the most significant technical and musical achievements of antiquity", and accompanied gladiator games and events in the amphitheatre, as well as stage performances. It was among the instruments that the emperor Nero played.[498]

Although certain forms of dance were disapproved of at times as non-Roman or unmanly, dancing was embedded in religious rituals of archaic Rome, such as those of the dancing armed Salian priests and of the Arval Brothers, priesthoods which underwent a revival during the Principate.[500] Ecstatic dancing was a feature of the international mystery religions, particularly the cult of Cybele as practised by her eunuch priests the Galli[501] and of Isis. In the secular realm, dancing girls from Syria and Cadiz were extremely popular.[502]

Like gladiators, entertainers were infames in the eyes of the law, little better than slaves even if they were technically free. "Stars", however, could enjoy considerable wealth and celebrity, and mingled socially and often sexually with the upper classes, including emperors.[503] Performers supported each other by forming guilds, and several memorials for members of the theatre community survive.[504] Theatre and dance were often condemned by Christian polemicists in the later Empire,[497] and Christians who integrated dance traditions and music into their worship practices were regarded by the Church Fathers as shockingly "pagan."[505] St. Augustine is supposed to have said that bringing clowns, actors, and dancers into a house was like inviting in a gang of unclean spirits.[506][507]

Literacy, books, and education Wiki letter w.svg This article is missing information about the use of papyrus or parchment scrolls, which were very common before the invention of the codex. Please expand the article to include this information. Further details may exist on the talk page. (April 2017) Main article: Education in ancient Rome

Pride in literacy was displayed in portraiture through emblems of reading and writing, as in this example of a couple from Pompeii (Portrait of Paquius Proculo) Estimates of the average literacy rate in the Empire range from 5 to 30% or higher, depending in part on the definition of "literacy".[508][509][510][511] The Roman obsession with documents and public inscriptions indicates the high value placed on the written word.[512][513][514][515][516] The Imperial bureaucracy was so dependent on writing that the Babylonian Talmud declared "if all seas were ink, all reeds were pen, all skies parchment, and all men scribes, they would be unable to set down the full scope of the Roman government's concerns."[517] Laws and edicts were posted in writing as well as read out. Illiterate Roman subjects would have someone such as a government scribe (scriba) read or write their official documents for them.[510][518] Public art and religious ceremonies were ways to communicate imperial ideology regardless of ability to read.[519] Although the Romans were not a "People of the Book", they had an extensive priestly archive, and inscriptions appear throughout the Empire in connection with statues and small votives dedicated by ordinary people to divinities, as well as on binding tablets and other "magic spells", with hundreds of examples collected in the Greek Magical Papyri.[520][521][522][523] The military produced a vast amount of written reports and service records,[524] and literacy in the army was "strikingly high".[525] Urban graffiti, which include literary quotations, and low-quality inscriptions with misspellings and solecisms indicate casual literacy among non-elites.[526][527][n 18][81] In addition, numeracy was necessary for any form of commerce.[513][528] Slaves were numerate and literate in significant numbers, and some were highly educated.[529]

Books were expensive, since each copy had to be written out individually on a roll of papyrus (volumen) by scribes who had apprenticed to the trade.[530] The codex—a book with pages bound to a spine—was still a novelty in the time of the poet Martial (1st century AD),[531][532] but by the end of the 3rd century was replacing the volumen[530][533] and was the regular form for books with Christian content.[534] Commercial production of books had been established by the late Republic,[535] and by the 1st century AD certain neighbourhoods of Rome were known for their bookshops (tabernae librariae), which were found also in Western provincial cities such as Lugdunum (present-day Lyon, France).[536][537] The quality of editing varied wildly, and some ancient authors complain about error-ridden copies,[535][538] as well as plagiarism or forgery, since there was no copyright law.[535] A skilled slave copyist (servus litteratus) could be valued as highly as 100,000 sesterces.[539][540]

Reconstruction of a writing tablet: the stylus was used to inscribe letters into the wax surface for drafts, casual letterwriting, and schoolwork, while texts meant to be permanent were copied onto papyrus Collectors amassed personal libraries,[541] such as that of the Villa of the Papyri in Herculaneum, and a fine library was part of the cultivated leisure (otium) associated with the villa lifestyle.[542] Significant collections might attract "in-house" scholars; Lucian mocked mercenary Greek intellectuals who attached themselves to philistine Roman patrons.[543] An individual benefactor might endow a community with a library: Pliny the Younger gave the city of Comum a library valued at 1 million sesterces, along with another 100,000 to maintain it.[544][545] Imperial libraries housed in state buildings were open to users as a privilege on a limited basis, and represented a literary canon from which disreputable writers could be excluded.[546][547] Books considered subversive might be publicly burned,[548] and Domitian crucified copyists for reproducing works deemed treasonous.[549][550]

Literary texts were often shared aloud at meals or with reading groups.[551][552] Scholars such as Pliny the Elder engaged in "multitasking" by having works read aloud to them while they dined, bathed or travelled, times during which they might also dictate drafts or notes to their secretaries.[553] The multivolume Attic Nights of Aulus Gellius is an extended exploration of how Romans constructed their literary culture.[554] The reading public expanded from the 1st through the 3rd century, and while those who read for pleasure remained a minority, they were no longer confined to a sophisticated ruling elite, reflecting the social fluidity of the Empire as a whole and giving rise to "consumer literature" meant for entertainment.[555] Illustrated books, including erotica, were popular, but are poorly represented by extant fragments.[556]

Primary education

A teacher with two students, as a third arrives with his loculus, a writing case that would contain pens, ink pot, and a sponge to correct errors[557] Traditional Roman education was moral and practical. Stories about great men and women, or cautionary tales about individual failures, were meant to instil Roman values (mores maiorum). Parents and family members were expected to act as role models, and parents who worked for a living passed their skills on to their children, who might also enter apprenticeships for more advanced training in crafts or trades.[558] Formal education was available only to children from families who could pay for it, and the lack of state intervention in access to education contributed to the low rate of literacy.[559][560]

Young children were attended by a pedagogus, or less frequently a female pedagoga, usually a Greek slave or former slave.[561] The pedagogue kept the child safe, taught self-discipline and public behaviour, attended class and helped with tutoring.[562] The emperor Julian recalled his pedagogue Mardonius, a Gothic eunuch slave who reared him from the age of 7 to 15, with affection and gratitude. Usually, however, pedagogues received little respect.[563]

Primary education in reading, writing, and arithmetic might take place at home for privileged children whose parents hired or bought a teacher.[564] Others attended a school that was "public," though not state-supported, organized by an individual schoolmaster (ludimagister) who accepted fees from multiple parents.[565] Vernae (homeborn slave children) might share in home- or public-schooling.[566] Schools became more numerous during the Empire, and increased the opportunities for children to acquire an education.[560] School could be held regularly in a rented space, or in any available public niche, even outdoors. Boys and girls received primary education generally from ages 7 to 12, but classes were not segregated by grade or age.[567] For the socially ambitious, bilingual education in Greek as well as Latin was a must.[560]

Quintilian provides the most extensive theory of primary education in Latin literature. According to Quintilian, each child has in-born ingenium, a talent for learning or linguistic intelligence that is ready to be cultivated and sharpened, as evidenced by the young child's ability to memorize and imitate. The child incapable of learning was rare. To Quintilian, ingenium represented a potential best realized in the social setting of school, and he argued against homeschooling. He also recognized the importance of play in child development,[n 19] and disapproved of corporal punishment because it discouraged love of learning—in contrast to the practice in most Roman primary schools of routinely striking children with a cane (ferula) or birch rod for being slow or disruptive.[568]

Secondary education

Mosaic from Pompeii depicting the Academy of Plato At the age of 14, upperclass males made their rite of passage into adulthood, and began to learn leadership roles in political, religious, and military life through mentoring from a senior member of their family or a family friend.[569] Higher education was provided by grammatici or rhetores.[570] The grammaticus or "grammarian" taught mainly Greek and Latin literature, with history, geography, philosophy or mathematics treated as explications of the text.[571] With the rise of Augustus, contemporary Latin authors such as Vergil and Livy also became part of the curriculum.[572] The rhetor was a teacher of oratory or public speaking. The art of speaking (ars dicendi) was highly prized as a marker of social and intellectual superiority, and eloquentia ("speaking ability, eloquence") was considered the "glue" of a civilized society.[573] Rhetoric was not so much a body of knowledge (though it required a command of references to the literary canon[574]) as it was a mode of expression and decorum that distinguished those who held social power.[575] The ancient model of rhetorical training—"restraint, coolness under pressure, modesty, and good humour"[576]—endured into the 18th century as a Western educational ideal.[577]

In Latin, illiteratus (Greek agrammatos) could mean both "unable to read and write" and "lacking in cultural awareness or sophistication."[578] Higher education promoted career advancement, particularly for an equestrian in Imperial service: "eloquence and learning were considered marks of a well-bred man and worthy of reward".[579] The poet Horace, for instance, was given a top-notch education by his father, a prosperous former slave.[580][581][582]

Urban elites throughout the Empire shared a literary culture embued with Greek educational ideals (paideia).[583] Hellenistic cities sponsored schools of higher learning as an expression of cultural achievement.[584] Young men from Rome who wished to pursue the highest levels of education often went abroad to study rhetoric and philosophy, mostly to one of several Greek schools in Athens. The curriculum in the East was more likely to include music and physical training along with literacy and numeracy.[585] On the Hellenistic model, Vespasian endowed chairs of grammar, Latin and Greek rhetoric, and philosophy at Rome, and gave teachers special exemptions from taxes and legal penalties, though primary schoolmasters did not receive these benefits. Quintilian held the first chair of grammar.[586][587] In the eastern empire, Berytus (present-day Beirut) was unusual in offering a Latin education, and became famous for its school of Roman law.[588] The cultural movement known as the Second Sophistic (1st–3rd century AD) promoted the assimilation of Greek and Roman social, educational, and aesthetic values, and the Greek proclivities for which Nero had been criticized were regarded from the time of Hadrian onward as integral to Imperial culture.[589]

Educated women

Portrait of a literary woman from Pompeii (ca. 50 AD) Literate women ranged from cultured aristocrats to girls trained to be calligraphers and scribes.[590][591] The "girlfriends" addressed in Augustan love poetry, although fictional, represent an ideal that a desirable woman should be educated, well-versed in the arts, and independent to a frustrating degree.[592][593] Education seems to have been standard for daughters of the senatorial and equestrian orders during the Empire.[566] A highly educated wife was an asset for the socially ambitious household, but one that Martial regards as an unnecessary luxury.[590]

The woman who achieved the greatest prominence in the ancient world for her learning was Hypatia of Alexandria, who educated young men in mathematics, philosophy, and astronomy, and advised the Roman prefect of Egypt on politics. Her influence put her into conflict with the bishop of Alexandria, Cyril, who may have been implicated in her violent death in 415 at the hands of a Christian mob.[594]

The shape of literacy Literacy began to decline, perhaps dramatically, during the socio-political Crisis of the Third Century.[595] After the Christianization of the Roman Empire the Christians and Church Fathers adopted and used Latin and Greek pagan literature, philosophy and natural science with a vengeance to biblical interpretation.[596]

Edward Grant writes that:

With the total triumph of Christianity at the end of the fourth century, the Church might have reacted against Greek pagan learning in general, and Greek philosophy in particular, finding much in the latter that was unacceptable or perhaps even offensive. They might have launched a major effort to suppress pagan learning as a danger to the Church and its doctrines.

But they did not. Why not?

Perhaps it was in the slow dissemination of Christianity. After four centuries as members of a distinct religion, Christians had learned to live with Greek secular learning and to utilize it for their own benefit. Their education was heavily infiltrated by Latin and Greek pagan literature and philosophy… Although Christians found certain aspects of pagan culture and learning unacceptable, they did not view them as a cancer to be cut out of the Christian body.[597]

Julian, the only emperor after the conversion of Constantine to reject Christianity, banned Christians from teaching the Classical curriculum, on the grounds that they might corrupt the minds of youth.[587]

While the book roll had emphasized the continuity of the text, the codex format encouraged a "piecemeal" approach to reading by means of citation, fragmented interpretation, and the extraction of maxims.[598]

In the 5th and 6th centuries, due to the gradual decline and fall of the Western Roman Empire, reading became rarer even for those within the Church hierarchy.[599] However, in the Eastern Roman Empire, also known as Byzantine Empire, reading continued throughout the Middle Ages as reading was of primary importance as an instrument of the Byzantine civilization.[600]

Literature Main article: Latin literature See also: Roman historiography, Church Fathers, and Latin poetry

Statue in Constanța, Romania (the ancient colony Tomis), commemorating Ovid's exile In the traditional literary canon, literature under Augustus, along with that of the late Republic, has been viewed as the "Golden Age" of Latin literature, embodying the classical ideals of "unity of the whole, the proportion of the parts, and the careful articulation of an apparently seamless composition."[601] The three most influential Classical Latin poets—Vergil, Horace, and Ovid—belong to this period. Vergil wrote the Aeneid, creating a national epic for Rome in the manner of the Homeric epics of Greece. Horace perfected the use of Greek lyric metres in Latin verse. Ovid's erotic poetry was enormously popular, but ran afoul of the Augustan moral programme; it was one of the ostensible causes for which the emperor exiled him to Tomis (present-day Constanța, Romania), where he remained to the end of his life. Ovid's Metamorphoses was a continuous poem of fifteen books weaving together Greco-Roman mythology from the creation of the universe to the deification of Julius Caesar. Ovid's versions of Greek myths became one of the primary sources of later classical mythology, and his work was so influential in the Middle Ages that the 12th and 13th centuries have been called the "Age of Ovid."[602]

The principal Latin prose author of the Augustan age is the historian Livy, whose account of Rome's founding and early history became the most familiar version in modern-era literature. Vitruvius's book De Architectura, the only complete work on architecture to survive from antiquity, also belongs to this period.

Latin writers were immersed in the Greek literary tradition, and adapted its forms and much of its content, but Romans regarded satire as a genre in which they surpassed the Greeks. Horace wrote verse satires before fashioning himself as an Augustan court poet, and the early Principate also produced the satirists Persius and Juvenal. The poetry of Juvenal offers a lively curmudgeon's perspective on urban society.

The period from the mid-1st century through the mid-2nd century has conventionally been called the "Silver Age" of Latin literature. Under Nero, disillusioned writers reacted to Augustanism.[603] The three leading writers—Seneca the philosopher, dramatist, and tutor of Nero; Lucan, his nephew, who turned Caesar's civil war into an epic poem; and the novelist Petronius (Satyricon)—all committed suicide after incurring the emperor's displeasure. Seneca and Lucan were from Hispania, as was the later epigrammatist and keen social observer Martial, who expressed his pride in his Celtiberian heritage.[81] Martial and the epic poet Statius, whose poetry collection Silvae had a far-reaching influence on Renaissance literature,[604] wrote during the reign of Domitian.

The so-called "Silver Age" produced several distinguished writers, including the encyclopedist Pliny the Elder; his nephew, known as Pliny the Younger; and the historian Tacitus. The Natural History of the elder Pliny, who died during disaster relief efforts in the wake of the eruption of Vesuvius, is a vast collection on flora and fauna, gems and minerals, climate, medicine, freaks of nature, works of art, and antiquarian lore. Tacitus's reputation as a literary artist matches or exceeds his value as a historian;[605] his stylistic experimentation produced "one of the most powerful of Latin prose styles."[606] The Twelve Caesars by his contemporary Suetonius is one of the primary sources for imperial biography.

Among Imperial historians who wrote in Greek are Dionysius of Halicarnassus, the Jewish historian Josephus, and the senator Cassius Dio. Other major Greek authors of the Empire include the biographer and antiquarian Plutarch, the geographer Strabo, and the rhetorician and satirist Lucian. Popular Greek romance novels were part of the development of long-form fiction works, represented in Latin by the Satyricon of Petronius and The Golden Ass of Apuleius.

From the 2nd to the 4th centuries, the Christian authors who would become the Latin Church Fathers were in active dialogue with the Classical tradition, within which they had been educated. Tertullian, a convert to Christianity from Roman Africa, was the contemporary of Apuleius and one of the earliest prose authors to establish a distinctly Christian voice. After the conversion of Constantine, Latin literature is dominated by the Christian perspective.[607] When the orator Symmachus argued for the preservation of Rome's religious traditions, he was effectively opposed by Ambrose, the bishop of Milan and future saint—a debate preserved by their missives.[608]

Brescia Casket, an ivory box with Biblical imagery (late 4th century) In the late 4th century, Jerome produced the Latin translation of the Bible that became authoritative as the Vulgate. Augustine, another of the Church Fathers from the province of Africa, has been called "one of the most influential writers of western culture", and his Confessions is sometimes considered the first autobiography of Western literature. In The City of God against the Pagans, Augustine builds a vision of an eternal, spiritual Rome, a new imperium sine fine that will outlast the collapsing Empire.

In contrast to the unity of Classical Latin, the literary aesthetic of late antiquity has a tessellated quality that has been compared to the mosaics characteristic of the period.[609] A continuing interest in the religious traditions of Rome prior to Christian dominion is found into the 5th century, with the Saturnalia of Macrobius and The Marriage of Philology and Mercury of Martianus Capella. Prominent Latin poets of late antiquity include Ausonius, Prudentius, Claudian, and Sidonius. Ausonius (d. ca. 394), the Bordelaise tutor of the emperor Gratian, was at least nominally a Christian, though throughout his occasionally obscene mixed-genre poems, he retains a literary interest in the Greco-Roman gods and even druidism. The imperial panegyrist Claudian (d. 404) was a vir illustris who appears never to have converted. Prudentius (d. ca. 413), born in Hispania Tarraconensis and a fervent Christian, was thoroughly versed in the poets of the Classical tradition,[610] and transforms their vision of poetry as a monument of immortality into an expression of the poet's quest for eternal life culminating in Christian salvation.[611] Sidonius (d. 486), a native of Lugdunum, was a Roman senator and bishop of Clermont who cultivated a traditional villa lifestyle as he watched the Western empire succumb to barbarian incursions. His poetry and collected letters offer a unique view of life in late Roman Gaul from the perspective of a man who "survived the end of his world".[609][612]

Religion

A Roman priest, his head ritually covered with a fold of his toga, extends a patera in a gesture of libation (2nd–3rd century) Main articles: Religion in ancient Rome and Imperial cult (ancient Rome) See also: History of the Jews in the Roman Empire, Early Christianity, and Religious persecution in the Roman Empire

The Roman siege and destruction of Jerusalem, from a Western religious manuscript, c.1504 Religion in the Roman Empire encompassed the practices and beliefs the Romans regarded as their own, as well as the many cults imported to Rome or practised by peoples throughout the provinces. The Romans thought of themselves as highly religious, and attributed their success as a world power to their collective piety (pietas) in maintaining good relations with the gods (pax deorum). The archaic religion believed to have been handed down from the earliest kings of Rome was the foundation of the mos maiorum, "the way of the ancestors" or "tradition", viewed as central to Roman identity. There was no principle analogous to "separation of church and state". The priesthoods of the state religion were filled from the same social pool of men who held public office, and in the Imperial era, the Pontifex Maximus was the emperor.

Roman religion was practical and contractual, based on the principle of do ut des, "I give that you might give." Religion depended on knowledge and the correct practice of prayer, ritual, and sacrifice, not on faith or dogma, although Latin literature preserves learned speculation on the nature of the divine and its relation to human affairs. For ordinary Romans, religion was a part of daily life.[613] Each home had a household shrine at which prayers and libations to the family's domestic deities were offered. Neighbourhood shrines and sacred places such as springs and groves dotted the city. Apuleius (2nd century) described the everyday quality of religion in observing how people who passed a cult place might make a vow or a fruit offering, or merely sit for a while.[614][615] The Roman calendar was structured around religious observances. In the Imperial era, as many as 135 days of the year were devoted to religious festivals and games (ludi).[616] Women, slaves, and children all participated in a range of religious activities.

In the wake of the Republic's collapse, state religion had adapted to support the new regime of the emperors. As the first Roman emperor, Augustus justified the novelty of one-man rule with a vast programme of religious revivalism and reform. Public vows formerly made for the security of the republic now were directed at the wellbeing of the emperor. So-called "emperor worship" expanded on a grand scale the traditional Roman veneration of the ancestral dead and of the Genius, the divine tutelary of every individual. Upon death, an emperor could be made a state divinity (divus) by vote of the Senate. Imperial cult, influenced by Hellenistic ruler cult, became one of the major ways Rome advertised its presence in the provinces and cultivated shared cultural identity and loyalty throughout the Empire. Cultural precedent in the Eastern provinces facilitated a rapid dissemination of Imperial cult, extending as far as the Augustan military settlement at Najran, in present-day Saudi Arabia.[617] Rejection of the state religion became tantamount to treason against the emperor. This was the context for Rome's conflict with Christianity, which Romans variously regarded as a form of atheism and novel superstitio.

Statuettes representing Roman and Gallic deities, for personal devotion at private shrines The Romans are known for the great number of deities they honoured, a capacity that earned the mockery of early Christian polemicists.[n 20] As the Romans extended their dominance throughout the Mediterranean world, their policy in general was to absorb the deities and cults of other peoples rather than try to eradicate them.[n 21] One way that Rome promoted stability among diverse peoples was by supporting their religious heritage, building temples to local deities that framed their theology within the hierarchy of Roman religion. Inscriptions throughout the Empire record the side-by-side worship of local and Roman deities, including dedications made by Romans to local gods.[613][618][619][620] By the height of the Empire, numerous cults of pseudo-foreign gods (Roman reinventions of foreign gods) were cultivated at Rome and in the provinces, among them cults of Cybele, Isis, Epona, and of solar gods such as Mithras and Sol Invictus, found as far north as Roman Britain. Because Romans had never been obligated to cultivate one god or one cult only, religious tolerance was not an issue in the sense that it is for competing monotheistic systems.[621]

Mystery religions, which offered initiates salvation in the afterlife, were a matter of personal choice for an individual, practised in addition to carrying on one's family rites and participating in public religion. The mysteries, however, involved exclusive oaths and secrecy, conditions that conservative Romans viewed with suspicion as characteristic of "magic", conspiracy (coniuratio), and subversive activity. Sporadic and sometimes brutal attempts were made to suppress religionists who seemed to threaten traditional morality and unity. In Gaul, the power of the druids was checked, first by forbidding Roman citizens to belong to the order, and then by banning druidism altogether. At the same time, however, Celtic traditions were reinterpreted (interpretatio romana) within the context of Imperial theology, and a new Gallo-Roman religion coalesced, with its capital at the Sanctuary of the Three Gauls in Lugdunum (present-day Lyon, France). The sanctuary established precedent for Western cult as a form of Roman-provincial identity.[622]

This funerary stele from the 3rd century is among the earliest Christian inscriptions, written in both Greek and Latin: the abbreviation D.M. at the top refers to the Di Manes, the traditional Roman spirits of the dead, but accompanies Christian fish symbolism.

Relief from the Arch of Titus in Rome depicting a menorah and other spoils from the Temple of Jerusalem carried in Roman triumph. The monotheistic rigour of Judaism posed difficulties for Roman policy that led at times to compromise and the granting of special exemptions. Tertullian noted that the Jewish religion, unlike that of the Christians, was considered a religio licita, "legitimate religion." Wars between the Romans and the Jews occurred when conflict, political as well as religious, became intractable. When Caligula wanted to place a golden statue of his deified self in the Temple in Jerusalem, the potential sacrilege and likely war were prevented only by his timely death.[623] The Siege of Jerusalem in 70 AD led to the sacking of the temple and the dispersal of Jewish political power (see Jewish diaspora).

Christianity emerged in Roman Judea as a Jewish religious sect in the 1st century AD. The religion gradually spread out of Jerusalem, initially establishing major bases in first Antioch, then Alexandria, and over time throughout the Empire as well as beyond. Imperially authorized persecutions were limited and sporadic, with martyrdoms occurring most often under the authority of local officials.[624][625][626][627][628][629]

The first persecution by an emperor occurred under Nero, and was confined to the city of Rome. Tacitus reports that after the Great Fire of Rome in AD 64, some among the population held Nero responsible and that the emperor attempted to deflect blame onto the Christians.[630] After Nero, a major persecution occurred under the emperor Domitian[631][632] and a persecution in 177 took place at Lugdunum, the Gallo-Roman religious capital. A surviving letter from Pliny the Younger, governor of Bythinia, to the emperor Trajan describes his persecution and executions of Christians.[633] The Decian persecution of 246–251 was a serious threat to the Church, but ultimately strengthened Christian defiance.[634] Diocletian undertook what was to be the most severe persecution of Christians, lasting from 303 to 311.

In the early 4th century, Constantine I became the first emperor to convert to Christianity. During the rest of the fourth century Christianity became the dominant religion of the Empire. The emperor Julian, under the influence of his adviser Mardonius made a short-lived attempt to revive traditional and Hellenistic religion and to affirm the special status of Judaism, but in 380 (Edict of Thessalonica), under Theodosius I Christianity became the official state church of the Roman Empire, to the exclusion of all others. From the 2nd century onward, the Church Fathers had begun to condemn the diverse religions practised throughout the Empire collectively as "pagan."[635] Pleas for religious tolerance from traditionalists such as the senator Symmachus (d. 402) were rejected, and Christian monotheism became a feature of Imperial domination. Christian heretics as well as non-Christians were subject to exclusion from public life or persecution, but Rome's original religious hierarchy and many aspects of its ritual influenced Christian forms,[636][637] and many pre-Christian beliefs and practices survived in Christian festivals and local traditions.

Political legacy Main article: Legacy of the Roman Empire Several states claimed to be the Roman Empire's successors after the fall of the Western Roman Empire. The Holy Roman Empire, an attempt to resurrect the Empire in the West, was established in 800 when Pope Leo III crowned Frankish King Charlemagne as Roman Emperor on Christmas Day, though the empire and the imperial office did not become formalized for some decades. After the fall of Constantinople, the Russian Tsardom, as inheritor of the Byzantine Empire's Orthodox Christian tradition, counted itself the Third Rome (Constantinople having been the second). These concepts are known as Translatio imperii.[638]

When the Ottomans, who based their state on the Byzantine model, took Constantinople in 1453, Mehmed II established his capital there and claimed to sit on the throne of the Roman Empire.[639] He even went so far as to launch an invasion of Italy with the purpose of re-uniting the Empire and invited European artists to his capital, including Gentile Bellini.[640]

In the medieval West, "Roman" came to mean the church and the Pope of Rome. The Greek form Romaioi remained attached to the Greek-speaking Christian population of the Eastern Roman Empire, and is still used by Greeks in addition to their common appellation.[641]

The Roman Empire's territorial legacy of controlling the Italian peninsula would influence Italian nationalism and the unification of Italy (Risorgimento) in 1861.[642]

The Virginia State Capitol (left), built in the late 1700s, was modelled after the Maison Carrée, a Gallo-Roman temple built around 16 BC under Augustus In the United States, the founders were educated in the classical tradition,[643] and used classical models for landmarks and buildings in Washington, D.C., to avoid the feudal and religious connotations of European architecture such as castles and cathedrals.[644][645][646][647][648][649][650] In forming their theory of the mixed constitution, the founders looked to Athenian democracy and Roman republicanism for models, but regarded the Roman emperor as a figure of tyranny.[651][652] They nonetheless adopted Roman Imperial forms such as the dome, as represented by the US Capitol and numerous state capitol buildings, to express classical ideals through architecture.[644][653] Thomas Jefferson saw the Empire as a negative political lesson, but was a chief proponent of its architectural models. Jefferson's design for the Virginia State Capitol, for instance, is modelled directly from the Maison Carrée, a Gallo-Roman temple built under Augustus.[644][645][647][654][655] The renovations of the National Mall at the beginning of the 20th century have been viewed as expressing a more overt imperialist kinship with Rome.[656][657][658]

See also Ancient Rome portal icon Classical Civilisation portal Mediterranean portal Ancient Near East portal Daqin ("Great Qin"), the ancient Chinese name for the Roman Empire; see also Sino-Roman relations Fall of the Western Roman Empire Imperial Italy Italian Empire Notes

Other ways of referring to the "Roman Empire" among the Romans and Greeks themselves included Res publica Romana or Imperium Romanorum (also in Greek: Βασιλεία τῶν Ῥωμαίων – Basileía tôn Rhōmaíōn – ["Dominion (Literally 'kingdom' but also interpreted as 'empire') of the Romans"]) and Romania. Res publica means Roman "commonwealth" and can refer to both the Republican and the Imperial eras. Imperium Romanum (or "Romanorum") refers to the territorial extent of Roman authority. Populus Romanus ("the Roman people") was/is often used to indicate the Roman state in matters involving other nations. The term Romania, initially a colloquial term for the empire's territory as well as a collective name for its inhabitants, appears in Greek and Latin sources from the 4th century onward and was eventually carried over to the Eastern Roman Empire (see R. L. Wolff, "Romania: The Latin Empire of Constantinople" in Speculum 23 (1948), pp. 1–34 and especially pp. 2–3).
Between 1204 and 1261 there was an interregnum when the Empire was divided into the Empire of Nicaea, the Empire of Trebizond and the Despotate of Epirus, which were all contenders for rule of the Empire. The Empire of Nicaea is considered the legitimate continuation of the Roman Empire because it managed to re-take Constantinople.
The final emperor to rule over all of the Roman Empire's territories before its conversion to a diarchy.
Officially the final emperor of the Western empire.
Last emperor of the Eastern (Byzantine) empire.
Abbreviated "HS". Prices and values are usually expressed in sesterces; see #Currency and banking for currency denominations by period.
Translated as "power without end" in Southern
Prudentius (348–413) in particular Christianizes the theme in his poetry, as noted by Marc Mastrangelo, The Roman Self in Late Antiquity: Prudentius and the Poetics of the Soul (Johns Hopkins University Press, 2008), pp. 73, 203. St. Augustine, however, distinguished between the secular and eternal "Rome" in The City of God. See also J. Rufus Fears, "The Cult of Jupiter and Roman Imperial Ideology," Aufstieg und Niedergang der römischen Welt II.17.1 (1981), p. 136, on how Classical Roman ideology influenced Christian Imperial doctrine; Bang, Peter Fibiger (2011) "The King of Kings: Universal Hegemony, Imperial Power, and a New Comparative History of Rome," in The Roman Empire in Context: Historical and Comparative Perspectives. John Wiley & Sons; and the Greek concept of globalism (oikouménē).
The civis ("citizen") stands in explicit contrast to a peregrina, a foreign or non-Roman woman: A.N. Sherwin-White (1979) Roman Citizenship. Oxford University Press. pp. 211 and 268; Frier, pp. 31–32, 457. In the form of legal marriage called conubium, the father's legal status determined the child's, but conubium required that both spouses be free citizens. A soldier, for instance, was banned from marrying while in service, but if he formed a long-term union with a local woman while stationed in the provinces, he could marry her legally after he was discharged, and any children they had would be considered the offspring of citizens—in effect granting the woman retroactive citizenship. The ban was in place from the time of Augustus until it was rescinded by Septimius Severus in 197 AD. See Sara Elise Phang, The Marriage of Roman Soldiers (13 B.C.–A.D. 235): Law and Family in the Imperial Army (Brill, 2001), p. 2, and Pat Southern, The Roman Army: A Social and Institutional History (Oxford University Press, 2006), p. 144.
That is, a double standard was in place: a married woman could have sex only with her husband, but a married man did not commit adultery if he had sex with a prostitute, slave, or person of marginalized status. See McGinn, Thomas A. J. (1991). "Concubinage and the Lex Iulia on Adultery". Transactions of the American Philological Association. 121: 335–375 (342). doi:10.2307/284457. JSTOR 284457.; Martha C. Nussbaum (2002) "The Incomplete Feminism of Musonius Rufus, Platonist, Stoic, and Roman," in The Sleep of Reason: Erotic Experience and Sexual Ethics in Ancient Greece and Rome. University of Chicago Press. p. 305, noting that custom "allowed much latitude for personal negotiation and gradual social change"; Elaine Fantham, "Stuprum: Public Attitudes and Penalties for Sexual Offences in Republican Rome," in Roman Readings: Roman Response to Greek Literature from Plautus to Statius and Quintilian (Walter de Gruyter, 2011), p. 124, citing Papinian, De adulteriis I and Modestinus, Liber Regularum I. Eva Cantarella, Bisexuality in the Ancient World (Yale University Press, 1992, 2002, originally published 1988 in Italian), p. 104; Edwards, pp. 34–35.
The relation of the equestrian order to the "public horse" and Roman cavalry parades and demonstrations (such as the Lusus Troiae) is complex, but those who participated in the latter seem, for instance, to have been the equites who were accorded the high-status (and quite limited) seating at the theatre by the Lex Roscia theatralis. Senators could not possess the "public horse." See Wiseman, pp. 78–79.
Ancient Gades, in Roman Spain, and Patavium, in the Celtic north of Italy, were atypically wealthy cities, and having 500 equestrians in one city was unusual. Strabo 3.169, 5.213
Vout, p. 212. The college of centonarii is an elusive topic in scholarship, since they are also widely attested as urban firefighters; see Jinyu Liu (2009) Collegia Centonariorum: The Guilds of Textile Dealers in the Roman West. Brill. Liu sees them as "primarily tradesmen and/or manufacturers engaged in the production and distribution of low- or medium-quality woolen textiles and clothing, including felt and its products."
Julius Caesar first applied the Latin word oppidum to this type of settlement, and even called Avaricum (Bourges, France), a center of the Bituriges, an urbs, "city." Archaeology indicates that oppida were centers of religion, trade (including import/export), and industrial production, walled for the purposes of defense, but they may not have been inhabited by concentrated populations year-round: see Harding, D.W. (2007) The Archaeology of Celtic Art. Routledge. pp. 211–212. ISBN 113426464X; Collis, John (2000) "'Celtic' Oppida," in A Comparative Study of Thirty City-state Cultures. Danske Videnskabernes Selskab. pp. 229–238; Celtic Chiefdom, Celtic State: The Evolution of Complex Social Systems. Cambridge University Press, 1995, 1999, p. 61.
Such as the Consualia and the October Horse sacrifice: Humphrey, pp. 544, 558; Auguste Bouché-Leclercq, Manuel des Institutions Romaines (Hachette, 1886), p. 549; "Purificazione," in Thesaurus Cultus et Rituum Antiquorum (LIMC, 2004), p. 83.
Scholars are divided in their relative emphasis on the athletic and dance elements of these exercises: Lee, H. (1984). "Athletics and the Bikini Girls from Piazza Armerina". Stadion. 10: 45–75. sees them as gymnasts, while M. Torelli, "Piazza Armerina: Note di iconologia", in La Villa romana del Casale di Piazza Armerina, edited by G. Rizza (Catania, 1988), p. 152, thinks they are dancers at the games.
By Michael Rostovtzeff, as noted by Robin M. Jensen (1999) "The Dura-Europos Synagogue, Early-Christian Art and Religious Life in Dura Europos," in Jews, Christians and Polytheists in the Ancient Synagogue: Cultural Interaction during the Greco-Roman Period. Routledge. p. 154.
Political slogans and obscenities are widely preserved as graffiti in Pompeii: Antonio Varone, Erotica Pompeiana: Love Inscriptions on the Walls of Pompeii ("L'Erma" di Bretschneider, 2002). Soldiers sometimes inscribed sling bullets with aggressive messages: Phang, "Military Documents, Languages, and Literacy," p. 300.
Bloomer, W. Martin (2011) The School of Rome: Latin Studies and the Origins of Liberal Education (University of California Press, 2011), pp. 93–99; Morgan, Literate Education in the Hellenistic and Roman Worlds, p. 250. Quintilian uses the metaphor acuere ingenium, "to sharpen talent," as well as agricultural metaphors.
For an overview of the representation of Roman religion in early Christian authors, see R.P.C. Hanson, "The Christian Attitude to Pagan Religions up to the Time of Constantine the Great," and Carlos A. Contreras, "Christian Views of Paganism," in Aufstieg und Niedergang der römischen Welt II.23.1 (1980) 871–1022.
"This mentality," notes John T. Koch, "lay at the core of the genius of cultural assimilation which made the Roman Empire possible"; entry on "Interpretatio romana," in Celtic Culture: A Historical Encyclopedia (ABC-Clio, 2006), p. 974.

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Fagan, Garrett G. (2001). "The Genesis of the Roman Public Bath: Recent Approaches and Future Directions" (PDF). American Journal of Archaeology. 105 (3): 403. doi:10.2307/507363. JSTOR 507363.
Ward, Roy Bowen (1992). "Women in Roman Baths". Harvard Theological Review. 85 (2): 125–147. doi:10.1017/S0017816000028820 (inactive 2018-06-28). JSTOR 1509900.
Clarke, pp. 1–2.
Clarke, pp. 11–12.
Clarke, p. 2.
Stambaugh, pp. 144, 147
Clarke, pp. 12, 17, 22ff.
Taylor, Rabun (2005). "Roman Oscilla: An Assessment". Res: Anthropology and aesthetics. 48: 83–105. doi:10.1086/RESv48n1ms20167679. JSTOR 20167679.
Gazda, Elaine K. (1991) "Introduction", in Roman Art in the Private Sphere: Architecture and Décor of the Domus, Villa, and Insula. University of Michigan Press. p. 9. ISBN 047210196X.
Clarke, p. 19.
Jashemski, Wilhelmina Feemster; Meyer, Frederick G. (2002). The Natural History of Pompeii. Cambridge University Press. ISBN 978-0-521-80054-9.
Horace, Satire 2.6
Holzberg, Niklas (2002) The Ancient Fable: An Introduction. Indiana University Press. p. 35
Bovie, Smith Palmer (2002) Introduction to Horace. Satires and Epistles. University of Chicago Press. pp. 92–93.
Morris, p. 191.
Boardman, p. 679.
Morris, pp. 195–196.
Morris, p. 191, reckoning that the surplus of wheat from the province of Egypt alone could meet and exceed the needs of the city of Rome and the provincial armies.
Wiseman, T. P. (2012). "The Census in the First Century B.C". Journal of Roman Studies. 59: 59. doi:10.2307/299848. JSTOR 299848.
Keane, Catherine (2006) Figuring Genre in Roman Satire. Oxford University Press. p. 36
Köhne, Eckhart (2000) "Bread and Circuses: The Politics of Entertainment," in Gladiators and Caesars: The Power of Spectacle in Ancient Rome. University of California Press. p. 8.
Juvenal, Satire 10.77–81.
Stambaugh, pp. 144, 178
Hinds, Kathryn (2010) Everyday Life in the Roman Empire. Marshall Cavendish. p. 90.
Holleran, p. 136ff.
Gagarin, p. 299.
Faas, Patrick (1994, 2005) Around the Roman Table: Food and Feasting in Ancient Rome. University of Chicago Press. p. 29.
Boardman, p. 681.
Pliny the Elder, Natural History 19.83–84; Emily Gowers, The Loaded Table: Representation of Food in Roman Literature (Oxford University Press, 1993, 2003), p. 17
Gagarin, p. 198.
Stambaugh, p. 144.
Holleran, pp. 136–137.
Holleran, pp. 134–135.
Stambaugh, p. 146
Holleran, p. 134.
Grant, Mark (2000) Galen on Food and Diet. Routledge. pp. 7, 11.
Potter (2009), p. 354.
Potter (2009), p. 356.
Roller, Matthew B. (2006) Dining Posture in Ancient Rome. Princeton University Press. p. 96ff.
Potter (2009), p. 359.
Alcock, Joan P. (2006) Food in the Ancient World. Greenwood Press. p. 184.
Donahue, John (2004) The Roman Community at Table during the Principate. University of Michigan Press. p. 9.
Cathy K. Kaufman, "Remembrance of Meals Past: Cooking by Apicius' Book," in Food and the Memory: Proceedings of the Oxford Symposium on Food and Cooker p. 125ff.
Suetonius, Life of Vitellius 13.2; Gowers, The Loaded Table, p. 20.
Gagarin, p. 201.
Tacitus, Germania 23; Gowers, The Loaded Table, p. 18.
Flandrin, Jean Louis; Montanari, Massimo (1999). Food: A Culinary History from Antiquity to the Present. Columbia University Press. pp. 165–167. ISBN 978-0-231-11154-6.
Potter (2009), pp. 365–366.
Bowersock, p. 455
Franklin, James L. Jr. (2001) Pompeis Difficile Est: Studies in the Political Life of Imperial Pompeii. University of Michigan Press. p. 137
Laurence, Ray (2007) Roman Pompeii: Space and Society. Routledge. p. 173; recounted by Tacitus, Annals 14.17.
Mary Beard, J.A. North, and S.R.F. Price, Religions of Rome: A History (Cambridge University Press, 1998), p. 66.
Dyson, p. 240.
Versnel, H.S. (1971) Triumphus: An Inquiry into the Origin, Development and Meaning of the Roman Triumph. Brill. pp. 96–97.
Potter (1999), p. 242.
Potter (1999), pp. 235–236.
Potter (1999), pp. 223–224.
Potter (1999), p. 303.
Humphrey, pp. 1–3.
Edmondson, p. 112.
Dyson, pp. 237, 239.
Edmondson, pp. 73–74, 106
Auguet, p. 54
McClelland, John (2007) Body and Mind: Sport in Europe from the Roman Empire to the Renaissance. Routledge. p. 67.
Dyson, pp. 238–239
Gagarin, p. 85
Humphrey, p. 461
McClelland, John (2007) Body and Mind: Sport in Europe from the Roman Empire to the Renaissance. Routledge. p. 61.
Thomas Wiedemann, Emperors and Gladiators (Routledge, 1992, 1995), p. 15.
Humphrey, pp. 459, 461, 512, 630–631
Dyson, p. 237
Dyson, p. 238.
Potter (1999), p. 296
Dyson, pp. 238–239.
Humphrey, p. 238
Potter (1999), p. 299.
Humphrey, pp. 18–21
Gagarin, p. 84.
Auguet, pp. 131–132
Potter (1999), p. 237.
Auguet, p. 144
Dickie, Matthew (2001) Magic and Magicians in the Greco-Roman World. Routledge. pp. 282–287
Eva D'Ambra, "Racing with Death: Circus Sarcophagi and the Commemoration of Children in Roman Italy" in Constructions of Childhood in Ancient Greece and Italy (American School of Classical Studies at Athens, 2007), pp. 348–349
Rüpke, p. 289.
Potter (2009), p. 354
Edwards, p. 59
Potter (1999), p. 305.
Cassio Dio 54.2.2; Res Gestae Divi Augusti 22.1, 3
Edwards, p. 49
Edmondson, p. 70.
Cassius Dio 66.25
Edwards, p. 55
Edwards, p. 49.
Edwards, p. 50.
Potter (1999), p. 307
McClelland, Body and Mind, p. 66, citing also Marcus Junkelmann.
Suetonius, Nero 12.2
Edmondson, p. 73.
Tertullian, De spectaculis 12
Edwards, pp. 59–60
Potter (1999), p. 224.
McDonald, Marianne and Walton, J. Michael (2007) Introduction to The Cambridge Companion to Greek and Roman Theatre. Cambridge University Press. p. 8.
Kyle, Donald G. (1998) Spectacles of Death in Ancient Rome. Routledge. p. 81
Edwards, p. 63.
Pliny, Panegyric 33.1
Edwards, p. 52.
Edwards, pp. 66–67, 72.
Edwards, p. 212.
Bowersock, G.W. (1995) Martyrdom and Rome. Cambridge University Press. pp. 25–26
Cavallo, p. 79
Huber-Rebenich, Gerlinde (1999) "Hagiographic Fiction as Entertainment," in Latin Fiction: The Latin Novel in Context. Routlege. pp. 158–178
Llewelyn, S.R. and Nobbs, A.M. (2002) "The Earliest Dated Reference to Sunday in the Papyri," in New Documents Illustrating Early Christianity. Wm. B. Eerdmans. p. 109
Hildebrandt, Henrik (2006) "Early Christianity in Roman Pannonia—Fact or Fiction?" in Studia Patristica: Papers Presented at the Fourteenth International Conference on Patristic Studies Held in Oxford 2003. Peeters. pp. 59–64
Ando, p. 382.
Oxford Latin Dictionary (Oxford: Clarendon Press, 1982, 1985 reprint), pp. 1048–1049
Habinek (2005), pp. 5, 143.
Rawson (2003), p. 128.
McDaniel, Walton Brooks (1906). "Some Passages concerning Ball-Games". Transactions and Proceedings of the American Philological Association. 37: 121. doi:10.2307/282704. JSTOR 282704.
Rawson (2003), pp. 129–130.
Eyben, Emiel (1977) Restless Youth in Ancient Rome. Routledge, pp. 79–82, 110.
Dunbabin, Katherine M.D. (1999) Mosaics of the Greek and Roman World. Cambridge University Press. p. 133. ISBN 0521002303.
Hanson, Ann Ellis (1991) "The Restructuring of Female Physiology at Rome," in Les écoles médicales à Rome. Université de Nantes. pp. 260, 264, particularly citing the Gynecology of Soranus.
Austin, R. G. (2009). "Roman Board Games. II". Greece and Rome. 4 (11): 76. doi:10.1017/S0017383500003119. JSTOR 640979.
Austin, R. G. (1934). "Roman Board Games. I". Greece and Rome. 4 (10): 24–34. doi:10.1017/s0017383500002941. JSTOR 641231.
Gagarin, p. 230.
Coon, Lynda L. (1997) Sacred Fictions: Holy Women and Hagiography in Late Antiquity. University of Pennsylvania Press. pp. 57–58.
Vout, p. 216
Bieber, Margarete (1959). "Roman Men in Greek Himation (Romani Palliati) a Contribution to the History of Copying". Proceedings of the American Philosophical Society. 103 (3): 374–417. JSTOR 985474.
Vout, p. 218.
Vout, pp. 204–220, especially pp. 206, 211
Métraux, Guy P.R. (2008) "Prudery and Chic in Late Antique Clothing," in Roman Dress and the Fabrics of Roman Culture. University of Toronto Press. p. 286.
Gagarin, p. 231.
Quintilian, Institutio Oratoria 11.3.137–149
Métraux, Guy P.R. (2008) "Prudery and Chic in Late Antique Clothing," in Roman Dress and the Fabrics of Roman Culture. University of Toronto Press. pp. 282–283.
Cleland, Liza (2007) Greek and Roman Dress from A to Z. Routledge. p. 194.
Modern copy of a 2nd-century original, from the Louvre.
Tertullian, De Pallio 5.2
Vout, p. 217.
Gagarin, p. 232.
D'Amato, Raffaele (2005) Roman Military Clothing (3) AD 400 to 640. Osprey. pp. 7–9. ISBN 184176843X.
Wickham, Chris (2009) The Inheritance of Rome. Penguin Books. p. 106. ISBN 978-0-670-02098-0
Kousser, p. 1
Potter (2009), pp. 75–76.
Potter (2009), pp. 82–83.
Gazda, Elaine K. (1991) "Introduction", in Roman Art in the Private Sphere: Architecture and Décor of the Domus, Villa, and Insula. University of Michigan Press. pp. 1–3. ISBN 047210196X.
Paul Zanker, Pompeii: Public and Private Life, translated by Deborah Lucas Schneider (Harvard University Press, 1998, originally published 1995 in German), p. 189.
Kousser, pp. 4–5, 8.
Gagarin, pp. 312–313.
Toynbee, J. M. C. (December 1971). "Roman Art". The Classical Review. 21 (3): 439–442. doi:10.1017/S0009840X00221331. JSTOR 708631.
Zanker, Paul (1988) The Power of Images in the Age of Augustus. University of Michigan Press. p. 5ff.
Gagarin, p. 451.
Fejfer, Jane (2008) Roman Portraits in Context. Walter de Gruyter. p. 10.
Gagarin, p. 453.
Mattusch, Carol C. (2005) The Villa dei Papiri at Herculaneum: Life and Afterlife of a Sculpture Collection. Getty Publications. p. 322.
Kousser, p. 13
Strong, Donald (1976, 1988) Roman Art. Yale University Press. 2nd ed., p. 11.
Gagarin, pp. 274–275.
Gagarin, p. 242.
Kleiner, Fred S. (2007) A History of Roman Art. Wadsworth. p. 272.
Newby, Zahra (2011) "Myth and Death: Roman Mythological Sarcophagi," in A Companion to Greek Mythology. Blackwell. p. 301.
Elsner, p. 1.
Elsner, p. 12.
Elsner, p. 14.
Elsner, pp. 1, 9.
Hachlili, Rachel (1998) Ancient Jewish Art and Archaeology in the Diaspora. Brill. pp. 96ff.
Schreckenberg, Heinz and Schubert, Kurt (1991) Jewish Historiography and Iconography in Early and Medieval Christianity. Fortress Press. pp. 171ff.
Gagarin, p. 463.
Gagarin, p. 459.
Gagarin, pp. 459–460.
Dunbabin, Katherine M.D. (1999) Mosaics of the Greek and Roman World. Cambridge University Press. p. 254ff. ISBN 0521002303.
Gagarin, p. 202.
Butcher, Kevin (2003) Roman Syria and the Near East. Getty Publications. p. 201ff. ISBN 0892367156.
Bowman, p. 421.
Fantham, R. Elaine (1989). "Mime: The Missing Link in Roman Literary History". The Classical World. 82 (3): 153. doi:10.2307/4350348. JSTOR 4350348.
Slater, William J. (2002). "Mime Problems: Cicero Ad fam. 7.1 and Martial 9.38". Phoenix. 56 (3/4): 315. doi:10.2307/1192603. JSTOR 1192603.
Potter (1999), p. 257.
Gian Biagio Conte (1994) Latin Literature: A History. Johns Hopkins University Press. p. 128.
Franklin, James L. (1987). "Pantomimists at Pompeii: Actius Anicetus and His Troupe". The American Journal of Philology. 108: 95. doi:10.2307/294916. JSTOR 294916.
Starks, John H. Jr. (2008) "Pantomime Actresses in Latin Inscriptions," in New Directions in Ancient Pantomime. Oxford University Press. p. 95; p. 14ff.
Naerebout, p. 146.
Ginsberg‐Klar, Maria E. (2010). "The archaeology of musical instruments in Germany during the Roman period". World Archaeology. 12 (3): 313. doi:10.1080/00438243.1981.9979806. JSTOR 124243.
Habinek (2005), p. 90ff.
Naerebout, pp. 146ff.
Naerebout, pp. 154, 157.
Naerebout, pp. 156–157.
Richlin, Amy (1993). "Not before Homosexuality: The Materiality of the cinaedus and the Roman Law against Love between Men". Journal of the History of Sexuality. 3 (4): 539–540. JSTOR 3704392.
Csapo, Eric and Slater, William J. (1994) The Context of Ancient Drama. University of Michigan Press. p. 377.
MacMullen, Ramsay (1984) Christianizing the Roman Empire: (A. D. 100–400). Yale University Press. pp. 74–75, 84.
As quoted by Alcuin, Epistula 175 (Nescit homo, qui histriones et mimos et saltatores introduct in domum suam, quam magna eos immundorum sequitur turba spiritum)
Hen, Yitzhak (1995) Culture and Religion in Merovingian Gaul, AD 481–751. Brill. p. 230.
Harris, p. 5
Johnson (2009), pp. 3–4
Kraus, T.J. (2000). "(Il)literacy in Non-Literary Papyri from Graeco-Roman Egypt: Further Aspects of the Educational Ideal in Ancient Literary Sources and Modern Times". Mnemosyme. 53 (3): 322–342 (325–327). doi:10.1163/156852500510633. JSTOR 4433101.
Peachin, pp. 89, 97–98.
Mattern, Susan P. (1999) Rome and the Enemy: Imperial Strategy in the Principate. University of California Press. p. 197
Morgan, Teresa (1998) Literate Education in the Hellenistic and Roman Worlds. Cambridge University Press. pp. 1–2
Johnson (2009), pp. 46ff.
Peachin, p. 97.
Clifford Ando poses the question as "what good would 'posted edicts' do in a world of low literacy?' in Ando, p. 101 (see also p. 87 on "the government's obsessive documentation").
Ando, pp. 86–87.
Ando, p. 101
Ando, pp. 152, 210.
Beard, Mary (1991) "Ancient Literacy and the Written Word in Roman Religion," in Literacy in the Roman World. University of Michigan Press. p. 59ff
Dickie, Matthew (2001) Magic and Magicians in the Greco-Roman World. Routledge. pp. pp. 94–95, 181–182, and 196
Potter (2009), p. 555
Harris, pp. 29, 218–219.
Phang, Sara Elise (2011) "Military Documents, Languages, and Literacy," in A Companion to the Roman Army. Blackwell. pp. 286–301.
Mattern, Rome and the Enemy, p. 197, citing Harris, pp. 253–255.
Harris, pp. 9, 48, 215, 248, 258–269
Johnson (2009), pp. 47, 54, 290ff.
Mattern, Rome and the Enemy, p. 197
Gagarin, pp. 19–20.
Johnson (2010), pp. 17–18.
Martial, Epigrams 1.2 and 14.184–92, as cited by Johnson (2010), p. 17
Cavallo, pp. 83–84.
Cavallo, pp. 84–85.
Cavallo, p. 84.
Marshall, p. 253.
Cavallo, p. 71
Marshall, p. 253, citing on the book trade in the provinces Pliny the Younger, Epistulae 9.11.2; Martial, Epigrams 7.88; Horace, Carmina 2.20.13f. and Ars Poetica 345; Ovid, Tristia 4.9.21 and 4.10.128; Pliny the Elder, Natural History 35.2.11; Sidonius, Epistulae 9.7.1.
Strabo 13.1.54, 50.13.419; Martial, Epigrams 2.8; Lucian, Adversus Indoctum 1
According to Seneca, Epistulae 27.6f.
Marshall, p. 254.
Marshall, pp. 252–264.
Cavallo, pp. 67–68.
Marshall, pp. 257, 260.
Pliny, Epistulae 1.8.2; CIL 5.5262 (= ILS 2927)
Marshall, p. 255.
Marshall, 261–262
Cavallo, p. 70.
Tacitus, Agricola 2.1 and Annales 4.35 and 14.50; Pliny the Younger, Epistulae 7.19.6; Suetonius, Augustus 31, Tiberius 61.3, and Caligula 16
Suetonius, Domitian 10; Quintilian, Institutio Oratoria 9.2.65
Marshall, p. 263.
Johnson (2009), pp. 114ff., pp. 186ff.
Potter (2009), p. 372.
Johnson (2010) p. 14.
Johnson (2009), pp. 320ff.
Cavallo, pp. 68–69, 78–79.
Cavallo, pp. 81–82.
Peachin, p. 95.
Peachin, pp. 84–85.
Laes, p. 108
Peachin, p. 89.
Laes, pp. 113–116.
Peachin, pp. 90, 92
Laes, pp. 116–121.
Peachin, pp. 87–89.
Laes, p. 122.
Peachin, p. 90.
Laes, pp. 107–108, 132.
Peachin, pp. 93–94.
Peachin, pp. 88, 106
Laes, p. 109.
Laes, p. 132.
Potter (2009), pp. 439, 442.
Peachin, pp. 102–103, 105.
Peachin, pp. 104–105.
Peachin, pp. 103, 106.
Peachin, p. 110.
Peachin, p. 107.
Harris, p. 5.
Saller, R. P. (2012). "Promotion and Patronage in Equestrian Careers". Journal of Roman Studies. 70: 44. doi:10.2307/299555. JSTOR 299555.
Armstron, David (2010) "The Biographical and Social Foundations of Horace's Poetic Voice," in A Companion to Horace. Blackwell. p. 11
Lyne, R.O.A.M. (1995) Horace: Beyond the Public Poetry. Yale University Press. pp. 2–3
Peachin, p. 94.
Potter (2009), p. 598.
Laes, pp. 109–110.
Peachin, p. 88.
Laes, p. 110
Gagarin, p. 19.
Gagarin, p. 18.
The wide-ranging 21st-century scholarship on the Second Sophistic includes Being Greek under Rome: Cultural Identity, the Second Sophistic and the Development of Empire, edited by Simon Goldhill (Cambridge University Press, 2001); Paideia: The World of the Second Sophistic, edited by Barbara E. Borg (De Gruyter, 2004); and Tim Whitmarsh, The Second Sophistic (Oxford University Press, 2005).
Habinek, Thomas N. (1998) The Politics of Latin Literature: Writing, Identity, and Empire in Ancient Rome. Princeton University Press. pp. 122–123
Rawson (2003), p. 80.
James, Sharon L. (2003) Learned Girls and Male Persuasion: Gender and Reading in Roman Love Elegy. University of California Press. pp. 21–25
Johnson, W.R. "Propertius," pp. 42–43, and Sharon L. James, "Elegy and New Comedy," p. 262, both in A Companion to Roman Love Elegy. Blackwell, 2012.
Gagarin, p. 20.
Harris, p. 3.
Numbers, Ronald (2009). Galileo Goes to Jail and Other Myths about Science and Religion. Harvard University Press. p. 18. ISBN 978-0-674-03327-6.
Grant, Edvard. (1996) “The Foundations of Modern Science in the Middle Ages. Cambridge University Press. Page 4.
Cavallo, pp. 87–89.
Cavallo, p. 86.
Cavallo, p. 15-16.
Roberts, p. 3.
Aetas Ovidiana; Charles McNelis, "Ovidian Strategies in Early Imperial Literature," in A Companion to Ovid (Blackwell, 2007), p. 397.
Roberts, p. 8.
van Dam, Harm-Jan (2008) "Wandering Woods Again: From Poliziano to Grotius," in The Poetry of Statius. Brill. p. 45ff.
Jonathan Master, "The Histories," in A Companion to Tacitus (Blackwell, 2012), p. 88.
Sage, Michael M. (1990) "Tacitus' Historical Works: A Survey and Appraisal," Aufstieg und Niedergang der römischen Welt II.33.2, p. 853.
Albrecht, p. 1294.
Albrecht, p. 1443.
Roberts, p. 70.
Albrecht, p. 1359ff.
"Not since Vergil had there been a Roman poet so effective at establishing a master narrative for his people": Marc Mastrangelo, The Roman Self in Late Antiquity: Prudentius and the Poetics of the Soul (Johns Hopkins University Press, 2008), p. 3.
Bowersock, p. 694
Rüpke, p. 4.
Apuleius, Florides 1.1
Rüpke, p. 279.
Matthew Bunson, A Dictionary of the Roman Empire (Oxford University Press, 1995), p. 246.
The caesareum at Najaran was possibly known later as the "Kaaba of Najran": جواد علي, المفصل في تاريخ العرب قبل الإسلام (Jawad Ali, Al-Mufassal fi Tarikh Al-'Arab Qabl Al-Islam; "Commentary on the History of the Arabs Before Islam"), Baghdad, 1955–1983; P. Harland, "Imperial Cults within Local Cultural Life: Associations in Roman Asia", originally published in Ancient History Bulletin / Zeitschrift für Alte Geschichte 17 (2003) 91–103.
Isaac, Benjamin H. (2004) The Invention of Racism in Classical Antiquity. Princeton University Press. p. 449
Frend, W.H.C. (1967) Martyrdom and Persecution in the Early Church: A Study of Conflict from the Maccabees to Donatus. Doubleday. p. 106
Huskinson, Janet (2000) Experiencing Rome: Culture, Identity and Power in the Roman Empire. Routledge. p. 261. See, for instance, the altar dedicated by a Roman citizen and depicting a sacrifice conducted in the Roman manner for the Germanic goddess Vagdavercustis in the 2nd century AD.
Momigliano, Arnaldo (1986). "The Disadvantages of Monotheism for a Universal State". Classical Philology. 81 (4): 285–297. doi:10.1086/367003. JSTOR 269977.
Fishwick, Duncan (1991). The Imperial Cult in the Latin West: Studies in the Ruler Cult of the Western Provinces of the Roman Empire, Vol. 1, Brill. pp. 97–149. ISBN 90-04-07179-2.
Ben-Sasson, H.H. (1976) A History of the Jewish People, Harvard University Press. pp. 254–256. ISBN 0-674-39731-2
Bowman, p. 616
Frend, W.H.C. (2006) "Persecutions: Genesis and Legacy," Cambridge History of Christianity: Origins to Constantine. Cambridge University Press. Vol. 1, p. 510. ISBN 0521812399.
Barnes, T. D. (2012). "Legislation against the Christians". Journal of Roman Studies. 58: 32. doi:10.2307/299693. JSTOR 299693.
Sainte-Croix, G.E.M de (1963). "Why Were the Early Christians Persecuted?". Past & Present. 26: 6–38. doi:10.1093/past/26.1.6.
Musurillo, Herbert (1972) The Acts of the Christian Martyrs. Oxford: Clarendon Press. pp. lviii–lxii
Sherwin-White, A. N. (1952). "The Early Persecutions and Roman Law Again". The Journal of Theological Studies (2): 199. doi:10.1093/jts/III.2.199. JSTOR 23952852.
Tacitus, Annals XV.44
Eusebius of Caesarea (425). Church History.
Smallwood, E.M. (1956). "'Domitian's attitude towards the Jews and Judaism". Classical Philology. 51: 1–13. doi:10.1086/363978.
Pliny, Epistle to Trajan on the Christians
Frend, W. H. C. (1959). "The Failure of the Persecutions in the Roman Empire". Past and Present. 16: 10. doi:10.1093/past/16.1.10. JSTOR 650151.
Bowersock, p. 625
Rüpke, pp. 406–426
On vocabulary, see Schilling, Robert (1992) "The Decline and Survival of Roman Religion", Roman and European Mythologies. University of Chicago Press. p. 110.
Burgan, Michael (2009). Empire of Ancient Rome. Infobase Publishing. pp. 113–114. ISBN 978-1-4381-2659-3.
Noble, Thomas F. X.; Strauss, Barry; Osheim, Duane J.; Neuschel, Kristen B.; Accampo, Elinor Ann (2010). Western Civilization: Beyond Boundaries, 1300–1815. Cengage Learning. p. 352. ISBN 978-1-4240-6959-0.
Goffman, Daniel (2002). The Ottoman Empire and Early Modern Europe. Cambridge University Press. p. 107.
Encyclopædia Britannica, History of Europe, The Romans, 2008, O.Ed.
Collier, Martin (2003). Italian Unification, 1820–71. Heinemann. p. 22. ISBN 0-435-32754-2.
Briggs, Ward (2010) "United States," in A Companion to the Classical Tradition. Blackwell. p. 279ff.
Meinig, D.W. (1986) The Shaping of America: A Geographical Perspective on 500 Years of History. Atlantic America, 1492–1800. Yale University Press. Vol. 1. pp. 432–435. ISBN 0300038828.
Vale, Lawrence J. (1992) Architecture, Power, and National Identity. Yale University Press. pp. 11, 66–67
Mallgrave, Harry Francis (2005) Modern Architectural Theory: A Historical Survey, 1673–1968. Cambridge University Press. pp. 144–145
Kornwall, James D. (2011) Architecture and Town Planning in Colonial North America. Johns Hopkins University Press, vol. 3. pp. 1246, 1405–1408. ISBN 0801859867.
Wood, pp. 73–74
Onuf, Peter S. and Cole, Nicholas P. introduction to Thomas Jefferson, the Classical World, and Early America. University of Virginia Press. p. 5
Dietler, Michael (2010). Archaeologies of Colonialism: Consumption, Entanglement, and Violence in Ancient Mediterranean France. University of California Press. ISBN 978-0-520-26551-6.
Briggs, W. (2010) "United States," in A Companion to the Classical Tradition. Blackwell. pp. 282–286
Wood, pp. 60, 66, 73–74, 239.
Gelernter, Mark (1999) A History of American Architecture: Buildings in Their Cultural and Technological Context. University Press of New England. p. 13.
Wilson, Richard Guy (2011) "Thomas Jefferson's Classical Architecture: An American Agenda," in Thomas Jefferson, the Classical World, and Early America. University of Virginia Press. p. 122
Spahn, Hannah (2011) Thomas Jefferson, Time, and History. University of Virginia Press. pp. 144–145, 163–167
Wood, pp. 228–330
Lears, Jackson (2009) Rebirth of a Nation: The Making of Modern America, 1877–1920. HarperCollins. pp. 277–278
Gutheim, Frederick and Lee, Antoinette J. (2006) Worthy of the Nation: Washington, DC, from L'Enfant to the National Capital Planning Committee. Johns Hopkins University Press, 2nd ed. pp. 137, 152.

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Late Antiquity: A Guide to the Postclassical World. Harvard University Press. ISBN 978-0-674-51173-6. Bowman, Alan; Garnsey, Peter; Cameron, Averil, eds. (2005). The Cambridge Ancient History: Volume 12, The Crisis of Empire, AD 193–337. Cambridge University Press. ISBN 978-0-521-30199-2. Bradley, Keith (1994). Slavery and Society at Rome. Cambridge University Press. ISBN 978-0-521-37887-1. Cavallo, Guglielmo; Chartier, Roger (1999). A History of Reading in the West. Polity Press. ISBN 978-0-7456-1936-1. Clarke, John R. (1991). The Houses of Roman Italy, 100 B.C.-A.D. 250: Ritual, Space, and Decoration. University of California Press. ISBN 978-0-520-08429-2. Dyson, Stephen L. (2010). Rome: A Living Portrait of an Ancient City. JHU Press. ISBN 978-1-4214-0101-0. Edmondson, J.C. (1996). "Dynamic Arenas: Gladiatorial Presentations in the City of Rome and the Construction of Roman Society during the Early Empire". Roman Theater and Society. University of Michigan Press. Edwards, Catharine (2007). Death in Ancient Rome. Yale University Press. ISBN 0-300-11208-4. Elsner, Jaś; Huskinson, Janet (2011). Life, Death and Representation: Some New Work on Roman Sarcophagi. Walter de Gruyter. ISBN 978-3-11-020213-7. Frier, Bruce W.; McGinn, Thomas A. (2004). A Casebook on Roman Family Law. Oxford University Press. ISBN 978-0-19-516185-4. Gagarin, Michael, ed. (2010). The Oxford Encyclopedia of Ancient Greece and Rome. Oxford University Press. ISBN 978-0-19-517072-6. Goldsworthy, Adrian (2003). The Complete Roman Army. London: Thames & Hudson. ISBN 0-500-05124-0. Goldsworthy, Adrian Keith (2009). How Rome Fell: Death of a Superpower. New Haven, Connecticut: Yale University Press. ISBN 978-0-300-13719-4. Habinek, Thomas N. (2005). The World of Roman Song: From Ritualized Speech to Social Order. JHU Press. ISBN 978-0-8018-8105-3. Harris, W. V. (1989). Ancient Literacy. Harvard University Press. ISBN 0674033817. Holleran, Claire (2012). Shopping in Ancient Rome: The Retail Trade in the Late Republic and the Principate. OUP Oxford. ISBN 978-0-19-969821-9. Humphrey, John H. (1986). Roman Circuses: Arenas for Chariot Racing. University of California Press. ISBN 978-0-520-04921-5. Huzar, Eleanor Goltz (1978). Mark Antony: a Biography. Minneapolis: University of Minnesota Press. ISBN 0-8166-0863-6. Johnson, William A; Parker, Holt N (2009). Ancient Literacies: The Culture of Reading in Greece and Rome. Oxford University Press. ISBN 978-0-19-971286-1. Johnson, William A. (2010). Readers and Reading Culture in the High Roman Empire: A Study of Elite Communities. Oxford University Press. ISBN 978-0-19-972105-4. Jones, A. H. M. (1960). "The Cloth Industry Under the Roman Empire". The Economic History Review. 13 (2): 183–192. doi:10.1111/j.1468-0289.1960.tb02114.x. Kelly, Christopher (2007). The Roman Empire: A Very Short Introduction. Oxford University Press. ISBN 0192803913. Kousser, Rachel Meredith (2008). Hellenistic and Roman Ideal Sculpture: The Allure of the Classical. Cambridge University Press. ISBN 978-0-521-87782-4. Laes, Christian (2011). Children in the Roman Empire: Outsiders Within. Cambridge University Press. ISBN 978-0-521-89746-4. Marshall, Anthony J. (1976). "Library Resources and Creative Writing at Rome". Phoenix. 30 (3): 252–264. doi:10.2307/1087296. JSTOR 1087296. Millar, Fergus (2012). "Empire and City, Augustus to Julian: Obligations, Excuses and Status". Journal of Roman Studies. 73: 76. doi:10.2307/300073. JSTOR 300073. Mommsen, Theodore (2005) [1909]. William P. Dickson, ed. The provinces of the Roman empire from Caesar to Diocletian. Translated by William P. Dickson. Ann Arbor, Michigan: University of Michigan Library. Morris, Ian; Scheidel, Walter (2009). The Dynamics of Ancient Empires: State Power from Assyria to Byzantium. Oxford University Press. ISBN 978-0-19-970761-4. Naerebout, Frederick G. (2009). "Dance in the Roman Empire and Its Discontents". Ritual Dynamics and Religious Change in the Roman Empire. Proceedings of the Eighth Workshop of the International Network Impact of Empire (Heidelberg, July 5–7, 2007), Brill. Nicolet, Claude (1991). Space, Geography, and Politics in the Early Roman Empire. University of Michigan Press. ISBN 0-472-10096-3. Peachin, Michael, ed. (2011). The Oxford Handbook of Social Relations in the Roman World. Oxford University Press. ISBN 978-0-19-518800-4. Potter, David Stone; Mattingly, D. J. (1999). Life, Death, and Entertainment in the Roman Empire. University of Michigan Press. ISBN 0-472-08568-9. Potter, David S., ed. (2009). A Companion to the Roman Empire. John Wiley & Sons. ISBN 978-1-4051-9918-6. Rochette, Bruno (2012). "Language Policies in the Roman Republic and Empire". A Companion to the Latin Language. doi:10.1002/9781444343397.ch30. ISBN 9781444343397. Rawson, Beryl (1987). The Family in Ancient Rome: New Perspectives. Cornell University Press. ISBN 0-8014-9460-5. Rawson, Beryl (2003). Children and Childhood in Roman Italy. OUP Oxford. ISBN 978-0-19-151423-4. Roberts, Michael John (1989). The jeweled style: poetry and poetics in late antiquity. Cornell University Press. ISBN 978-0-8014-2265-2. Rüpke, Jörg (2007). A Companion to Roman Religion. Wiley. ISBN 978-0-470-76645-3. Stambaugh, John E. (1988). The Ancient Roman City. JHU Press. ISBN 978-0-8018-3692-3. Sullivan, Richard, D. (1990). Near Eastern Royalty and Rome, 100-30 BC. Toronto: University of Toronto Press. ISBN 0-8020-2682-6. Vout, Caroline (2009). "The Myth of the Toga: Understanding the History of Roman Dress". Greece and Rome. 43 (2): 204–220. doi:10.1093/gr/43.2.204. JSTOR 643096. Winterling, Aloys (2009). Politics and Society in Imperial Rome. John Wiley & Sons. ISBN 978-1-4051-7969-0. Wiseman, T.P. (1970). "The Definition of Eques Romanus". Historia. 19 (1): 67–83. Wood, Gordon S. (2011). The Idea of America: Reflections on the Birth of the United States. Penguin Publishing Group. ISBN 978-1-101-51514-3. External links Roman Empire at Wikipedia's sister projects Definitions from Wiktionary Media from Wikimedia Commons News from Wikinews Quotations from Wikiquote Texts from Wikisource Textbooks from Wikibooks Travel guide from Wikivoyage Resources from Wikiversity Library resources about Roman Empire Online books Resources in your library Resources in other libraries Romans for Children, a BBC website on ancient Rome for children at primary-school level. Interactive map of the Roman Empire at Vici.org Historical Atlas showing the expansion of the Roman Empire. 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Languages Bân-lâm-gú 贛語 客家語/Hak-kâ-ngî Монгол ئۇيغۇرچە / Uyghurche Vahcuengh 吴语 粵語 中文 143 more Edit links This page was last edited on 20 February 2019, at 08:00 (UTC). Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Privacy policyAbout WikipediaDisclaimersContact WikipediaDevelopersCookie statementMobile view This article is about the chemical element and its most stable form, O 2. For other forms of this element, see Allotropes of oxygen. For other uses, see Oxygen (disambiguation) and O2 (disambiguation). Oxygen, 8O A transparent beaker containing a light blue fluid with gas bubbles Liquid oxygen boiling Oxygen Allotropes O2, O3 (Ozone) Appearance gas: colorless liquid: pale blue Standard atomic weight Ar, std(O) [15.99903, 15.99977] conventional: 15.999 Oxygen in the periodic table Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Sodium Magnesium Aluminium Silicon Phosphorus Sulfur Chlorine Argon Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon Caesium Barium Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury (element) Thallium Lead Bismuth Polonium Astatine Radon Francium Radium Actinium Thorium Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium Rutherfordium Dubnium Seaborgium Bohrium Hassium Meitnerium Darmstadtium Roentgenium Copernicium Nihonium Flerovium Moscovium Livermorium Tennessine Oganesson – ↑ O ↓ S nitrogen ← oxygen → fluorine Atomic number (Z) 8 Group group 16 (chalcogens) Period period 2 Block p-block Element category reactive nonmetal Electron configuration [He] 2s2 2p4 Electrons per shell 2, 6 Physical properties Phase at STP gas Melting point 54.36 K ​(−218.79 °C, ​−361.82 °F) Boiling point 90.188 K ​(−182.962 °C, ​−297.332 °F) Density (at STP) 1.429 g/L when liquid (at b.p.) 1.141 g/cm3 Triple point 54.361 K, ​0.1463 kPa Critical point 154.581 K, 5.043 MPa Heat of fusion (O2) 0.444 kJ/mol Heat of vaporization (O2) 6.82 kJ/mol Molar heat capacity (O2) 29.378 J/(mol·K) Vapor pressure P (Pa) 1 10 100 1 k 10 k 100 k at T (K) 61 73 90 Atomic properties Oxidation states −2, −1, +1, +2 Electronegativity Pauling scale: 3.44 Ionization energies 1st: 1313.9 kJ/mol 2nd: 3388.3 kJ/mol 3rd: 5300.5 kJ/mol (more) Covalent radius 66±2 pm Van der Waals radius 152 pm Color lines in a spectral range Spectral lines of oxygen Other properties Natural occurrence primordial Crystal structure ​cubicCubic crystal structure for oxygen Speed of sound 330 m/s (gas, at 27 °C) Thermal conductivity 26.58×10−3 W/(m·K) Magnetic ordering paramagnetic Magnetic susceptibility +3449.0·10−6 cm3/mol (293 K)[1] CAS Number 7782-44-7 History Discovery Carl Wilhelm Scheele (1771) Named by Antoine Lavoisier (1777) Main isotopes of oxygen Iso­tope Abun­dance Half-life (t1/2) Decay mode Pro­duct 16O 99.76% stable 17O 0.04% stable 18O 0.20% stable viewtalkedit | references Oxygen is a chemical element with symbol O and atomic number 8. It is a member of the chalcogen group on the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as well as with other compounds. By mass, oxygen is the third-most abundant element in the universe, after hydrogen and helium. At standard temperature and pressure, two atoms of the element bind to form dioxygen, a colorless and odorless diatomic gas with the formula O 2. Diatomic oxygen gas constitutes 20.8% of the Earth's atmosphere. As compounds including oxides, the element makes up almost half of the Earth's crust.

Dioxygen is used in cellular respiration and many major classes of organic molecules in living organisms contain oxygen, such as proteins, nucleic acids, carbohydrates, and fats, as do the major constituent inorganic compounds of animal shells, teeth, and bone. Most of the mass of living organisms is oxygen as a component of water, the major constituent of lifeforms. Oxygen is continuously replenished in Earth's atmosphere by photosynthesis, which uses the energy of sunlight to produce oxygen from water and carbon dioxide. Oxygen is too chemically reactive to remain a free element in air without being continuously replenished by the photosynthetic action of living organisms. Another form (allotrope) of oxygen, ozone (O 3), strongly absorbs ultraviolet UVB radiation and the high-altitude ozone layer helps protect the biosphere from ultraviolet radiation. However, ozone present at the surface is a byproduct of smog and thus a pollutant.

Oxygen was isolated by Michael Sendivogius before 1604, but it is commonly believed that the element was discovered independently by Carl Wilhelm Scheele, in Uppsala, in 1773 or earlier, and Joseph Priestley in Wiltshire, in 1774. Priority is often given for Priestley because his work was published first. Priestley, however, called oxygen "dephlogisticated air", and did not recognize it as a chemical element. The name oxygen was coined in 1777 by Antoine Lavoisier, who first recognized oxygen as a chemical element and correctly characterized the role it plays in combustion.

Common uses of oxygen include production of steel, plastics and textiles, brazing, welding and cutting of steels and other metals, rocket propellant, oxygen therapy, and life support systems in aircraft, submarines, spaceflight and diving.

Contents 1 History 1.1 Early experiments 1.2 Phlogiston theory 1.3 Discovery 1.4 Lavoisier's contribution 1.5 Later history 2 Characteristics 2.1 Properties and molecular structure 2.2 Allotropes 2.3 Physical properties 2.4 Isotopes and stellar origin 2.5 Occurrence 2.6 Analysis 3 Biological role of O2 3.1 Photosynthesis and respiration 3.2 Living organisms 3.3 Build-up in the atmosphere 4 Industrial production 5 Storage 6 Applications 6.1 Medical 6.2 Life support and recreational use 6.3 Industrial 7 Compounds 7.1 Oxides and other inorganic compounds 7.2 Organic compounds 8 Safety and precautions 8.1 Toxicity 8.2 Combustion and other hazards 9 See also 10 Notes 11 References 11.1 General references 12 External links History Early experiments One of the first known experiments on the relationship between combustion and air was conducted by the 2nd century BCE Greek writer on mechanics, Philo of Byzantium. In his work Pneumatica, Philo observed that inverting a vessel over a burning candle and surrounding the vessel's neck with water resulted in some water rising into the neck.[2] Philo incorrectly surmised that parts of the air in the vessel were converted into the classical element fire and thus were able to escape through pores in the glass. Many centuries later Leonardo da Vinci built on Philo's work by observing that a portion of air is consumed during combustion and respiration.[3]

In the late 17th century, Robert Boyle proved that air is necessary for combustion. English chemist John Mayow (1641–1679) refined this work by showing that fire requires only a part of air that he called spiritus nitroaereus.[4] In one experiment, he found that placing either a mouse or a lit candle in a closed container over water caused the water to rise and replace one-fourteenth of the air's volume before extinguishing the subjects.[5] From this he surmised that nitroaereus is consumed in both respiration and combustion.

Mayow observed that antimony increased in weight when heated, and inferred that the nitroaereus must have combined with it.[4] He also thought that the lungs separate nitroaereus from air and pass it into the blood and that animal heat and muscle movement result from the reaction of nitroaereus with certain substances in the body.[4] Accounts of these and other experiments and ideas were published in 1668 in his work Tractatus duo in the tract "De respiratione".[5]

Phlogiston theory Main article: Phlogiston theory Robert Hooke, Ole Borch, Mikhail Lomonosov, and Pierre Bayen all produced oxygen in experiments in the 17th and the 18th century but none of them recognized it as a chemical element.[6] This may have been in part due to the prevalence of the philosophy of combustion and corrosion called the phlogiston theory, which was then the favored explanation of those processes.[7]

Established in 1667 by the German alchemist J. J. Becher, and modified by the chemist Georg Ernst Stahl by 1731,[8] phlogiston theory stated that all combustible materials were made of two parts. One part, called phlogiston, was given off when the substance containing it was burned, while the dephlogisticated part was thought to be its true form, or calx.[3]

Highly combustible materials that leave little residue, such as wood or coal, were thought to be made mostly of phlogiston; non-combustible substances that corrode, such as iron, contained very little. Air did not play a role in phlogiston theory, nor were any initial quantitative experiments conducted to test the idea; instead, it was based on observations of what happens when something burns, that most common objects appear to become lighter and seem to lose something in the process.[3]

Discovery A drawing of an elderly man sitting by a table and facing parallel to the drawing. His left arm rests on a notebook, legs crossed. Joseph Priestley is usually given priority in the discovery. Polish alchemist, philosopher, and physician Michael Sendivogius in his work De Lapide Philosophorum Tractatus duodecim e naturae fonte et manuali experientia depromti (1604) described a substance contained in air, referring to it as 'cibus vitae' (food of life[9]), and this substance is identical with oxygen.[10] Sendivogius, during his experiments performed between 1598 and 1604, properly recognized that the substance is equivalent to the gaseous byproduct released by the thermal decomposition of potassium nitrate. In Bugaj’s view, the isolation of oxygen and the proper association of the substance to that part of air which is required for life, lends sufficient weight to the discovery of oxygen by Sendivogius.[10] This discovery of Sendivogius was however frequently denied by the generations of scientists and chemists which succeeded him.[9]

It is also commonly claimed that oxygen was first discovered by Swedish pharmacist Carl Wilhelm Scheele. He had produced oxygen gas by heating mercuric oxide and various nitrates in 1771–2.[11][12][3] Scheele called the gas "fire air" because it was then the only known agent to support combustion. He wrote an account of this discovery in a manuscript titled Treatise on Air and Fire, which he sent to his publisher in 1775. That document was published in 1777.[13]

In the meantime, on August 1, 1774, an experiment conducted by the British clergyman Joseph Priestley focused sunlight on mercuric oxide (HgO) contained in a glass tube, which liberated a gas he named "dephlogisticated air".[12] He noted that candles burned brighter in the gas and that a mouse was more active and lived longer while breathing it. After breathing the gas himself, Priestley wrote: "The feeling of it to my lungs was not sensibly different from that of common air, but I fancied that my breast felt peculiarly light and easy for some time afterwards."[6] Priestley published his findings in 1775 in a paper titled "An Account of Further Discoveries in Air," which was included in the second volume of his book titled Experiments and Observations on Different Kinds of Air.[3][14] Because he published his findings first, Priestley is usually given priority in the discovery.

The French chemist Antoine Laurent Lavoisier later claimed to have discovered the new substance independently. Priestley visited Lavoisier in October 1774 and told him about his experiment and how he liberated the new gas. Scheele also dispatched a letter to Lavoisier on September 30, 1774, that described his discovery of the previously unknown substance, but Lavoisier never acknowledged receiving it (a copy of the letter was found in Scheele's belongings after his death).[13]

Lavoisier's contribution Lavoisier conducted the first adequate quantitative experiments on oxidation and gave the first correct explanation of how combustion works.[12] He used these and similar experiments, all started in 1774, to discredit the phlogiston theory and to prove that the substance discovered by Priestley and Scheele was a chemical element.

A drawing of a young man facing towards the viewer, but looking on the side. He wear a white curly wig, dark suit and white scarf. Antoine Lavoisier discredited the phlogiston theory. In one experiment, Lavoisier observed that there was no overall increase in weight when tin and air were heated in a closed container.[12] He noted that air rushed in when he opened the container, which indicated that part of the trapped air had been consumed. He also noted that the tin had increased in weight and that increase was the same as the weight of the air that rushed back in. This and other experiments on combustion were documented in his book Sur la combustion en général, which was published in 1777.[12] In that work, he proved that air is a mixture of two gases; 'vital air', which is essential to combustion and respiration, and azote (Gk. ἄζωτον "lifeless"), which did not support either. Azote later became nitrogen in English, although it has kept the earlier name in French and several other European languages.[12]

Lavoisier renamed 'vital air' to oxygène in 1777 from the Greek roots ὀξύς (oxys) (acid, literally "sharp", from the taste of acids) and -γενής (-genēs) (producer, literally begetter), because he mistakenly believed that oxygen was a constituent of all acids.[15] Chemists (such as Sir Humphry Davy in 1812) eventually determined that Lavoisier was wrong in this regard (hydrogen forms the basis for acid chemistry), but by then the name was too well established.[16]

Oxygen entered the English language despite opposition by English scientists and the fact that the Englishman Priestley had first isolated the gas and written about it. This is partly due to a poem praising the gas titled "Oxygen" in the popular book The Botanic Garden (1791) by Erasmus Darwin, grandfather of Charles Darwin.[13]

Later history A metal frame structure stands on the snow near a tree. A middle-aged man wearing a coat, boots, leather gloves and a cap stands by the structure and holds it with his right hand. Robert H. Goddard and a liquid oxygen-gasoline rocket John Dalton's original atomic hypothesis presumed that all elements were monatomic and that the atoms in compounds would normally have the simplest atomic ratios with respect to one another. For example, Dalton assumed that water's formula was HO, leading to the conclusion that the atomic mass of oxygen was 8 times that of hydrogen, instead of the modern value of about 16.[17] In 1805, Joseph Louis Gay-Lussac and Alexander von Humboldt showed that water is formed of two volumes of hydrogen and one volume of oxygen; and by 1811 Amedeo Avogadro had arrived at the correct interpretation of water's composition, based on what is now called Avogadro's law and the diatomic elemental molecules in those gases.[18][a]

By the late 19th century scientists realized that air could be liquefied and its components isolated by compressing and cooling it. Using a cascade method, Swiss chemist and physicist Raoul Pierre Pictet evaporated liquid sulfur dioxide in order to liquefy carbon dioxide, which in turn was evaporated to cool oxygen gas enough to liquefy it. He sent a telegram on December 22, 1877 to the French Academy of Sciences in Paris announcing his discovery of liquid oxygen.[19] Just two days later, French physicist Louis Paul Cailletet announced his own method of liquefying molecular oxygen.[19] Only a few drops of the liquid were produced in each case and no meaningful analysis could be conducted. Oxygen was liquefied in a stable state for the first time on March 29, 1883 by Polish scientists from Jagiellonian University, Zygmunt Wróblewski and Karol Olszewski.[20]

In 1891 Scottish chemist James Dewar was able to produce enough liquid oxygen for study.[21] The first commercially viable process for producing liquid oxygen was independently developed in 1895 by German engineer Carl von Linde and British engineer William Hampson. Both men lowered the temperature of air until it liquefied and then distilled the component gases by boiling them off one at a time and capturing them separately.[22] Later, in 1901, oxyacetylene welding was demonstrated for the first time by burning a mixture of acetylene and compressed O 2. This method of welding and cutting metal later became common.[22]

In 1923, the American scientist Robert H. Goddard became the first person to develop a rocket engine that burned liquid fuel; the engine used gasoline for fuel and liquid oxygen as the oxidizer. Goddard successfully flew a small liquid-fueled rocket 56 m at 97 km/h on March 16, 1926 in Auburn, Massachusetts, US.[22][23]

Oxygen levels in the atmosphere are trending slightly downward globally, possibly because of fossil-fuel burning.[24]

Characteristics Properties and molecular structure

Orbital diagram, after Barrett (2002),[25] showing the participating atomic orbitals from each oxygen atom, the molecular orbitals that result from their overlap, and the aufbau filling of the orbitals with the 12 electrons, 6 from each O atom, beginning from the lowest energy orbitals, and resulting in covalent double bond character from filled orbitals (and cancellation of the contributions of the pairs of σ and σ* and π and π* orbital pairs). At standard temperature and pressure, oxygen is a colorless, odorless, and tasteless gas with the molecular formula O 2, referred to as dioxygen.[26]

As dioxygen, two oxygen atoms are chemically bound to each other. The bond can be variously described based on level of theory, but is reasonably and simply described as a covalent double bond that results from the filling of molecular orbitals formed from the atomic orbitals of the individual oxygen atoms, the filling of which results in a bond order of two. More specifically, the double bond is the result of sequential, low-to-high energy, or Aufbau, filling of orbitals, and the resulting cancellation of contributions from the 2s electrons, after sequential filling of the low σ and σ* orbitals; σ overlap of the two atomic 2p orbitals that lie along the O-O molecular axis and π overlap of two pairs of atomic 2p orbitals perpendicular to the O-O molecular axis, and then cancellation of contributions from the remaining two of the six 2p electrons after their partial filling of the lowest π and π* orbitals.[25]

This combination of cancellations and σ and π overlaps results in dioxygen's double bond character and reactivity, and a triplet electronic ground state. An electron configuration with two unpaired electrons, as is found in dioxygen orbitals (see the filled π* orbitals in the diagram) that are of equal energy—i.e., degenerate—is a configuration termed a spin triplet state. Hence, the ground state of the O 2 molecule is referred to as triplet oxygen.[27][b] The highest energy, partially filled orbitals are antibonding, and so their filling weakens the bond order from three to two. Because of its unpaired electrons, triplet oxygen reacts only slowly with most organic molecules, which have paired electron spins; this prevents spontaneous combustion.[28]

Liquid oxygen, temporarily suspended in a magnet owing to its paramagnetism In the triplet form, O 2 molecules are paramagnetic. That is, they impart magnetic character to oxygen when it is in the presence of a magnetic field, because of the spin magnetic moments of the unpaired electrons in the molecule, and the negative exchange energy between neighboring O 2 molecules.[21] Liquid oxygen is so magnetic that, in laboratory demonstrations, a bridge of liquid oxygen may be supported against its own weight between the poles of a powerful magnet.[29][c]

Singlet oxygen is a name given to several higher-energy species of molecular O 2 in which all the electron spins are paired. It is much more reactive with common organic molecules than is molecular oxygen per se. In nature, singlet oxygen is commonly formed from water during photosynthesis, using the energy of sunlight.[30] It is also produced in the troposphere by the photolysis of ozone by light of short wavelength,[31] and by the immune system as a source of active oxygen.[32] Carotenoids in photosynthetic organisms (and possibly animals) play a major role in absorbing energy from singlet oxygen and converting it to the unexcited ground state before it can cause harm to tissues.[33]

Allotropes Main article: Allotropes of oxygen

Space-filling model representation of dioxygen (O2) molecule The common allotrope of elemental oxygen on Earth is called dioxygen, O 2, the major part of the Earth's atmospheric oxygen (see Occurrence). O2 has a bond length of 121 pm and a bond energy of 498 kJ/mol,[34] which is smaller than the energy of other double bonds or pairs of single bonds in the biosphere and responsible for the exothermic reaction of O2 with any organic molecule.[28][35] Due to its energy content, O2 is used by complex forms of life, such as animals, in cellular respiration. Other aspects of O 2 are covered in the remainder of this article.

Trioxygen (O 3) is usually known as ozone and is a very reactive allotrope of oxygen that is damaging to lung tissue.[36] Ozone is produced in the upper atmosphere when O 2 combines with atomic oxygen made by the splitting of O 2 by ultraviolet (UV) radiation.[15] Since ozone absorbs strongly in the UV region of the spectrum, the ozone layer of the upper atmosphere functions as a protective radiation shield for the planet.[15] Near the Earth's surface, it is a pollutant formed as a by-product of automobile exhaust.[36] At low earth orbit altitudes, sufficient atomic oxygen is present to cause corrosion of spacecraft.[37]

The metastable molecule tetraoxygen (O 4) was discovered in 2001,[38][39] and was assumed to exist in one of the six phases of solid oxygen. It was proven in 2006 that this phase, created by pressurizing O 2 to 20 GPa, is in fact a rhombohedral O 8 cluster.[40] This cluster has the potential to be a much more powerful oxidizer than either O 2 or O 3 and may therefore be used in rocket fuel.[38][39] A metallic phase was discovered in 1990 when solid oxygen is subjected to a pressure of above 96 GPa[41] and it was shown in 1998 that at very low temperatures, this phase becomes superconducting.[42]

Physical properties

Oxygen discharge (spectrum) tube See also: Liquid oxygen and solid oxygen Oxygen dissolves more readily in water than nitrogen, and in freshwater more readily than seawater. Water in equilibrium with air contains approximately 1 molecule of dissolved O 2 for every 2 molecules of N 2 (1:2), compared with an atmospheric ratio of approximately 1:4. The solubility of oxygen in water is temperature-dependent, and about twice as much (14.6 mg·L−1) dissolves at 0 °C than at 20 °C (7.6 mg·L−1).[6][43] At 25 °C and 1 standard atmosphere (101.3 kPa) of air, freshwater contains about 6.04 milliliters (mL) of oxygen per liter, and seawater contains about 4.95 mL per liter.[44] At 5 °C the solubility increases to 9.0 mL (50% more than at 25 °C) per liter for water and 7.2 mL (45% more) per liter for sea water.

Oxygen gas dissolved in water at sea-level 5 °C 25 °C Freshwater 9.0 mL 6.04 mL Seawater 7.2 mL 4.95 mL Oxygen condenses at 90.20 K (−182.95 °C, −297.31 °F), and freezes at 54.36 K (−218.79 °C, −361.82 °F).[45] Both liquid and solid O 2 are clear substances with a light sky-blue color caused by absorption in the red (in contrast with the blue color of the sky, which is due to Rayleigh scattering of blue light). High-purity liquid O 2 is usually obtained by the fractional distillation of liquefied air.[46] Liquid oxygen may also be condensed from air using liquid nitrogen as a coolant.[47]

Oxygen is a highly reactive substance and must be segregated from combustible materials.[47]

The spectroscopy of molecular oxygen is associated with the atmospheric processes of aurora and airglow.[48] The absorption in the Herzberg continuum and Schumann–Runge bands in the ultraviolet produces atomic oxygen that is important in the chemistry of the middle atmosphere.[49] Excited state singlet molecular oxygen is responsible for red chemiluminescence in solution.[50]

Isotopes and stellar origin Main article: Isotopes of oxygen A concentric-sphere diagram, showing, from the core to the outer shell, iron, silicon, oxygen, neon, carbon, helium and hydrogen layers. Late in a massive star's life, 16O concentrates in the O-shell, 17O in the H-shell and 18O in the He-shell. Naturally occurring oxygen is composed of three stable isotopes, 16O, 17O, and 18O, with 16O being the most abundant (99.762% natural abundance).[51]

Most 16O is synthesized at the end of the helium fusion process in massive stars but some is made in the neon burning process.[52] 17O is primarily made by the burning of hydrogen into helium during the CNO cycle, making it a common isotope in the hydrogen burning zones of stars.[52] Most 18O is produced when 14N (made abundant from CNO burning) captures a 4He nucleus, making 18O common in the helium-rich zones of evolved, massive stars.[52]

Fourteen radioisotopes have been characterized. The most stable are 15O with a half-life of 122.24 seconds and 14O with a half-life of 70.606 seconds.[51] All of the remaining radioactive isotopes have half-lives that are less than 27 s and the majority of these have half-lives that are less than 83 milliseconds.[51] The most common decay mode of the isotopes lighter than 16O is β+ decay[53][54][55] to yield nitrogen, and the most common mode for the isotopes heavier than 18O is beta decay to yield fluorine.[51]

Occurrence See also: Silicate minerals, Category:Oxide minerals, Stellar population, Cosmochemistry, and Astrochemistry Ten most common elements in the Milky Way Galaxy estimated spectroscopically[56] Z Element Mass fraction in parts per million 1 Hydrogen 739,000 71 × mass of oxygen (red bar) 2 Helium 240,000 23 × mass of oxygen (red bar) 8 Oxygen 10,400

6 Carbon 4,600

10 Neon 1,340

26 Iron 1,090

7 Nitrogen 960

14 Silicon 650

12 Magnesium 580

16 Sulfur 440

Oxygen is the most abundant chemical element by mass in the Earth's biosphere, air, sea and land. Oxygen is the third most abundant chemical element in the universe, after hydrogen and helium.[57] About 0.9% of the Sun's mass is oxygen.[12] Oxygen constitutes 49.2% of the Earth's crust by mass[58] as part of oxide compounds such as silicon dioxide and is the most abundant element by mass in the Earth's crust. It is also the major component of the world's oceans (88.8% by mass).[12] Oxygen gas is the second most common component of the Earth's atmosphere, taking up 20.8% of its volume and 23.1% of its mass (some 1015 tonnes).[12][59][d] Earth is unusual among the planets of the Solar System in having such a high concentration of oxygen gas in its atmosphere: Mars (with 0.1% O 2 by volume) and Venus have much less. The O 2 surrounding those planets is produced solely by the action of ultraviolet radiation on oxygen-containing molecules such as carbon dioxide.

The unusually high concentration of oxygen gas on Earth is the result of the oxygen cycle. This biogeochemical cycle describes the movement of oxygen within and between its three main reservoirs on Earth: the atmosphere, the biosphere, and the lithosphere. The main driving factor of the oxygen cycle is photosynthesis, which is responsible for modern Earth's atmosphere. Photosynthesis releases oxygen into the atmosphere, while respiration, decay, and combustion remove it from the atmosphere. In the present equilibrium, production and consumption occur at the same rate.[60]

World map showing that the sea-surface oxygen is depleted around the equator and increases towards the poles. Cold water holds more dissolved O 2. Free oxygen also occurs in solution in the world's water bodies. The increased solubility of O 2 at lower temperatures (see Physical properties) has important implications for ocean life, as polar oceans support a much higher density of life due to their higher oxygen content.[61] Water polluted with plant nutrients such as nitrates or phosphates may stimulate growth of algae by a process called eutrophication and the decay of these organisms and other biomaterials may reduce the O 2 content in eutrophic water bodies. Scientists assess this aspect of water quality by measuring the water's biochemical oxygen demand, or the amount of O 2 needed to restore it to a normal concentration.[62]

Analysis Time evolution of oxygen-18 concentration on the scale of 500 million years showing many local peaks. 500 million years of climate change vs 18O Paleoclimatologists measure the ratio of oxygen-18 and oxygen-16 in the shells and skeletons of marine organisms to determine the climate millions of years ago (see oxygen isotope ratio cycle). Seawater molecules that contain the lighter isotope, oxygen-16, evaporate at a slightly faster rate than water molecules containing the 12% heavier oxygen-18, and this disparity increases at lower temperatures.[63] During periods of lower global temperatures, snow and rain from that evaporated water tends to be higher in oxygen-16, and the seawater left behind tends to be higher in oxygen-18. Marine organisms then incorporate more oxygen-18 into their skeletons and shells than they would in a warmer climate.[63] Paleoclimatologists also directly measure this ratio in the water molecules of ice core samples as old as hundreds of thousands of years.

Planetary geologists have measured the relative quantities of oxygen isotopes in samples from the Earth, the Moon, Mars, and meteorites, but were long unable to obtain reference values for the isotope ratios in the Sun, believed to be the same as those of the primordial solar nebula. Analysis of a silicon wafer exposed to the solar wind in space and returned by the crashed Genesis spacecraft has shown that the Sun has a higher proportion of oxygen-16 than does the Earth. The measurement implies that an unknown process depleted oxygen-16 from the Sun's disk of protoplanetary material prior to the coalescence of dust grains that formed the Earth.[64]

Oxygen presents two spectrophotometric absorption bands peaking at the wavelengths 687 and 760 nm. Some remote sensing scientists have proposed using the measurement of the radiance coming from vegetation canopies in those bands to characterize plant health status from a satellite platform.[65] This approach exploits the fact that in those bands it is possible to discriminate the vegetation's reflectance from its fluorescence, which is much weaker. The measurement is technically difficult owing to the low signal-to-noise ratio and the physical structure of vegetation; but it has been proposed as a possible method of monitoring the carbon cycle from satellites on a global scale.

Biological role of O2 Main article: Dioxygen in biological reactions Photosynthesis and respiration A diagram of photosynthesis processes, including income of water and carbon dioxide, illumination and release of oxygen. Reactions produce ATP and NADPH in a Calvin cycle with a sugar as a by product. Photosynthesis splits water to liberate O 2 and fixes CO 2 into sugar in what is called a Calvin cycle. In nature, free oxygen is produced by the light-driven splitting of water during oxygenic photosynthesis. According to some estimates, green algae and cyanobacteria in marine environments provide about 70% of the free oxygen produced on Earth, and the rest is produced by terrestrial plants.[66] Other estimates of the oceanic contribution to atmospheric oxygen are higher, while some estimates are lower, suggesting oceans produce ~45% of Earth's atmospheric oxygen each year.[67]

A simplified overall formula for photosynthesis is:[68]

6 CO2 + 6 H 2O + photons → C 6H 12O 6 + 6 O 2 or simply

carbon dioxide + water + sunlight → glucose + dioxygen Photolytic oxygen evolution occurs in the thylakoid membranes of photosynthetic organisms and requires the energy of four photons.[e] Many steps are involved, but the result is the formation of a proton gradient across the thylakoid membrane, which is used to synthesize adenosine triphosphate (ATP) via photophosphorylation.[69] The O 2 remaining (after production of the water molecule) is released into the atmosphere.[f]

Oxygen is used in mitochondria to generate ATP during oxidative phosphorylation. The reaction for aerobic respiration is essentially the reverse of photosynthesis and is simplified as:

C 6H 12O 6 + 6 O 2 → 6 CO2 + 6 H 2O + 2880 kJ/mol In vertebrates, O 2 diffuses through membranes in the lungs and into red blood cells. Hemoglobin binds O 2, changing color from bluish red to bright red[36] (CO 2 is released from another part of hemoglobin through the Bohr effect). Other animals use hemocyanin (molluscs and some arthropods) or hemerythrin (spiders and lobsters).[59] A liter of blood can dissolve 200 cm3 of O 2.[59]

Until the discovery of anaerobic metazoa,[70] oxygen was thought to be a requirement for all complex life.[71]

Reactive oxygen species, such as superoxide ion (O− 2) and hydrogen peroxide (H 2O 2), are reactive by-products of oxygen use in organisms.[59] Parts of the immune system of higher organisms create peroxide, superoxide, and singlet oxygen to destroy invading microbes. Reactive oxygen species also play an important role in the hypersensitive response of plants against pathogen attack.[69] Oxygen is damaging to obligately anaerobic organisms, which were the dominant form of early life on Earth until O 2 began to accumulate in the atmosphere about 2.5 billion years ago during the Great Oxygenation Event, about a billion years after the first appearance of these organisms.[72][73]

An adult human at rest inhales 1.8 to 2.4 grams of oxygen per minute.[74] This amounts to more than 6 billion tonnes of oxygen inhaled by humanity per year.[g]

Living organisms

Partial pressures of oxygen in the human body (PO2) Unit Alveolar pulmonary gas pressures Arterial blood oxygen Venous blood gas kPa 14.2 11[75]-13[75] 4.0[75]-5.3[75] mmHg 107 75[76]-100[76] 30[77]-40[77] The free oxygen partial pressure in the body of a living vertebrate organism is highest in the respiratory system, and decreases along any arterial system, peripheral tissues, and venous system, respectively. Partial pressure is the pressure that oxygen would have if it alone occupied the volume.[78]

Build-up in the atmosphere Main article: Geological history of oxygen A graph showing time evolution of oxygen pressure on Earth; the pressure increases from zero to 0.2 atmospheres. O 2 build-up in Earth's atmosphere: 1) no O 2 produced; 2) O 2 produced, but absorbed in oceans & seabed rock; 3) O 2 starts to gas out of the oceans, but is absorbed by land surfaces and formation of ozone layer; 4–5) O 2 sinks filled and the gas accumulates Free oxygen gas was almost nonexistent in Earth's atmosphere before photosynthetic archaea and bacteria evolved, probably about 3.5 billion years ago. Free oxygen first appeared in significant quantities during the Paleoproterozoic eon (between 3.0 and 2.3 billion years ago).[79] For the first billion years, any free oxygen produced by these organisms combined with dissolved iron in the oceans to form banded iron formations. When such oxygen sinks became saturated, free oxygen began to outgas from the oceans 3–2.7 billion years ago, reaching 10% of its present level around 1.7 billion years ago.[79][80]

The presence of large amounts of dissolved and free oxygen in the oceans and atmosphere may have driven most of the extant anaerobic organisms to extinction during the Great Oxygenation Event (oxygen catastrophe) about 2.4 billion years ago. Cellular respiration using O 2 enables aerobic organisms to produce much more ATP than anaerobic organisms.[81] Cellular respiration of O 2 occurs in all eukaryotes, including all complex multicellular organisms such as plants and animals.

Since the beginning of the Cambrian period 540 million years ago, atmospheric O 2 levels have fluctuated between 15% and 30% by volume.[82] Towards the end of the Carboniferous period (about 300 million years ago) atmospheric O 2 levels reached a maximum of 35% by volume,[82] which may have contributed to the large size of insects and amphibians at this time.[83]

Variations in atmospheric oxygen concentration have shaped past climates. When oxygen declined, atmospheric density dropped, which in turn increased surface evaporation, causing precipitation increases and warmer temperatures.[84]

At the current rate of photosynthesis it would take about 2,000 years to regenerate the entire O 2 in the present atmosphere.[85]

Industrial production A drawing of three vertical pipes connected at the bottom and filled with oxygen (left pipe), water (middle) and hydrogen (right). Anode and cathode electrodes are inserted into the left and right pipes and externally connected to a battery. Hofmann electrolysis apparatus used in electrolysis of water. See also: Air separation, Oxygen evolution, and Fractional distillation One hundred million tonnes of O 2 are extracted from air for industrial uses annually by two primary methods.[13] The most common method is fractional distillation of liquefied air, with N 2 distilling as a vapor while O 2 is left as a liquid.[13]

The other primary method of producing O 2 is passing a stream of clean, dry air through one bed of a pair of identical zeolite molecular sieves, which absorbs the nitrogen and delivers a gas stream that is 90% to 93% O 2.[13] Simultaneously, nitrogen gas is released from the other nitrogen-saturated zeolite bed, by reducing the chamber operating pressure and diverting part of the oxygen gas from the producer bed through it, in the reverse direction of flow. After a set cycle time the operation of the two beds is interchanged, thereby allowing for a continuous supply of gaseous oxygen to be pumped through a pipeline. This is known as pressure swing adsorption. Oxygen gas is increasingly obtained by these non-cryogenic technologies (see also the related vacuum swing adsorption).[86]

Oxygen gas can also be produced through electrolysis of water into molecular oxygen and hydrogen. DC electricity must be used: if AC is used, the gases in each limb consist of hydrogen and oxygen in the explosive ratio 2:1. A similar method is the electrocatalytic O 2 evolution from oxides and oxoacids. Chemical catalysts can be used as well, such as in chemical oxygen generators or oxygen candles that are used as part of the life-support equipment on submarines, and are still part of standard equipment on commercial airliners in case of depressurization emergencies. Another air separation method is forcing air to dissolve through ceramic membranes based on zirconium dioxide by either high pressure or an electric current, to produce nearly pure O 2 gas.[62]

Storage

Oxygen and MAPP gas compressed gas cylinders with regulators Oxygen storage methods include high pressure oxygen tanks, cryogenics and chemical compounds. For reasons of economy, oxygen is often transported in bulk as a liquid in specially insulated tankers, since one liter of liquefied oxygen is equivalent to 840 liters of gaseous oxygen at atmospheric pressure and 20 °C (68 °F).[13] Such tankers are used to refill bulk liquid oxygen storage containers, which stand outside hospitals and other institutions that need large volumes of pure oxygen gas. Liquid oxygen is passed through heat exchangers, which convert the cryogenic liquid into gas before it enters the building. Oxygen is also stored and shipped in smaller cylinders containing the compressed gas; a form that is useful in certain portable medical applications and oxy-fuel welding and cutting.[13]

Applications See also: Breathing gas, Redox, and Combustion Medical A gray device with a label DeVILBISS LT4000 and some text on the front panel. A green plastic pipe is running from the device. An oxygen concentrator in an emphysema patient's house Main article: Oxygen therapy Uptake of O 2 from the air is the essential purpose of respiration, so oxygen supplementation is used in medicine. Treatment not only increases oxygen levels in the patient's blood, but has the secondary effect of decreasing resistance to blood flow in many types of diseased lungs, easing work load on the heart. Oxygen therapy is used to treat emphysema, pneumonia, some heart disorders (congestive heart failure), some disorders that cause increased pulmonary artery pressure, and any disease that impairs the body's ability to take up and use gaseous oxygen.[87]

Treatments are flexible enough to be used in hospitals, the patient's home, or increasingly by portable devices. Oxygen tents were once commonly used in oxygen supplementation, but have since been replaced mostly by the use of oxygen masks or nasal cannulas.[88]

Hyperbaric (high-pressure) medicine uses special oxygen chambers to increase the partial pressure of O 2 around the patient and, when needed, the medical staff.[89] Carbon monoxide poisoning, gas gangrene, and decompression sickness (the 'bends') are sometimes addressed with this therapy.[90] Increased O 2 concentration in the lungs helps to displace carbon monoxide from the heme group of hemoglobin.[91][92] Oxygen gas is poisonous to the anaerobic bacteria that cause gas gangrene, so increasing its partial pressure helps kill them.[93][94] Decompression sickness occurs in divers who decompress too quickly after a dive, resulting in bubbles of inert gas, mostly nitrogen and helium, forming in the blood. Increasing the pressure of O 2 as soon as possible helps to redissolve the bubbles back into the blood so that these excess gasses can be exhaled naturally through the lungs.[87][95][96] Normobaric oxygen administration at the highest available concentration is frequently used as first aid for any diving injury that may involve inert gas bubble formation in the tissues. There is epidemiological support for its use from a statistical study of cases recorded in a long term database.[97][98][99]

Life support and recreational use

Low pressure pure O 2 is used in space suits. An application of O 2 as a low-pressure breathing gas is in modern space suits, which surround their occupant's body with the breathing gas. These devices use nearly pure oxygen at about one-third normal pressure, resulting in a normal blood partial pressure of O 2. This trade-off of higher oxygen concentration for lower pressure is needed to maintain suit flexibility.[100][101]

Scuba and surface-supplied underwater divers and submariners also rely on artificially delivered O 2. Submarines, submersibles and atmospheric diving suits usually operate at normal atmospheric pressure. Breathing air is scrubbed of carbon dioxide by chemical extraction and oxygen is replaced to maintain a constant partial pressure. Ambient pressure divers breathe air or gas mixtures with an oxygen fraction suited to the operating depth. Pure or nearly pure O 2 use in diving at pressures higher than atmospheric is usually limited to rebreathers, or decompression at relatively shallow depths (~6 meters depth, or less),[102][103] or medical treatment in recompression chambers at pressures up to 2.8 bar, where acute oxygen toxicity can be managed without the risk of drowning. Deeper diving requires significant dilution of O 2 with other gases, such as nitrogen or helium, to prevent oxygen toxicity.[102]

People who climb mountains or fly in non-pressurized fixed-wing aircraft sometimes have supplemental O 2 supplies.[h] Pressurized commercial airplanes have an emergency supply of O 2 automatically supplied to the passengers in case of cabin depressurization. Sudden cabin pressure loss activates chemical oxygen generators above each seat, causing oxygen masks to drop. Pulling on the masks "to start the flow of oxygen" as cabin safety instructions dictate, forces iron filings into the sodium chlorate inside the canister.[62] A steady stream of oxygen gas is then produced by the exothermic reaction.

Oxygen, as a mild euphoric, has a history of recreational use in oxygen bars and in sports. Oxygen bars are establishments found in the United States since the late 1990s that offer higher than normal O 2 exposure for a minimal fee.[104] Professional athletes, especially in American football, sometimes go off-field between plays to don oxygen masks to boost performance. The pharmacological effect is doubted; a placebo effect is a more likely explanation.[104] Available studies support a performance boost from oxygen enriched mixtures only if it is breathed during aerobic exercise.[105]

Other recreational uses that do not involve breathing include pyrotechnic applications, such as George Goble's five-second ignition of barbecue grills.[106]

Industrial An elderly worker in a helmet is facing his side to the viewer in an industrial hall. The hall is dark but is illuminated yellow glowing splashes of a melted substance. Most commercially produced O 2 is used to smelt and/or decarburize iron. Smelting of iron ore into steel consumes 55% of commercially produced oxygen.[62] In this process, O 2 is injected through a high-pressure lance into molten iron, which removes sulfur impurities and excess carbon as the respective oxides, SO 2 and CO 2. The reactions are exothermic, so the temperature increases to 1,700 °C.[62]

Another 25% of commercially produced oxygen is used by the chemical industry.[62] Ethylene is reacted with O 2 to create ethylene oxide, which, in turn, is converted into ethylene glycol; the primary feeder material used to manufacture a host of products, including antifreeze and polyester polymers (the precursors of many plastics and fabrics).[62]

Most of the remaining 20% of commercially produced oxygen is used in medical applications, metal cutting and welding, as an oxidizer in rocket fuel, and in water treatment.[62] Oxygen is used in oxyacetylene welding burning acetylene with O 2 to produce a very hot flame. In this process, metal up to 60 cm (24 in) thick is first heated with a small oxy-acetylene flame and then quickly cut by a large stream of O 2.[107]

Compounds Main article: Compounds of oxygen Water flowing from a bottle into a glass. Water (H 2O) is the most familiar oxygen compound. The oxidation state of oxygen is −2 in almost all known compounds of oxygen. The oxidation state −1 is found in a few compounds such as peroxides.[108] Compounds containing oxygen in other oxidation states are very uncommon: −1/2 (superoxides), −1/3 (ozonides), 0 (elemental, hypofluorous acid), +1/2 (dioxygenyl), +1 (dioxygen difluoride), and +2 (oxygen difluoride).[109]

Oxides and other inorganic compounds Water (H 2O) is an oxide of hydrogen and the most familiar oxygen compound. Hydrogen atoms are covalently bonded to oxygen in a water molecule but also have an additional attraction (about 23.3 kJ/mol per hydrogen atom) to an adjacent oxygen atom in a separate molecule.[110] These hydrogen bonds between water molecules hold them approximately 15% closer than what would be expected in a simple liquid with just van der Waals forces.[111][i]

A rusty piece of a bolt. Oxides, such as iron oxide or rust, form when oxygen combines with other elements. Due to its electronegativity, oxygen forms chemical bonds with almost all other elements to give corresponding oxides. The surface of most metals, such as aluminium and titanium, are oxidized in the presence of air and become coated with a thin film of oxide that passivates the metal and slows further corrosion. Many oxides of the transition metals are non-stoichiometric compounds, with slightly less metal than the chemical formula would show. For example, the mineral FeO (wüstite) is written as Fe 1 − xO, where x is usually around 0.05.[112]

Oxygen is present in the atmosphere in trace quantities in the form of carbon dioxide (CO 2). The Earth's crustal rock is composed in large part of oxides of silicon (silica SiO 2, as found in granite and quartz), aluminium (aluminium oxide Al 2O 3, in bauxite and corundum), iron (iron(III) oxide Fe 2O 3, in hematite and rust), and calcium carbonate (in limestone). The rest of the Earth's crust is also made of oxygen compounds, in particular various complex silicates (in silicate minerals). The Earth's mantle, of much larger mass than the crust, is largely composed of silicates of magnesium and iron.

Water-soluble silicates in the form of Na 4SiO 4, Na 2SiO 3, and Na 2Si 2O 5 are used as detergents and adhesives.[113]

Oxygen also acts as a ligand for transition metals, forming transition metal dioxygen complexes, which feature metal–O 2. This class of compounds includes the heme proteins hemoglobin and myoglobin.[114] An exotic and unusual reaction occurs with PtF 6, which oxidizes oxygen to give O2+PtF6−, dioxygenyl hexafluoroplatinate.[115]

Organic compounds A ball structure of a molecule. Its backbone is a zig-zag chain of three carbon atoms connected in the center to an oxygen atom and on the end to 6 hydrogens. Acetone is an important feeder material in the chemical industry.

 Oxygen
 Carbon
 Hydrogen

Among the most important classes of organic compounds that contain oxygen are (where "R" is an organic group): alcohols (R-OH); ethers (R-O-R); ketones (R-CO-R); aldehydes (R-CO-H); carboxylic acids (R-COOH); esters (R-COO-R); acid anhydrides (R-CO-O-CO-R); and amides (R-C(O)-NR 2). There are many important organic solvents that contain oxygen, including: acetone, methanol, ethanol, isopropanol, furan, THF, diethyl ether, dioxane, ethyl acetate, DMF, DMSO, acetic acid, and formic acid. Acetone ((CH 3) 2CO) and phenol (C 6H 5OH) are used as feeder materials in the synthesis of many different substances. Other important organic compounds that contain oxygen are: glycerol, formaldehyde, glutaraldehyde, citric acid, acetic anhydride, and acetamide. Epoxides are ethers in which the oxygen atom is part of a ring of three atoms. The element is similarly found in almost all biomolecules that are important to (or generated by) life.

Oxygen reacts spontaneously with many organic compounds at or below room temperature in a process called autoxidation.[116] Most of the organic compounds that contain oxygen are not made by direct action of O 2. Organic compounds important in industry and commerce that are made by direct oxidation of a precursor include ethylene oxide and peracetic acid.[113]

Safety and precautions The NFPA 704 standard rates compressed oxygen gas as nonhazardous to health, nonflammable and nonreactive, but an oxidizer. Refrigerated liquid oxygen (LOX) is given a health hazard rating of 3 (for increased risk of hyperoxia from condensed vapors, and for hazards common to cryogenic liquids such as frostbite), and all other ratings are the same as the compressed gas form.[117]

Toxicity Main article: Oxygen toxicity A diagraph showing a man torso and listing symptoms of oxygen toxicity: Eyes – visual field loss, near)sightedness, cataract formation, bleeding, fibrosis; Head – seizures; Muscles – twitching; Respiratory system – jerky breathing, irritation, coughing, pain, shortness of breath, tracheobronchitis, acute respiratory distress syndrome. Main symptoms of oxygen toxicity[118] Oxygen gas (O 2) can be toxic at elevated partial pressures, leading to convulsions and other health problems.[102][j][119] Oxygen toxicity usually begins to occur at partial pressures more than 50 kilopascals (kPa), equal to about 50% oxygen composition at standard pressure or 2.5 times the normal sea-level O 2 partial pressure of about 21 kPa. This is not a problem except for patients on mechanical ventilators, since gas supplied through oxygen masks in medical applications is typically composed of only 30%–50% O 2 by volume (about 30 kPa at standard pressure).[6]

At one time, premature babies were placed in incubators containing O 2-rich air, but this practice was discontinued after some babies were blinded by the oxygen content being too high.[6]

Breathing pure O 2 in space applications, such as in some modern space suits, or in early spacecraft such as Apollo, causes no damage due to the low total pressures used.[100][120] In the case of spacesuits, the O 2 partial pressure in the breathing gas is, in general, about 30 kPa (1.4 times normal), and the resulting O 2 partial pressure in the astronaut's arterial blood is only marginally more than normal sea-level O 2 partial pressure.[121]

Oxygen toxicity to the lungs and central nervous system can also occur in deep scuba diving and surface supplied diving.[6][102] Prolonged breathing of an air mixture with an O 2 partial pressure more than 60 kPa can eventually lead to permanent pulmonary fibrosis.[122] Exposure to a O 2 partial pressures greater than 160 kPa (about 1.6 atm) may lead to convulsions (normally fatal for divers). Acute oxygen toxicity (causing seizures, its most feared effect for divers) can occur by breathing an air mixture with 21% O 2 at 66 m (217 ft) or more of depth; the same thing can occur by breathing 100% O 2 at only 6 m (20 ft).[122][123][124][125]

Combustion and other hazards The inside of a small spaceship, charred and apparently destroyed. The interior of the Apollo 1 Command Module. Pure O 2 at higher than normal pressure and a spark led to a fire and the loss of the Apollo 1 crew. Highly concentrated sources of oxygen promote rapid combustion. Fire and explosion hazards exist when concentrated oxidants and fuels are brought into close proximity; an ignition event, such as heat or a spark, is needed to trigger combustion.[28][126] Oxygen is the oxidant, not the fuel, but nevertheless the source of most of the chemical energy released in combustion.[28][35]

Concentrated O 2 will allow combustion to proceed rapidly and energetically.[126] Steel pipes and storage vessels used to store and transmit both gaseous and liquid oxygen will act as a fuel; and therefore the design and manufacture of O 2 systems requires special training to ensure that ignition sources are minimized.[126] The fire that killed the Apollo 1 crew in a launch pad test spread so rapidly because the capsule was pressurized with pure O 2 but at slightly more than atmospheric pressure, instead of the ​1⁄3 normal pressure that would be used in a mission.[k][128]

Liquid oxygen spills, if allowed to soak into organic matter, such as wood, petrochemicals, and asphalt can cause these materials to detonate unpredictably on subsequent mechanical impact.[126]

See also Geological history of oxygen Hypoxia (environmental) for O 2 depletion in aquatic ecology Ocean deoxygenation Hypoxia (medical), a lack of oxygen Limiting oxygen concentration Oxygen compounds Oxygen plant Oxygen sensor Books View or order collections of articles OxygenPeriod 2 elementsChalcogensChemical elements (sorted alphabetically)Chemical elements (sorted by number) Portals Access related topics Papapishu-Lab-icon-6.svgChemistry portalWHO Rod.svgMedicine portal Find out more on Wikipedia's Sister projects Media from CommonsDefinitions from WiktionaryTextbooks from WikibooksLearning resources from Wikiversity Notes

These results were mostly ignored until 1860. Part of this rejection was due to the belief that atoms of one element would have no chemical affinity towards atoms of the same element, and part was due to apparent exceptions to Avogadro's law that were not explained until later in terms of dissociating molecules.
An orbital is a concept from quantum mechanics that models an electron as a wave-like particle that has a spatial distribution about an atom or molecule.
Oxygen's paramagnetism can be used analytically in paramagnetic oxygen gas analysers that determine the purity of gaseous oxygen. ("Company literature of Oxygen analyzers (triplet)". Servomex. Archived from the original on March 8, 2008. Retrieved December 15, 2007.)
Figures given are for values up to 50 miles (80 km) above the surface
Thylakoid membranes are part of chloroplasts in algae and plants while they simply are one of many membrane structures in cyanobacteria. In fact, chloroplasts are thought to have evolved from cyanobacteria that were once symbiotic partners with the progenitors of plants and algae.
Water oxidation is catalyzed by a manganese-containing enzyme complex known as the oxygen evolving complex (OEC) or water-splitting complex found associated with the lumenal side of thylakoid membranes. Manganese is an important cofactor, and calcium and chloride are also required for the reaction to occur. (Raven 2005)
(1.8 grams/min/person)×(60 min/h)×(24 h/day)×(365 days/year)×(6.6 billion people)/1,000,000 g/t=6.24 billion tonnes
The reason is that increasing the proportion of oxygen in the breathing gas at low pressure acts to augment the inspired O

2 partial pressure nearer to that found at sea-level.

Also, since oxygen has a higher electronegativity than hydrogen, the charge difference makes it a polar molecule. The interactions between the different dipoles of each molecule cause a net attraction force.
Since O

2's partial pressure is the fraction of O 2 times the total pressure, elevated partial pressures can occur either from high O 2 fraction in breathing gas or from high breathing gas pressure, or a combination of both.

No single ignition source of the fire was conclusively identified, although some evidence points to an arc from an electrical spark.[127]

References

Weast, Robert (1984). CRC, Handbook of Chemistry and Physics. Boca Raton, Florida: Chemical Rubber Company Publishing. pp. E110. ISBN 0-8493-0464-4.
Jastrow, Joseph (1936). Story of Human Error. Ayer Publishing. p. 171. ISBN 978-0-8369-0568-7.
Cook & Lauer 1968, p.499.
Wikisource Chisholm, Hugh, ed. (1911). "Mayow, John" . Encyclopædia Britannica. 17 (11th ed.). Cambridge University Press. pp. 938–939.
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General references Cook, Gerhard A.; Lauer, Carol M. (1968). "Oxygen". In Clifford A. Hampel. The Encyclopedia of the Chemical Elements. New York: Reinhold Book Corporation. pp. 499–512. LCCN 68-29938. Emsley, John (2001). "Oxygen". Nature's Building Blocks: An A-Z Guide to the Elements. Oxford, England: Oxford University Press. pp. 297–304. ISBN 978-0-19-850340-8. Raven, Peter H.; Evert, Ray F.; Eichhorn, Susan E. (2005). Biology of Plants (7th ed.). New York: W.H. Freeman and Company Publishers. pp. 115–27. ISBN 978-0-7167-1007-3. External links Listen to this article (info/dl) MENU0:00

This audio file was created from a revision of the article "Oxygen" dated 2008-06-23, and does not reflect subsequent edits to the article. (Audio help) More spoken articles Oxygen at The Periodic Table of Videos (University of Nottingham) Oxidizing Agents > Oxygen Oxygen (O2) Properties, Uses, Applications Roald Hoffmann article on "The Story of O" WebElements.com – Oxygen Oxygen on In Our Time at the BBC Scripps Institute: Atmospheric Oxygen has been dropping for 20 years vte Periodic table (Large cells) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 H He 2 Li Be B C N O F Ne 3 Na Mg Al Si P S Cl Ar 4 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 5 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 6 Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 7 Fr Ra Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og Alkali metal Alkaline earth metal Lan­thanide Actinide Transition metal Post-​transition metal Metalloid Reactive nonmetal Noble gas Unknown chemical properties vte Diatomic chemical elements Authority control Edit this at Wikidata BNE: XX534245 BNF: cb11977353d (data) GND: 4051803-6 LCCN: sh85096329 NDL: 00570181 Categories: Spoken articlesOxygenChemical elementsChalcogensDiatomic nonmetalsOxidizing agentsBiology and pharmacology of chemical elementsBreathing gasesChemical substances for emergency medicineE-number additives Navigation menu Not logged inTalkContributionsCreate accountLog inArticleTalkReadView sourceView historySearch

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Languages Bân-lâm-gú 贛語 客家語/Hak-kâ-ngî Монгол ئۇيغۇرچە / Uyghurche Vahcuengh 吴语 粵語 中文 177 more Edit links This page was last edited on 22 February 2019, at 07:32 (UTC). Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Privacy policyAbout WikipediaDisclaimersContact WikipediaDevelopersCookie statementMobile view Page semi-protected Energy From Wikipedia, the free encyclopedia Jump to navigationJump to search This article is about the scalar physical quantity. For an overview of and topical guide to energy, see Outline of energy. For other uses, see Energy (disambiguation). "Energetic" redirects here. For other uses, see Energetic (disambiguation). Energy Sun in February (black version).jpg The Sun is the source of energy for most of life on Earth. As a star, the Sun is heated to high temperatures by the conversion of nuclear binding energy due to the fusion of hydrogen in its core. This energy is ultimately transferred (released) into space mainly in the form of radiant (light) energy. Common symbols E SI unit joule Other units erg, calorie, kcal, BTU, kW⋅h, eV In SI base units J = kg m2 s−2 Extensive? yes Conserved? yes Dimension M L2 T−2 In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.[note 1] Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.

Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature.

Mass and energy are closely related. Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.

Living organisms require available energy to stay alive, such as the energy humans get from food. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy. The processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth.

Contents 1 Forms 2 History 3 Units of measure 4 Scientific use 4.1 Classical mechanics 4.2 Chemistry 4.3 Biology 4.4 Earth sciences 4.5 Cosmology 4.6 Quantum mechanics 4.7 Relativity 5 Transformation 5.1 Conservation of energy and mass in transformation 5.2 Reversible and non-reversible transformations 6 Conservation of energy 7 Energy transfer 7.1 Closed systems 7.2 Open systems 8 Thermodynamics 8.1 Internal energy 8.2 First law of thermodynamics 8.3 Equipartition of energy 9 See also 10 Notes 11 References 12 Further reading 12.1 Journals 13 External links Forms

This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Energy" – news · newspapers · books · scholar · JSTOR (September 2016) (Learn how and when to remove this template message)

In a typical lightning strike, 500 megajoules of electric potential energy is converted into the same amount of energy in other forms, mostly light energy, sound energy and thermal energy.

Thermal energy is energy of microscopic constituents of matter, which may include both kinetic and potential energy. The total energy of a system can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways. Kinetic energy is determined by the movement of an object – or the composite motion of the components of an object – and potential energy reflects the potential of an object to have motion, and generally is a function of the position of an object within a field or may be stored in the field itself.

While these two categories are sufficient to describe all forms of energy, it is often convenient to refer to particular combinations of potential and kinetic energy as its own form. For example, macroscopic mechanical energy is the sum of translational and rotational kinetic and potential energy in a system neglects the kinetic energy due to temperature, and nuclear energy which combines utilize potentials from the nuclear force and the weak force), among others.[citation needed]

Some forms of energy (that an object or system can have as a measurable property) Type of energy Description Mechanical the sum of macroscopic translational and rotational kinetic and potential energies Electric potential energy due to or stored in electric fields Magnetic potential energy due to or stored in magnetic fields Gravitational potential energy due to or stored in gravitational fields Chemical potential energy due to chemical bonds Ionization potential energy that binds an electron to its atom or molecule Nuclear potential energy that binds nucleons to form the atomic nucleus (and nuclear reactions) Chromodynamic potential energy that binds quarks to form hadrons Elastic potential energy due to the deformation of a material (or its container) exhibiting a restorative force Mechanical wave kinetic and potential energy in an elastic material due to a propagated deformational wave Sound wave kinetic and potential energy in a fluid due to a sound propagated wave (a particular form of mechanical wave) Radiant potential energy stored in the fields of propagated by electromagnetic radiation, including light Rest potential energy due to an object's rest mass Thermal kinetic energy of the microscopic motion of particles, a form of disordered equivalent of mechanical energy History Main articles: History of energy and timeline of thermodynamics, statistical mechanics, and random processes

Thomas Young – the first to use the term "energy" in the modern sense. The word energy derives from the Ancient Greek: ἐνέργεια, translit. energeia, lit. 'activity, operation',[1] which possibly appears for the first time in the work of Aristotle in the 4th century BC. In contrast to the modern definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness and pleasure.

In the late 17th century, Gottfried Leibniz proposed the idea of the Latin: vis viva, or living force, which defined as the product of the mass of an object and its velocity squared; he believed that total vis viva was conserved. To account for slowing due to friction, Leibniz theorized that thermal energy consisted of the random motion of the constituent parts of matter, although it would be more than a century until this was generally accepted. The modern analog of this property, kinetic energy, differs from vis viva only by a factor of two.

In 1807, Thomas Young was possibly the first to use the term "energy" instead of vis viva, in its modern sense.[2] Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, and in 1853, William Rankine coined the term "potential energy". The law of conservation of energy was also first postulated in the early 19th century, and applies to any isolated system. It was argued for some years whether heat was a physical substance, dubbed the caloric, or merely a physical quantity, such as momentum. In 1845 James Prescott Joule discovered the link between mechanical work and the generation of heat.

These developments led to the theory of conservation of energy, formalized largely by William Thomson (Lord Kelvin) as the field of thermodynamics. Thermodynamics aided the rapid development of explanations of chemical processes by Rudolf Clausius, Josiah Willard Gibbs, and Walther Nernst. It also led to a mathematical formulation of the concept of entropy by Clausius and to the introduction of laws of radiant energy by Jožef Stefan. According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.[3] Thus, since 1918, theorists have understood that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time.

Units of measure

Joule's apparatus for measuring the mechanical equivalent of heat. A descending weight attached to a string causes a paddle immersed in water to rotate. Main article: Units of energy In 1843, James Prescott Joule independently discovered the mechanical equivalent in a series of experiments. The most famous of them used the "Joule apparatus": a descending weight, attached to a string, caused rotation of a paddle immersed in water, practically insulated from heat transfer. It showed that the gravitational potential energy lost by the weight in descending was equal to the internal energy gained by the water through friction with the paddle.

In the International System of Units (SI), the unit of energy is the joule, named after James Prescott Joule. It is a derived unit. It is equal to the energy expended (or work done) in applying a force of one newton through a distance of one metre. However energy is also expressed in many other units not part of the SI, such as ergs, calories, British Thermal Units, kilowatt-hours and kilocalories, which require a conversion factor when expressed in SI units.

The SI unit of energy rate (energy per unit time) is the watt, which is a joule per second. Thus, one joule is one watt-second, and 3600 joules equal one watt-hour. The CGS energy unit is the erg and the imperial and US customary unit is the foot pound. Other energy units such as the electronvolt, food calorie or thermodynamic kcal (based on the temperature change of water in a heating process), and BTU are used in specific areas of science and commerce.

Scientific use Classical mechanics Part of a series of articles about Classical mechanics {{\vec {F}}=m{\vec {a}}} {\vec {F}}=m{\vec {a}} Second law of motion History Timeline Branches[show] Fundamentals[show] Formulations[show] Core topics[show] Rotation[show] Scientists[show] vte Main articles: Mechanics, Mechanical work, and Thermodynamics In classical mechanics, energy is a conceptually and mathematically useful property, as it is a conserved quantity. Several formulations of mechanics have been developed using energy as a core concept.

Work, a function of energy, is force times distance.

{W=\int _{C}\mathbf {F} \cdot \mathrm {d} \mathbf {s} } W=\int _{C}\mathbf {F} \cdot \mathrm {d} \mathbf {s} This says that the work ( {W} W) is equal to the line integral of the force F along a path C; for details see the mechanical work article. Work and thus energy is frame dependent. For example, consider a ball being hit by a bat. In the center-of-mass reference frame, the bat does no work on the ball. But, in the reference frame of the person swinging the bat, considerable work is done on the ball.

The total energy of a system is sometimes called the Hamiltonian, after William Rowan Hamilton. The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems. These classical equations have remarkably direct analogs in nonrelativistic quantum mechanics.[4]

Another energy-related concept is called the Lagrangian, after Joseph-Louis Lagrange. This formalism is as fundamental as the Hamiltonian, and both can be used to derive the equations of motion or be derived from them. It was invented in the context of classical mechanics, but is generally useful in modern physics. The Lagrangian is defined as the kinetic energy minus the potential energy. Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (such as systems with friction).

Noether's theorem (1918) states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalisation of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian; for example, dissipative systems with continuous symmetries need not have a corresponding conservation law.

Chemistry In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is invariably accompanied by an increase or decrease of energy of the substances involved. Some energy is transferred between the surroundings and the reactants of the reaction in the form of heat or light; thus the products of a reaction may have more or less energy than the reactants. A reaction is said to be exergonic if the final state is lower on the energy scale than the initial state; in the case of endergonic reactions the situation is the reverse. Chemical reactions are invariably not possible unless the reactants surmount an energy barrier known as the activation energy. The speed of a chemical reaction (at given temperature T) is related to the activation energy E, by the Boltzmann's population factor e−E/kT – that is the probability of molecule to have energy greater than or equal to E at the given temperature T. This exponential dependence of a reaction rate on temperature is known as the Arrhenius equation.The activation energy necessary for a chemical reaction can be in the form of thermal energy.

Biology Main articles: Bioenergetics and Food energy

Basic overview of energy and human life. In biology, energy is an attribute of all biological systems from the biosphere to the smallest living organism. Within an organism it is responsible for growth and development of a biological cell or an organelle of a biological organism. Energy is thus often said to be stored by cells in the structures of molecules of substances such as carbohydrates (including sugars), lipids, and proteins, which release energy when reacted with oxygen in respiration. In human terms, the human equivalent (H-e) (Human energy conversion) indicates, for a given amount of energy expenditure, the relative quantity of energy needed for human metabolism, assuming an average human energy expenditure of 12,500 kJ per day and a basal metabolic rate of 80 watts. For example, if our bodies run (on average) at 80 watts, then a light bulb running at 100 watts is running at 1.25 human equivalents (100 ÷ 80) i.e. 1.25 H-e. For a difficult task of only a few seconds' duration, a person can put out thousands of watts, many times the 746 watts in one official horsepower. For tasks lasting a few minutes, a fit human can generate perhaps 1,000 watts. For an activity that must be sustained for an hour, output drops to around 300; for an activity kept up all day, 150 watts is about the maximum.[5] The human equivalent assists understanding of energy flows in physical and biological systems by expressing energy units in human terms: it provides a "feel" for the use of a given amount of energy.[6]

Sunlight's radiant energy is also captured by plants as chemical potential energy in photosynthesis, when carbon dioxide and water (two low-energy compounds) are converted into the high-energy compounds carbohydrates, lipids, and proteins. Plants also release oxygen during photosynthesis, which is utilized by living organisms as an electron acceptor, to release the energy of carbohydrates, lipids, and proteins. Release of the energy stored during photosynthesis as heat or light may be triggered suddenly by a spark, in a forest fire, or it may be made available more slowly for animal or human metabolism, when these molecules are ingested, and catabolism is triggered by enzyme action.

Any living organism relies on an external source of energy – radiant energy from the Sun in the case of green plants, chemical energy in some form in the case of animals – to be able to grow and reproduce. The daily 1500–2000 Calories (6–8 MJ) recommended for a human adult are taken as a combination of oxygen and food molecules, the latter mostly carbohydrates and fats, of which glucose (C6H12O6) and stearin (C57H110O6) are convenient examples. The food molecules are oxidised to carbon dioxide and water in the mitochondria

{{\ce {C6H12O6 + 6O2 -> 6CO2 + 6H2O}}} {{\ce {C6H12O6 + 6O2 -> 6CO2 + 6H2O}}} C57H110O6 + 81.5O2 → 57CO2 + 55H2O and some of the energy is used to convert ADP into ATP.

ADP + HPO42− → ATP + H2O The rest of the chemical energy in O2[7] and the carbohydrate or fat is converted into heat: the ATP is used as a sort of "energy currency", and some of the chemical energy it contains is used for other metabolism when ATP reacts with OH groups and eventually splits into ADP and phosphate (at each stage of a metabolic pathway, some chemical energy is converted into heat). Only a tiny fraction of the original chemical energy is used for work:[note 2]

gain in kinetic energy of a sprinter during a 100 m race: 4 kJ gain in gravitational potential energy of a 150 kg weight lifted through 2 metres: 3 kJ Daily food intake of a normal adult: 6–8 MJ It would appear that living organisms are remarkably inefficient (in the physical sense) in their use of the energy they receive (chemical or radiant energy), and it is true that most real machines manage higher efficiencies. In growing organisms the energy that is converted to heat serves a vital purpose, as it allows the organism tissue to be highly ordered with regard to the molecules it is built from. The second law of thermodynamics states that energy (and matter) tends to become more evenly spread out across the universe: to concentrate energy (or matter) in one specific place, it is necessary to spread out a greater amount of energy (as heat) across the remainder of the universe ("the surroundings").[note 3] Simpler organisms can achieve higher energy efficiencies than more complex ones, but the complex organisms can occupy ecological niches that are not available to their simpler brethren. The conversion of a portion of the chemical energy to heat at each step in a metabolic pathway is the physical reason behind the pyramid of biomass observed in ecology: to take just the first step in the food chain, of the estimated 124.7 Pg/a of carbon that is fixed by photosynthesis, 64.3 Pg/a (52%) are used for the metabolism of green plants,[8] i.e. reconverted into carbon dioxide and heat.

Earth sciences In geology, continental drift, mountain ranges, volcanoes, and earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior,[9] while meteorological phenomena like wind, rain, hail, snow, lightning, tornadoes and hurricanes are all a result of energy transformations brought about by solar energy on the atmosphere of the planet Earth.

Sunlight may be stored as gravitational potential energy after it strikes the Earth, as (for example) water evaporates from oceans and is deposited upon mountains (where, after being released at a hydroelectric dam, it can be used to drive turbines or generators to produce electricity). Sunlight also drives many weather phenomena, save those generated by volcanic events. An example of a solar-mediated weather event is a hurricane, which occurs when large unstable areas of warm ocean, heated over months, give up some of their thermal energy suddenly to power a few days of violent air movement.

In a slower process, radioactive decay of atoms in the core of the Earth releases heat. This thermal energy drives plate tectonics and may lift mountains, via orogenesis. This slow lifting represents a kind of gravitational potential energy storage of the thermal energy, which may be later released to active kinetic energy in landslides, after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a store that has been produced ultimately from the same radioactive heat sources. Thus, according to present understanding, familiar events such as landslides and earthquakes release energy that has been stored as potential energy in the Earth's gravitational field or elastic strain (mechanical potential energy) in rocks. Prior to this, they represent release of energy that has been stored in heavy atoms since the collapse of long-destroyed supernova stars created these atoms.

Cosmology In cosmology and astronomy the phenomena of stars, nova, supernova, quasars and gamma-ray bursts are the universe's highest-output energy transformations of matter. All stellar phenomena (including solar activity) are driven by various kinds of energy transformations. Energy in such transformations is either from gravitational collapse of matter (usually molecular hydrogen) into various classes of astronomical objects (stars, black holes, etc.), or from nuclear fusion (of lighter elements, primarily hydrogen). The nuclear fusion of hydrogen in the Sun also releases another store of potential energy which was created at the time of the Big Bang. At that time, according to theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements. This meant that hydrogen represents a store of potential energy that can be released by fusion. Such a fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into sunlight.

Quantum mechanics Main article: Energy operator In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: {E=h\nu } E=h\nu (where {h} h is Planck's constant and {\nu } \nu the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.

Relativity When calculating kinetic energy (work to accelerate a massive body from zero speed to some finite speed) relativistically – using Lorentz transformations instead of Newtonian mechanics – Einstein discovered an unexpected by-product of these calculations to be an energy term which does not vanish at zero speed. He called it rest energy: energy which every massive body must possess even when being at rest. The amount of energy is directly proportional to the mass of the body:

{E_{0}=mc^{2}} {E_{0}=mc^{2}}, where

m is the mass of the body, c is the speed of light in vacuum, {E_{0}} E_{0} is the rest energy. For example, consider electron–positron annihilation, in which the rest energy of these two individual particles (equivalent to their rest mass) is converted to the radiant energy of the photons produced in the process. In this system the matter and antimatter (electrons and positrons) are destroyed and changed to non-matter (the photons). However, the total mass and total energy do not change during this interaction. The photons each have no rest mass but nonetheless have radiant energy which exhibits the same inertia as did the two original particles. This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from the radiant energy of two (or more) annihilating photons.

In general relativity, the stress–energy tensor serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation.[10]

Energy and mass are manifestations of one and the same underlying physical property of a system. This property is responsible for the inertia and strength of gravitational interaction of the system ("mass manifestations"), and is also responsible for the potential ability of the system to perform work or heating ("energy manifestations"), subject to the limitations of other physical laws.

In classical physics, energy is a scalar quantity, the canonical conjugate to time. In special relativity energy is also a scalar (although not a Lorentz scalar but a time component of the energy–momentum 4-vector).[10] In other words, energy is invariant with respect to rotations of space, but not invariant with respect to rotations of space-time (= boosts).

Transformation Main article: Energy transformation

Some forms of transfer of energy ("energy in transit") from one object or system to another Type of transfer process Description Heat that amount of thermal energy in transit spontaneously towards a lower-temperature object Work that amount of energy in transit due to a displacement in the direction of an applied force Transfer of material that amount of energy carried by matter that is moving from one system to another

A turbo generator transforms the energy of pressurised steam into electrical energy Energy may be transformed between different forms at various efficiencies. Items that transform between these forms are called transducers. Examples of transducers include a battery, from chemical energy to electric energy; a dam: gravitational potential energy to kinetic energy of moving water (and the blades of a turbine) and ultimately to electric energy through an electric generator; or a heat engine, from heat to work.

Examples of energy transformation include generating electric energy from heat energy via a steam turbine, or lifting an object against gravity using electrical energy driving a crane motor. Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object. If the object falls to the ground, gravity does mechanical work on the object which transforms the potential energy in the gravitational field to the kinetic energy released as heat on impact with the ground. Our Sun transforms nuclear potential energy to other forms of energy; its total mass does not decrease due to that in itself (since it still contains the same total energy even if in different forms), but its mass does decrease when the energy escapes out to its surroundings, largely as radiant energy.

There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

Energy is also transferred from potential energy ( {E_{p}} E_{p}) to kinetic energy ( {E_{k}} E_{k}) and then back to potential energy constantly. This is referred to as conservation of energy. In this closed system, energy cannot be created or destroyed; therefore, the initial energy and the final energy will be equal to each other. This can be demonstrated by the following:

{E_{pi}+E_{ki}=E_{pF}+E_{kF}} E_{pi}+E_{ki}=E_{pF}+E_{kF}

(4)

The equation can then be simplified further since {E_{p}=mgh} E_{p}=mgh (mass times acceleration due to gravity times the height) and {E_{k}={\frac {1}{2}}mv^{2}} E_{k}={\frac {1}{2}}mv^{2} (half mass times velocity squared). Then the total amount of energy can be found by adding {E_{p}+E_{k}=E_{total}} E_{p}+E_{k}=E_{total}.

Conservation of energy and mass in transformation Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J.J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Part of the rest energy (equivalent to rest mass) of matter may be converted to other forms of energy (still exhibiting mass), but neither energy nor mass can be destroyed; rather, both remain constant during any process. However, since {c^{2}} c^{2} is extremely large relative to ordinary human scales, the conversion of an everyday amount of rest mass (for example, 1 kg) from rest energy to other forms of energy (such as kinetic energy, thermal energy, or the radiant energy carried by light and other radiation) can liberate tremendous amounts of energy (~ {9\times 10^{16}} 9\times 10^{16} joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of an everyday amount energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure on a weighing scale, unless the energy loss is very large. Examples of large transformations between rest energy (of matter) and other forms of energy (e.g., kinetic energy into particles with rest mass) are found in nuclear physics and particle physics.

Reversible and non-reversible transformations Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).

As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.

Conservation of energy Main article: Conservation of energy The fact that energy can be neither created nor be destroyed is called the law of conservation of energy. In the form of the first law of thermodynamics, this states that a closed system's energy is constant unless energy is transferred in or out by work or heat, and that no energy is lost in transfer. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.[11]

While heat can always be fully converted into work in a reversible isothermal expansion of an ideal gas, for cyclic processes of practical interest in heat engines the second law of thermodynamics states that the system doing work always loses some energy as waste heat. This creates a limit to the amount of heat energy that can do work in a cyclic process, a limit called the available energy. Mechanical and other forms of energy can be transformed in the other direction into thermal energy without such limitations.[12] The total energy of a system can be calculated by adding up all forms of energy in the system.

Richard Feynman said during a 1961 lecture:[13]

There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law – it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

— The Feynman Lectures on Physics Most kinds of energy (with gravitational energy being a notable exception)[14] are subject to strict local conservation laws as well. In this case, energy can only be exchanged between adjacent regions of space, and all observers agree as to the volumetric density of energy in any given space. There is also a global law of conservation of energy, stating that the total energy of the universe cannot change; this is a corollary of the local law, but not vice versa.[12][13]

This law is a fundamental principle of physics. As shown rigorously by Noether's theorem, the conservation of energy is a mathematical consequence of translational symmetry of time,[15] a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.

Each of the basic forces of nature is associated with a different type of potential energy, and all types of potential energy (like all other types of energy) appears as system mass, whenever present. For example, a compressed spring will be slightly more massive than before it was compressed. Likewise, whenever energy is transferred between systems by any mechanism, an associated mass is transferred with it.

In quantum mechanics energy is expressed using the Hamiltonian operator. On any time scales, the uncertainty in the energy is by

{\Delta E\Delta t\geq {\frac {\hbar }{2}}} \Delta E\Delta t\geq {\frac {\hbar }{2}} which is similar in form to the Heisenberg Uncertainty Principle (but not really mathematically equivalent thereto, since H and t are not dynamically conjugate variables, neither in classical nor in quantum mechanics).

In particle physics, this inequality permits a qualitative understanding of virtual particles which carry momentum, exchange by which and with real particles, is responsible for the creation of all known fundamental forces (more accurately known as fundamental interactions). Virtual photons (which are simply lowest quantum mechanical energy state of photons) are also responsible for electrostatic interaction between electric charges (which results in Coulomb law), for spontaneous radiative decay of exited atomic and nuclear states, for the Casimir force, for van der Waals bond forces and some other observable phenomena.

Energy transfer Closed systems Energy transfer can be considered for the special case of systems which are closed to transfers of matter. The portion of the energy which is transferred by conservative forces over a distance is measured as the work the source system does on the receiving system. The portion of the energy which does not do work during the transfer is called heat.[note 4] Energy can be transferred between systems in a variety of ways. Examples include the transmission of electromagnetic energy via photons, physical collisions which transfer kinetic energy,[note 5] and the conductive transfer of thermal energy.

Energy is strictly conserved and is also locally conserved wherever it can be defined. In thermodynamics, for closed systems, the process of energy transfer is described by the first law:[note 6]

{\Delta {}E=W+Q} \Delta {}E=W+Q

(1)

where {E} E is the amount of energy transferred, {W} W represents the work done on the system, and {Q} Q represents the heat flow into the system. As a simplification, the heat term, {Q} Q, is sometimes ignored, especially when the thermal efficiency of the transfer is high.

{\Delta {}E=W} \Delta {}E=W

(2)

This simplified equation is the one used to define the joule, for example.

Open systems Beyond the constraints of closed systems, open systems can gain or lose energy in association with matter transfer (both of these process are illustrated by fueling an auto, a system which gains in energy thereby, without addition of either work or heat). Denoting this energy by {E} E, one may write

{\Delta {}E=W+Q+E.} \Delta {}E=W+Q+E.

(3)

Thermodynamics Internal energy Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to create the system. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometric aspects, as well as the motion of the particles, in form of kinetic energy. Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value, which is impossible to determine with thermodynamics alone.[16]

First law of thermodynamics The first law of thermodynamics asserts that energy (but not necessarily thermodynamic free energy) is always conserved[17] and that heat flow is a form of energy transfer. For homogeneous systems, with a well-defined temperature and pressure, a commonly used corollary of the first law is that, for a system subject only to pressure forces and heat transfer (e.g., a cylinder-full of gas) without chemical changes, the differential change in the internal energy of the system (with a gain in energy signified by a positive quantity) is given as

{\mathrm {d} E=T\mathrm {d} S-P\mathrm {d} V\,} \mathrm {d} E=T\mathrm {d} S-P\mathrm {d} V\,, where the first term on the right is the heat transferred into the system, expressed in terms of temperature T and entropy S (in which entropy increases and the change dS is positive when the system is heated), and the last term on the right hand side is identified as work done on the system, where pressure is P and volume V (the negative sign results since compression of the system requires work to be done on it and so the volume change, dV, is negative when work is done on the system).

This equation is highly specific, ignoring all chemical, electrical, nuclear, and gravitational forces, effects such as advection of any form of energy other than heat and pV-work. The general formulation of the first law (i.e., conservation of energy) is valid even in situations in which the system is not homogeneous. For these cases the change in internal energy of a closed system is expressed in a general form by

{\mathrm {d} E=\delta Q+\delta W} \mathrm {d} E=\delta Q+\delta W where {\delta Q} \delta Q is the heat supplied to the system and {\delta W} \delta W is the work applied to the system.

Equipartition of energy The energy of a mechanical harmonic oscillator (a mass on a spring) is alternatively kinetic and potential. At two points in the oscillation cycle it is entirely kinetic, and at two points it is entirely potential. Over the whole cycle, or over many cycles, net energy is thus equally split between kinetic and potential. This is called equipartition principle; total energy of a system with many degrees of freedom is equally split among all available degrees of freedom.

This principle is vitally important to understanding the behaviour of a quantity closely related to energy, called entropy. Entropy is a measure of evenness of a distribution of energy between parts of a system. When an isolated system is given more degrees of freedom (i.e., given new available energy states that are the same as existing states), then total energy spreads over all available degrees equally without distinction between "new" and "old" degrees. This mathematical result is called the second law of thermodynamics. The second law of thermodynamics is valid only for systems which are near or in equilibrium state. For non-equilibrium systems, the laws governing system's behavior are still debatable. One of the guiding principles for these systems is the principle of maximum entropy production.[18][19] It states that nonequilibrium systems behave in such a way to maximize its entropy production.[20]

See also

Book: Energy icon Energy portal icon Physics portal Combustion Index of energy articles Index of wave articles Mattergy Orders of magnitude (energy) Power station Transfer energy Notes

The second law of thermodynamics imposes limitations on the capacity of a system to transfer energy by performing work, since some of the system's energy might necessarily be consumed in the form of heat instead. See e.g. Lehrman, Robert L. (1973). "Energy Is Not The Ability To Do Work". The Physics Teacher. 11 (1): 15–18. Bibcode:1973PhTea..11...15L. doi:10.1119/1.2349846. ISSN 0031-921X.
These examples are solely for illustration, as it is not the energy available for work which limits the performance of the athlete but the power output of the sprinter and the force of the weightlifter. A worker stacking shelves in a supermarket does more work (in the physical sense) than either of the athletes, but does it more slowly.
Crystals are another example of highly ordered systems that exist in nature: in this case too, the order is associated with the transfer of a large amount of heat (known as the lattice energy) to the surroundings.
Although heat is "wasted" energy for a specific energy transfer,(see: waste heat) it can often be harnessed to do useful work in subsequent interactions. However, the maximum energy that can be "recycled" from such recovery processes is limited by the second law of thermodynamics.
The mechanism for most macroscopic physical collisions is actually electromagnetic, but it is very common to simplify the interaction by ignoring the mechanism of collision and just calculate the beginning and end result.
There are several sign conventions for this equation. Here, the signs in this equation follow the IUPAC convention.

References

Harper, Douglas. "Energy". Online Etymology Dictionary. Archived from the original on October 11, 2007. Retrieved May 1, 2007.
Smith, Crosbie (1998). The Science of Energy – a Cultural History of Energy Physics in Victorian Britain. The University of Chicago Press. ISBN 978-0-226-76420-7.
Lofts, G; O'Keeffe D; et al. (2004). "11 – Mechanical Interactions". Jacaranda Physics 1 (2 ed.). Milton, Queensland, Australia: John Willey & Sons Australia Ltd. p. 286. ISBN 978-0-7016-3777-4.
The Hamiltonian MIT OpenCourseWare website 18.013A Chapter 16.3 Accessed February 2007
"Retrieved on May-29-09". Uic.edu. Archived from the original on 2010-06-04. Retrieved 2010-12-12.
Bicycle calculator – speed, weight, wattage etc. "Bike Calculator". Archived from the original on 2009-05-13. Retrieved 2009-05-29..
Schmidt-Rohr, K (2015). "Why Combustions Are Always Exothermic, Yielding About 418 kJ per Mole of O2". J. Chem. Educ. 92 (12): 2094–2099. Bibcode:2015JChEd..92.2094S. doi:10.1021/acs.jchemed.5b00333.
Ito, Akihito; Oikawa, Takehisa (2004). "Global Mapping of Terrestrial Primary Productivity and Light-Use Efficiency with a Process-Based Model. Archived 2006-10-02 at the Wayback Machine" in Shiyomi, M. et al. (Eds.) Global Environmental Change in the Ocean and on Land. pp. 343–58.
"Earth's Energy Budget". Okfirst.ocs.ou.edu. Archived from the original on 2008-08-27. Retrieved 2010-12-12.
Misner, Thorne, Wheeler (1973). Gravitation. San Francisco: W.H. Freeman. ISBN 978-0-7167-0344-0.
Berkeley Physics Course Volume 1. Charles Kittel, Walter D Knight and Malvin A Ruderman
The Laws of Thermodynamics Archived 2006-12-15 at the Wayback Machine including careful definitions of energy, free energy, et cetera.
Feynman, Richard (1964). The Feynman Lectures on Physics; Volume 1. U.S.A: Addison Wesley. ISBN 978-0-201-02115-8.
"E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws". Physics.ucla.edu. 1918-07-16. Archived from the original on 2011-05-14. Retrieved 2010-12-12.
"Time Invariance". Ptolemy.eecs.berkeley.edu. Archived from the original on 2011-07-17. Retrieved 2010-12-12.
I. Klotz, R. Rosenberg, Chemical Thermodynamics - Basic Concepts and Methods, 7th ed., Wiley (2008), p.39
Kittel and Kroemer (1980). Thermal Physics. New York: W.H. Freeman. ISBN 978-0-7167-1088-2.
Onsager, L. (1931). "Reciprocal relations in irreversible processes". Phys. Rev. 37 (4): 405–26. Bibcode:1931PhRv...37..405O. doi:10.1103/PhysRev.37.405.
Martyushev, L.M.; Seleznev, V.D. (2006). "Maximum entropy production principle in physics, chemistry and biology". Phys. Rev. 426 (1): 1–45. Bibcode:2006PhR...426....1M. doi:10.1016/j.physrep.2005.12.001.
Belkin, A.; et., al. (2015). "Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production". Sci. Rep. 5: 8323. Bibcode:2015NatSR...5E8323B. doi:10.1038/srep08323. PMC 4321171. PMID 25662746.

Further reading Alekseev, G.N. (1986). Energy and Entropy. Moscow: Mir Publishers. The Biosphere (A Scientific American Book), San Francisco, W.H. Freeman and Co., 1970, ISBN 0-7167-0945-7. This book, originally a 1970 Scientific American issue, covers virtually every major concern and concept since debated regarding materials and energy resources, population trends, and environmental degradation. Crowell, Benjamin (2011), "ch. 11", Light and Matter, Fullerton, California: Light and Matter Energy and Power (A Scientific American Book), San Francisco, W.H. Freeman and Co., 1971, ISBN 0-7167-0938-4. Ross, John S. (23 April 2002). "Work, Power, Kinetic Energy" (PDF). Project PHYSNET. Michigan State University. Santos, Gildo M. "Energy in Brazil: a historical overview," The Journal of Energy History (2018) $1 online Smil, Vaclav (2008). Energy in nature and society: general energetics of complex systems. Cambridge, US: MIT Press. ISBN 978-0-262-19565-2. Walding, Richard; Rapkins, Greg; Rossiter, Glenn (1999). New Century Senior Physics. Melbourne, Australia: Oxford University Press. ISBN 978-0-19-551084-3. Journals The Journal of Energy History / Revue d'histoire de l'énergie (JEHRHE), 2018-

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The Universe represented as multiple disk-shaped slices across time, which passes from left to right. Science (from the Latin word scientia, meaning "knowledge")[1] is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.[2][a]

The earliest roots of science can be traced to Ancient Egypt and Mesopotamia in around 3500 to 3000 BCE.[3][4] Their contributions to mathematics, astronomy, and medicine entered and shaped Greek natural philosophy of classical antiquity, whereby formal attempts were made to explain events of the physical world based on natural causes.[3][4] After the fall of the Western Roman Empire, knowledge of Greek conceptions of the world deteriorated in Western Europe during the early centuries (400 to 1000 CE) of the Middle Ages[5] but was preserved in the Muslim world during the Islamic Golden Age.[6] The recovery and assimilation of Greek works and Islamic inquiries into Western Europe from the 10th to 13th century revived natural philosophy,[5][7] which was later transformed by the Scientific Revolution that began in the 16th century[8] as new ideas and discoveries departed from previous Greek conceptions and traditions.[9][10][11][12] The scientific method soon played a greater role in knowledge creation and it was not until the 19th century that many of the institutional and professional features of science began to take shape.[13][14][15]

Modern science is typically divided into three major branches that consist of the natural sciences (e.g., biology, chemistry, and physics), which study nature in the broadest sense; the social sciences (e.g., economics, psychology, and sociology), which study individuals and societies; and the formal sciences (e.g., logic, mathematics, and theoretical computer science), which study abstract concepts. There is disagreement,[16][17] however, on whether the formal sciences actually constitute a science as they do not rely on empirical evidence.[18] Disciplines that use existing scientific knowledge for practical purposes, such as engineering and medicine, are described as applied sciences.[19][20][21][22]

Science is based on research, which is commonly conducted in academic and research institutions as well as in government agencies and companies. The practical impact of scientific research has led to the emergence of science policies that seek to influence the scientific enterprise by prioritizing the development of commercial products, armaments, health care, and environmental protection.

Contents 1 History 1.1 Early cultures 1.2 Classical antiquity 1.3 Medieval science 1.4 Renaissance and early modern science 1.5 Age of Enlightenment 1.6 19th century 1.7 20th century 1.8 21st century 2 Branches of science 2.1 Natural science 2.2 Social science 2.3 Formal science 3 Scientific research 3.1 Scientific method 3.1.1 Role of mathematics 3.1.2 Verifiability 3.2 Philosophy of science 3.2.1 Certainty and science 3.2.2 Fringe science, pseudoscience, and junk science 3.3 Scientific literature 3.4 Practical impacts 4 Scientific community 4.1 Scientists 4.1.1 Women in science 4.2 Learned societies 5 Science and the public 5.1 Science policy 5.1.1 Funding of science 5.2 Public awareness of science 5.3 Science journalism 5.4 Politicization of science 6 See also 7 Notes 8 References 9 Sources 10 Further reading 11 External links History Main article: History of science Science in a broad sense existed before the modern era and in many historical civilizations.[23] Modern science is distinct in its approach and successful in its results, so it now defines what science is in the strictest sense of the term.[24][b] Science in its original sense was a word for a type of knowledge, rather than a specialized word for the pursuit of such knowledge. In particular, it was the type of knowledge which people can communicate to each other and share. For example, knowledge about the working of natural things was gathered long before recorded history and led to the development of complex abstract thought. This is shown by the construction of complex calendars, techniques for making poisonous plants edible, public works at national scale, such as those which harnessed the floodplain of the Yangtse with reservoirs,[25] dams, and dikes, and buildings such as the Pyramids. However, no consistent conscious distinction was made between knowledge of such things, which are true in every community, and other types of communal knowledge, such as mythologies and legal systems. Metallurgy was known in prehistory, and the Vinča culture was the earliest known producer of bronze-like alloys. It is thought that early experimentation with heating and mixing of substances over time developed into alchemy.

Early cultures Main article: History of science in early cultures

Clay models of animal livers dating between the nineteenth and eighteenth centuries BCE, found in the royal palace in Mari, Syria Neither the words nor the concepts "science" and "nature" were part of the conceptual landscape in the ancient near east.[26] The ancient Mesopotamians used knowledge about the properties of various natural chemicals for manufacturing pottery, faience, glass, soap, metals, lime plaster, and waterproofing;[27] they also studied animal physiology, anatomy, and behavior for divinatory purposes[27] and made extensive records of the movements of astronomical objects for their study of astrology.[28] The Mesopotamians had intense interest in medicine[27] and the earliest medical prescriptions appear in Sumerian during the Third Dynasty of Ur (c. 2112 BCE – c. 2004 BCE).[29] Nonetheless, the Mesopotamians seem to have had little interest in gathering information about the natural world for the mere sake of gathering information[27] and mainly only studied scientific subjects which had obvious practical applications or immediate relevance to their religious system.[27]

Classical antiquity Main article: History of science in classical antiquity See also: Nature (philosophy) In the classical world, there is no real ancient analog of a modern scientist. Instead, well-educated, usually upper-class, and almost universally male individuals performed various investigations into nature whenever they could afford the time.[30] Before the invention or discovery of the concept of "nature" (ancient Greek phusis) by the Pre-Socratic philosophers, the same words tend to be used to describe the natural "way" in which a plant grows,[31] and the "way" in which, for example, one tribe worships a particular god. For this reason, it is claimed these men were the first philosophers in the strict sense, and also the first people to clearly distinguish "nature" and "convention."[32]:209 Natural philosophy, the precursor of natural science, was thereby distinguished as the knowledge of nature and things which are true for every community, and the name of the specialized pursuit of such knowledge was philosophy – the realm of the first philosopher-physicists. They were mainly speculators or theorists, particularly interested in astronomy. In contrast, trying to use knowledge of nature to imitate nature (artifice or technology, Greek technē) was seen by classical scientists as a more appropriate interest for lower class artisans.[33]

The early Greek philosophers of the Milesian school, which was founded by Thales of Miletus and later continued by his successors Anaximander and Anaximenes, were the first to attempt to explain natural phenomena without relying on the supernatural.[34] The Pythagoreans developed a complex number philosophy[35]:467–68 and contributed significantly to the development of mathematical science.[35]:465 The theory of atoms was developed by the Greek philosopher Leucippus and his student Democritus.[36][37] The Greek doctor Hippocrates established the tradition of systematic medical science[38][39] and is known as "The Father of Medicine".[40]

Aristotle, 384–322 BCE, one of the early figures in the development of the scientific method.[41] A turning point in the history of early philosophical science was Socrates' example of applying philosophy to the study of human matters, including human nature, the nature of political communities, and human knowledge itself. The Socratic method as documented by Plato's dialogues is a dialectic method of hypothesis elimination: better hypotheses are found by steadily identifying and eliminating those that lead to contradictions. This was a reaction to the Sophist emphasis on rhetoric. The Socratic method searches for general, commonly held truths that shape beliefs and scrutinizes them to determine their consistency with other beliefs.[42] Socrates criticized the older type of study of physics as too purely speculative and lacking in self-criticism. Socrates was later, in the words of his Apology, accused of corrupting the youth of Athens because he did "not believe in the gods the state believes in, but in other new spiritual beings". Socrates refuted these claims,[43] but was sentenced to death.[44]: 30e

Aristotle later created a systematic programme of teleological philosophy: Motion and change is described as the actualization of potentials already in things, according to what types of things they are. In his physics, the Sun goes around the Earth, and many things have it as part of their nature that they are for humans. Each thing has a formal cause, a final cause, and a role in a cosmic order with an unmoved mover. The Socratics also insisted that philosophy should be used to consider the practical question of the best way to live for a human being (a study Aristotle divided into ethics and political philosophy). Aristotle maintained that man knows a thing scientifically "when he possesses a conviction arrived at in a certain way, and when the first principles on which that conviction rests are known to him with certainty".[45]

The Greek astronomer Aristarchus of Samos (310–230 BCE) was the first to propose a heliocentric model of the universe, with the Sun at the center and all the planets orbiting it.[46] Aristarchus's model was widely rejected because it was believed to violate the laws of physics.[46] The inventor and mathematician Archimedes of Syracuse made major contributions to the beginnings of calculus[47] and has sometimes been credited as its inventor,[47] although his proto-calculus lacked several defining features.[47] Pliny the Elder was a Roman writer and polymath, who wrote the seminal encyclopedia Natural History,[48][49][50] dealing with history, geography, medicine, astronomy, earth science, botany, and zoology.[48] Other scientists or proto-scientists in Antiquity were Theophrastus, Euclid, Herophilos, Hipparchus, Ptolemy, and Galen.

During late antiquity, in the Byzantine empire many Greek classical texts were preserved. Many Syriac translations were done by groups such as the Nestorians and Monophysites.[51] They played a role when they translated Greek classical texts into Arabic under the Caliphate, during which many types of classical learning were preserved and in some cases improved upon.[51][c] In addition, the neighboring Sassanid Empire established the medical Academy of Gondeshapur where Greek, Syriac and Persian physicians established the most important medical center of the ancient world during the 6th and 7th centuries.[52]

Medieval science

De potentiis anime sensitive, Gregor Reisch (1504) Margarita philosophica. Medieval science postulated a ventricle of the brain as the location for our common sense,[53]:189 where the forms from our sensory systems commingled. Further information: Byzantine science, Science in the medieval Islamic world, and European science in the Middle Ages Because of the collapse of the Western Roman Empire due to the Migration Period an intellectual decline took place in the western part of Europe in the 400s. In contrast, the Byzantine Empire resisted the attacks from the barbarians, and preserved and improved upon the learning. John Philoponus, a Byzantine scholar in the 500s, was the first scholar ever to question Aristotle's teaching of physics and to note its flaws. John Philoponus' criticism of Aristotelian principles of physics served as an inspiration to medieval scholars as well as to Galileo Galilei who ten centuries later, during the Scientific Revolution, extensively cited Philoponus in his works while making the case as to why Aristotelian physics was flawed.[54][55]

During late antiquity and the early Middle Ages, the Aristotelian approach to inquiries on natural phenomena was used. Aristotle's four causes prescribed that four "why" questions should be answered in order to explain things scientifically.[56] Some ancient knowledge was lost, or in some cases kept in obscurity, during the fall of the Western Roman Empire and periodic political struggles. However, the general fields of science (or "natural philosophy" as it was called) and much of the general knowledge from the ancient world remained preserved through the works of the early Latin encyclopedists like Isidore of Seville.[57] However, Aristotle's original texts were eventually lost in Western Europe, and only one text by Plato was widely known, the Timaeus, which was the only Platonic dialogue, and one of the few original works of classical natural philosophy, available to Latin readers in the early Middle Ages. Another original work that gained influence in this period was Ptolemy's Almagest, which contains a geocentric description of the solar system.

In the Byzantine empire, many Greek classical texts were preserved. Many Syriac translations were done by groups such as the Nestorians and Monophysites.[51] They played a role when they translated Greek classical texts into Arabic under the Caliphate, during which many types of classical learning were preserved and in some cases improved upon.[51][c]

The House of Wisdom was established in Abbasid-era Baghdad, Iraq,[58] where the Islamic study of Aristotelianism flourished. Al-Kindi (801–873) was the first of the Muslim Peripatetic philosophers, and is known for his efforts to introduce Greek and Hellenistic philosophy to the Arab world.[59] The Islamic Golden Age flourished from this time until the Mongol invasions of the 13th century. Ibn al-Haytham (Alhazen), as well as his predecessor Ibn Sahl, was familiar with Ptolemy's Optics, and used experiments as a means to gain knowledge.[d][60][61]:463–65 Furthermore, doctors and alchemists such as the Persians Avicenna and Al-Razi also greatly developed the science of Medicine with the former writing the Canon of Medicine, a medical encyclopedia used until the 18th century and the latter discovering multiple compounds like alcohol. Avicenna's canon is considered to be one of the most important publications in medicine and they both contributed significantly to the practice of experimental medicine, using clinical trials and experiments to back their claims.[62]

In Classical antiquity, Greek and Roman taboos had meant that dissection was usually banned in ancient times, but in Middle Ages it changed: medical teachers and students at Bologna began to open human bodies, and Mondino de Luzzi (c. 1275–1326) produced the first known anatomy textbook based on human dissection.[63][64]

By the eleventh century most of Europe had become Christian; stronger monarchies emerged; borders were restored; technological developments and agricultural innovations were made which increased the food supply and population. In addition, classical Greek texts started to be translated from Arabic and Greek into Latin, giving a higher level of scientific discussion in Western Europe.[65]

By 1088, the first university in Europe (the University of Bologna) had emerged from its clerical beginnings. Demand for Latin translations grew (for example, from the Toledo School of Translators); western Europeans began collecting texts written not only in Latin, but also Latin translations from Greek, Arabic, and Hebrew. Manuscript copies of Alhazen's Book of Optics also propagated across Europe before 1240,[66]:Intro. p. xx as evidenced by its incorporation into Vitello's Perspectiva. Avicenna's Canon was translated into Latin.[67] In particular, the texts of Aristotle, Ptolemy,[e] and Euclid, preserved in the Houses of Wisdom and also in the Byzantine Empire,[68] were sought amongst Catholic scholars. The influx of ancient texts caused the Renaissance of the 12th century and the flourishing of a synthesis of Catholicism and Aristotelianism known as Scholasticism in western Europe, which became a new geographic center of science. An experiment in this period would be understood as a careful process of observing, describing, and classifying.[69] One prominent scientist in this era was Roger Bacon. Scholasticism had a strong focus on revelation and dialectic reasoning, and gradually fell out of favour over the next centuries, as alchemy's focus on experiments that include direct observation and meticulous documentation slowly increased in importance.

Renaissance and early modern science Main article: Scientific Revolution

Astronomy became more accurate after Tycho Brahe devised his scientific instruments for measuring angles between two celestial bodies, before the invention of the telescope. Brahe's observations were the basis for Kepler's laws. Alhazen disproved Ptolemy's theory of vision,[70] but did not make any corresponding changes to Aristotle's metaphysics. The scientific revolution ran concurrently to a process where elements of Aristotle's metaphysics such as ethics, teleology and formal causality slowly fell out of favour. Scholars slowly came to realize that the universe itself might well be devoid of both purpose and ethical imperatives. The development from a physics infused with goals, ethics, and spirit, toward a physics where these elements do not play an integral role, took centuries. This development was enhanced by the Condemnations of 1277, where Aristotle's books were banned by the Catholic church. This allowed the theoretical possibility of vacuum and motion in a vacuum. A direct result was the emergence of the science of dynamics.

New developments in optics played a role in the inception of the Renaissance, both by challenging long-held metaphysical ideas on perception, as well as by contributing to the improvement and development of technology such as the camera obscura and the telescope. Before what we now know as the Renaissance started, Roger Bacon, Vitello, and John Peckham each built up a scholastic ontology upon a causal chain beginning with sensation, perception, and finally apperception of the individual and universal forms of Aristotle.[71] A model of vision later known as perspectivism was exploited and studied by the artists of the Renaissance. This theory uses only three of Aristotle's four causes: formal, material, and final.[72]

In the sixteenth century, Copernicus formulated a heliocentric model of the solar system unlike the geocentric model of Ptolemy's Almagest. This was based on a theorem that the orbital periods of the planets are longer as their orbs are farther from the centre of motion, which he found not to agree with Ptolemy's model.[73]

Kepler and others challenged the notion that the only function of the eye is perception, and shifted the main focus in optics from the eye to the propagation of light.[74][75]:102 Kepler modelled the eye as a water-filled glass sphere with an aperture in front of it to model the entrance pupil. He found that all the light from a single point of the scene was imaged at a single point at the back of the glass sphere. The optical chain ends on the retina at the back of the eye.[f] Kepler is best known, however, for improving Copernicus' heliocentric model through the discovery of Kepler's laws of planetary motion. Kepler did not reject Aristotelian metaphysics, and described his work as a search for the Harmony of the Spheres.

Galileo Galilei, regarded as the father of modern science.[76]: Vol. 24, No. 1, p. 36 Galileo made innovative use of experiment and mathematics. However, he became persecuted after Pope Urban VIII blessed Galileo to write about the Copernican system. Galileo had used arguments from the Pope and put them in the voice of the simpleton in the work "Dialogue Concerning the Two Chief World Systems", which greatly offended Urban VIII.[77]

In Northern Europe, the new technology of the printing press was widely used to publish many arguments, including some that disagreed widely with contemporary ideas of nature. René Descartes and Francis Bacon published philosophical arguments in favor of a new type of non-Aristotelian science. Descartes emphasized individual thought and argued that mathematics rather than geometry should be used in order to study nature. Bacon emphasized the importance of experiment over contemplation. Bacon further questioned the Aristotelian concepts of formal cause and final cause, and promoted the idea that science should study the laws of "simple" natures, such as heat, rather than assuming that there is any specific nature, or "formal cause", of each complex type of thing. This new science began to see itself as describing "laws of nature". This updated approach to studies in nature was seen as mechanistic. Bacon also argued that science should aim for the first time at practical inventions for the improvement of all human life.

Age of Enlightenment Main article: Age of Enlightenment

Isaac Newton, shown here in a 1689 portrait, made seminal contributions to classical mechanics, gravity, and optics. Newton shares credit with Gottfried Leibniz for the development of calculus. As a precursor to the Age of Enlightenment, Isaac Newton and Gottfried Wilhelm Leibniz succeeded in developing a new physics, now referred to as classical mechanics, which could be confirmed by experiment and explained using mathematics. Leibniz also incorporated terms from Aristotelian physics, but now being used in a new non-teleological way, for example, "energy" and "potential" (modern versions of Aristotelian "energeia and potentia"). This implied a shift in the view of objects: Where Aristotle had noted that objects have certain innate goals that can be actualized, objects were now regarded as devoid of innate goals. In the style of Francis Bacon, Leibniz assumed that different types of things all work according to the same general laws of nature, with no special formal or final causes for each type of thing. It is during this period that the word "science" gradually became more commonly used to refer to a type of pursuit of a type of knowledge, especially knowledge of nature – coming close in meaning to the old term "natural philosophy."

During this time, the declared purpose and value of science became producing wealth and inventions that would improve human lives, in the materialistic sense of having more food, clothing, and other things. In Bacon's words, "the real and legitimate goal of sciences is the endowment of human life with new inventions and riches", and he discouraged scientists from pursuing intangible philosophical or spiritual ideas, which he believed contributed little to human happiness beyond "the fume of subtle, sublime, or pleasing speculation".[78]

Science during the Enlightenment was dominated by scientific societies and academies, which had largely replaced universities as centres of scientific research and development. Societies and academies were also the backbone of the maturation of the scientific profession. Another important development was the popularization of science among an increasingly literate population. Philosophes introduced the public to many scientific theories, most notably through the Encyclopédie and the popularization of Newtonianism by Voltaire as well as by Émilie du Châtelet, the French translator of Newton's Principia.

Some historians have marked the 18th century as a drab period in the history of science;[79] however, the century saw significant advancements in the practice of medicine, mathematics, and physics; the development of biological taxonomy; a new understanding of magnetism and electricity; and the maturation of chemistry as a discipline, which established the foundations of modern chemistry.

Enlightenment philosophers chose a short history of scientific predecessors – Galileo, Boyle, and Newton principally – as the guides and guarantors of their applications of the singular concept of nature and natural law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded.[80]

19th century

Charles Darwin in 1854, by then working towards publication of On the Origin of Species. The nineteenth century is a particularly important period in the history of science since during this era many distinguishing characteristics of contemporary modern science began to take shape such as: transformation of the life and physical sciences, frequent use of precision instruments, emergence of terms like "biologist", "physicist", "scientist"; slowly moving away from antiquated labels like "natural philosophy" and "natural history", increased professionalization of those studying nature lead to reduction in amateur naturalists, scientists gained cultural authority over many dimensions of society, economic expansion and industrialization of numerous countries, thriving of popular science writings and emergence of science journals.[15]

Early in the 19th century, John Dalton suggested the modern atomic theory, based on Democritus's original idea of individible particles called atoms.

Combustion and chemical reactions were studied by Michael Faraday and reported in his lectures before the Royal Institution: The Chemical History of a Candle, 1861. Both John Herschel and William Whewell systematized methodology: the latter coined the term scientist.[81] When Charles Darwin published On the Origin of Species he established evolution as the prevailing explanation of biological complexity. His theory of natural selection provided a natural explanation of how species originated, but this only gained wide acceptance a century later.

The laws of conservation of energy, conservation of momentum and conservation of mass suggested a highly stable universe where there could be little loss of resources. With the advent of the steam engine and the industrial revolution, there was, however, an increased understanding that all forms of energy as defined by Newton were not equally useful; they did not have the same energy quality. This realization led to the development of the laws of thermodynamics, in which the cumulative energy quality of the universe is seen as constantly declining: the entropy of the universe increases over time.

The electromagnetic theory was also established in the 19th century, and raised new questions which could not easily be answered using Newton's framework. The phenomena that would allow the deconstruction of the atom were discovered in the last decade of the 19th century: the discovery of X-rays inspired the discovery of radioactivity. In the next year came the discovery of the first subatomic particle, the electron.

20th century

The DNA double helix is a molecule that encodes the genetic instructions used in the development and functioning of all known living organisms and many viruses. Einstein's theory of relativity and the development of quantum mechanics led to the replacement of classical mechanics with a new physics which contains two parts that describe different types of events in nature.

In the first half of the century, the development of antibiotics and artificial fertilizer made global human population growth possible. At the same time, the structure of the atom and its nucleus was discovered, leading to the release of "atomic energy" (nuclear power). In addition, the extensive use of technological innovation stimulated by the wars of this century led to revolutions in transportation (automobiles and aircraft), the development of ICBMs, a space race, and a nuclear arms race.

The molecular structure of DNA was discovered in 1953. The discovery of the cosmic microwave background radiation in 1964 led to a rejection of the Steady State theory of the universe in favour of the Big Bang theory of Georges Lemaître.

The development of spaceflight in the second half of the century allowed the first astronomical measurements done on or near other objects in space, including manned landings on the Moon. Space telescopes lead to numerous discoveries in astronomy and cosmology.

Widespread use of integrated circuits in the last quarter of the 20th century combined with communications satellites led to a revolution in information technology and the rise of the global internet and mobile computing, including smartphones. The need for mass systematization of long, intertwined causal chains and large amounts of data led to the rise of the fields of systems theory and computer-assisted scientific modelling, which are partly based on the Aristotelian paradigm.[82]

Harmful environmental issues such as ozone depletion, acidification, eutrophication and climate change came to the public's attention in the same period, and caused the onset of environmental science and environmental technology. In a 1967 article, Lynn Townsend White Jr. blamed the ecological crisis on the historical decline of the notion of spirit in nature.[83]

21st century

A simulated event in the CMS detector of the Large Hadron Collider, featuring a possible appearance of the Higgs boson. With the discovery of the Higgs boson in 2012, the last particle predicted by the Standard Model of particle physics was found. In 2015, gravitational waves, predicted by general relativity a century before, were first observed.[84][85]

The Human Genome Project was completed in 2003, determining the sequence of nucleotide base pairs that make up human DNA, and identifying and mapping all of the genes of the human genome.[86] Induced pluripotent stem cells were developed in 2006, a technology allowing adult cells to be transformed into stem cells capable of giving rise to any cell type found in the body, potentially of huge importance to the field of regenerative medicine.[87]

Branches of science Main article: Branches of science Modern science is commonly divided into three major branches that consist of the natural sciences, social sciences, and formal sciences. Each of these branches comprise various specialized yet overlapping scientific disciplines that often possess their own nomenclature and expertise.[88] Both natural and social sciences are empirical sciences[89] as their knowledge are based on empirical observations and are capable of being tested for its validity by other researchers working under the same conditions.[90]

There are also closely related disciplines that use science, such as engineering and medicine.

Natural science Main articles: Natural science and Outline of natural science

False-color composite of global oceanic and terrestrial photoautotroph abundance by the SeaWiFS Project, NASA/Goddard Space Flight Center, and ORBIMAGE. Natural science is concerned with the description, prediction, and understanding of natural phenomena based on empirical evidence from observation and experimentation. It can be divided into two main branches: life science (or biological science) and physical science. Physical science is subdivided into branches, including physics, chemistry, astronomy and earth science. These two branches may be further divided into more specialized disciplines. Modern natural science is the successor to the natural philosophy that began in Ancient Greece. Galileo, Descartes, Bacon, and Newton debated the benefits of using approaches which were more mathematical and more experimental in a methodical way. Still, philosophical perspectives, conjectures, and presuppositions, often overlooked, remain necessary in natural science.[91] Systematic data collection, including discovery science, succeeded natural history, which emerged in the 16th century by describing and classifying plants, animals, minerals, and so on.[92] Today, "natural history" suggests observational descriptions aimed at popular audiences.[93]

Social science Main articles: Social science and Outline of social science

In economics, the supply and demand model describes how prices vary as a result of a balance between product availability and demand. Social science is concerned with society and the relationships among individuals within a society. It has many branches that include, but are not limited to, anthropology, archaeology, communication studies, economics, history, human geography, jurisprudence, linguistics, political science, psychology, public health, and sociology. Social scientists may adopt various philosophical theories to study individuals and society. For example, positivist social scientists use methods resembling those of the natural sciences as tools for understanding society, and so define science in its stricter modern sense. Interpretivist social scientists, by contrast, may use social critique or symbolic interpretation rather than constructing empirically falsifiable theories, and thus treat science in its broader sense. In modern academic practice, researchers are often eclectic, using multiple methodologies (for instance, by combining both quantitative and qualitative research). The term "social research" has also acquired a degree of autonomy as practitioners from various disciplines share in its aims and methods.

Formal science Main articles: Formal science and Outline of formal science

A humanoid robotic hand (see Shadow Hand system). Formal science is involved in the study of formal systems. It includes mathematics,[94][95] systems theory, robotics, and theoretical computer science. The formal sciences share similarities with the other two branches by relying on objective, careful, and systematic study of an area of knowledge. They are, however, different from the empirical sciences as they rely exclusively on deductive reasoning, without the need for empirical evidence, to verify their abstract concepts.[18][96][97] The formal sciences are therefore a priori disciplines and because of this, there is disagreement on whether they actually constitute a science.[16][17] Nevertheless, the formal sciences play an important role in the empirical sciences. Calculus, for example, was initially invented to understand motion in physics.[98] Natural and social sciences that rely heavily on mathematical applications include mathematical physics, mathematical chemistry, mathematical biology, mathematical finance, and mathematical economics.

Scientific research See also: Research Scientific research can be labeled as either basic or applied research. Basic research is the search for knowledge and applied research is the search for solutions to practical problems using this knowledge. Although some scientific research is applied research into specific problems, a great deal of our understanding comes from the curiosity-driven undertaking of basic research. This leads to options for technological advance that were not planned or sometimes even imaginable. This point was made by Michael Faraday when allegedly in response to the question "what is the use of basic research?" he responded: "Sir, what is the use of a new-born child?".[99] For example, research into the effects of red light on the human eye's rod cells did not seem to have any practical purpose; eventually, the discovery that our night vision is not troubled by red light would lead search and rescue teams (among others) to adopt red light in the cockpits of jets and helicopters.[100]:106–10 Finally, even basic research can take unexpected turns, and there is some sense in which the scientific method is built to harness luck.

Scientific method Main article: Scientific method

The central star IRAS 10082-5647 was captured by the Advanced Camera for Surveys aboard the Hubble Space Telescope. Scientific research involves using the scientific method, which seeks to objectively explain the events of nature in a reproducible way.[g] An explanatory thought experiment or hypothesis is put forward as explanation using principles such as parsimony (also known as "Occam's Razor") and are generally expected to seek consilience – fitting well with other accepted facts related to the phenomena.[101] This new explanation is used to make falsifiable predictions that are testable by experiment or observation. The predictions are to be posted before a confirming experiment or observation is sought, as proof that no tampering has occurred. Disproof of a prediction is evidence of progress.[h][i] This is done partly through observation of natural phenomena, but also through experimentation that tries to simulate natural events under controlled conditions as appropriate to the discipline (in the observational sciences, such as astronomy or geology, a predicted observation might take the place of a controlled experiment). Experimentation is especially important in science to help establish causal relationships (to avoid the correlation fallacy).

When a hypothesis proves unsatisfactory, it is either modified or discarded.[102] If the hypothesis survived testing, it may become adopted into the framework of a scientific theory, a logically reasoned, self-consistent model or framework for describing the behavior of certain natural phenomena. A theory typically describes the behavior of much broader sets of phenomena than a hypothesis; commonly, a large number of hypotheses can be logically bound together by a single theory. Thus a theory is a hypothesis explaining various other hypotheses. In that vein, theories are formulated according to most of the same scientific principles as hypotheses. In addition to testing hypotheses, scientists may also generate a model, an attempt to describe or depict the phenomenon in terms of a logical, physical or mathematical representation and to generate new hypotheses that can be tested, based on observable phenomena.[103]

While performing experiments to test hypotheses, scientists may have a preference for one outcome over another, and so it is important to ensure that science as a whole can eliminate this bias.[104][105] This can be achieved by careful experimental design, transparency, and a thorough peer review process of the experimental results as well as any conclusions.[106][107] After the results of an experiment are announced or published, it is normal practice for independent researchers to double-check how the research was performed, and to follow up by performing similar experiments to determine how dependable the results might be.[108] Taken in its entirety, the scientific method allows for highly creative problem solving while minimizing any effects of subjective bias on the part of its users (especially the confirmation bias).[109]

Role of mathematics Main articles: Mathematics and Formal science

Calculus, the mathematics of continuous change, underpins many of the sciences. Mathematics is essential in the formation of hypotheses, theories, and laws[110] in the natural and social sciences. For example, it is used in quantitative scientific modeling, which can generate new hypotheses and predictions to be tested. It is also used extensively in observing and collecting measurements. Statistics, a branch of mathematics, is used to summarize and analyze data, which allow scientists to assess the reliability and variability of their experimental results.

Computational science applies computing power to simulate real-world situations, enabling a better understanding of scientific problems than formal mathematics alone can achieve. According to the Society for Industrial and Applied Mathematics, computation is now as important as theory and experiment in advancing scientific knowledge.[111]

Verifiability John Ziman points out that intersubjective verifiability is fundamental to the creation of all scientific knowledge.[112]:44 Ziman shows how scientists can identify patterns to each other across centuries; he refers to this ability as "perceptual consensibility."[113]:46 He then makes consensibility, leading to consensus, the touchstone of reliable knowledge.[113]:104

Philosophy of science See also: Philosophy of science

English philosopher and physician John Locke (1632–1704), a leading philosopher of British empiricism Scientists usually take for granted a set of basic assumptions that are needed to justify the scientific method: (1) that there is an objective reality shared by all rational observers; (2) that this objective reality is governed by natural laws; (3) that these laws can be discovered by means of systematic observation and experimentation.[24] Philosophy of science seeks a deep understanding of what these underlying assumptions mean and whether they are valid.

The belief that scientific theories should and do represent metaphysical reality is known as realism. It can be contrasted with anti-realism, the view that the success of science does not depend on it being accurate about unobservable entities such as electrons. One form of anti-realism is idealism, the belief that the mind or consciousness is the most basic essence, and that each mind generates its own reality.[j] In an idealistic world view, what is true for one mind need not be true for other minds.

There are different schools of thought in philosophy of science. The most popular position is empiricism,[k] which holds that knowledge is created by a process involving observation and that scientific theories are the result of generalizations from such observations.[114] Empiricism generally encompasses inductivism, a position that tries to explain the way general theories can be justified by the finite number of observations humans can make and hence the finite amount of empirical evidence available to confirm scientific theories. This is necessary because the number of predictions those theories make is infinite, which means that they cannot be known from the finite amount of evidence using deductive logic only. Many versions of empiricism exist, with the predominant ones being Bayesianism[115] and the hypothetico-deductive method.[116]:236

The Austrian-British philosopher of science Karl Popper (1902–1994) in 1990. He is best known for his work on empirical falsification. Empiricism has stood in contrast to rationalism, the position originally associated with Descartes, which holds that knowledge is created by the human intellect, not by observation.[116]:20 Critical rationalism is a contrasting 20th-century approach to science, first defined by Austrian-British philosopher Karl Popper. Popper rejected the way that empiricism describes the connection between theory and observation. He claimed that theories are not generated by observation, but that observation is made in the light of theories and that the only way a theory can be affected by observation is when it comes in conflict with it.[116]:63–67 Popper proposed replacing verifiability with falsifiability as the landmark of scientific theories and replacing induction with falsification as the empirical method.[116]:68 Popper further claimed that there is actually only one universal method, not specific to science: the negative method of criticism, trial and error.[117] It covers all products of the human mind, including science, mathematics, philosophy, and art.[118]

Another approach, instrumentalism, colloquially termed "shut up and multiply,"[119] emphasizes the utility of theories as instruments for explaining and predicting phenomena.[120] It views scientific theories as black boxes with only their input (initial conditions) and output (predictions) being relevant. Consequences, theoretical entities, and logical structure are claimed to be something that should simply be ignored and that scientists shouldn't make a fuss about (see interpretations of quantum mechanics). Close to instrumentalism is constructive empiricism, according to which the main criterion for the success of a scientific theory is whether what it says about observable entities is true.

Thomas Kuhn argued that the process of observation and evaluation takes place within a paradigm, a logically consistent "portrait" of the world that is consistent with observations made from its framing. He characterized normal science as the process of observation and "puzzle solving" which takes place within a paradigm, whereas revolutionary science occurs when one paradigm overtakes another in a paradigm shift.[121] Each paradigm has its own distinct questions, aims, and interpretations. The choice between paradigms involves setting two or more "portraits" against the world and deciding which likeness is most promising. A paradigm shift occurs when a significant number of observational anomalies arise in the old paradigm and a new paradigm makes sense of them. That is, the choice of a new paradigm is based on observations, even though those observations are made against the background of the old paradigm. For Kuhn, acceptance or rejection of a paradigm is a social process as much as a logical process. Kuhn's position, however, is not one of relativism.[122]

Finally, another approach often cited in debates of scientific skepticism against controversial movements like "creation science" is methodological naturalism. Its main point is that a difference between natural and supernatural explanations should be made and that science should be restricted methodologically to natural explanations.[l] That the restriction is merely methodological (rather than ontological) means that science should not consider supernatural explanations itself, but should not claim them to be wrong either. Instead, supernatural explanations should be left a matter of personal belief outside the scope of science. Methodological naturalism maintains that proper science requires strict adherence to empirical study and independent verification as a process for properly developing and evaluating explanations for observable phenomena.[123] The absence of these standards, arguments from authority, biased observational studies and other common fallacies are frequently cited by supporters of methodological naturalism as characteristic of the non-science they criticize.

Certainty and science A scientific theory is empirical[k][124] and is always open to falsification if new evidence is presented. That is, no theory is ever considered strictly certain as science accepts the concept of fallibilism.[m] The philosopher of science Karl Popper sharply distinguished truth from certainty. He wrote that scientific knowledge "consists in the search for truth," but it "is not the search for certainty ... All human knowledge is fallible and therefore uncertain."[125]:4

New scientific knowledge rarely results in vast changes in our understanding. According to psychologist Keith Stanovich, it may be the media's overuse of words like "breakthrough" that leads the public to imagine that science is constantly proving everything it thought was true to be false.[100]:119–38 While there are such famous cases as the theory of relativity that required a complete reconceptualization, these are extreme exceptions. Knowledge in science is gained by a gradual synthesis of information from different experiments by various researchers across different branches of science; it is more like a climb than a leap.[100]:123 Theories vary in the extent to which they have been tested and verified, as well as their acceptance in the scientific community.[n] For example, heliocentric theory, the theory of evolution, relativity theory, and germ theory still bear the name "theory" even though, in practice, they are considered factual.[126] Philosopher Barry Stroud adds that, although the best definition for "knowledge" is contested, being skeptical and entertaining the possibility that one is incorrect is compatible with being correct. Therefore, scientists adhering to proper scientific approaches will doubt themselves even once they possess the truth.[127] The fallibilist C. S. Peirce argued that inquiry is the struggle to resolve actual doubt and that merely quarrelsome, verbal, or hyperbolic doubt is fruitless[128] – but also that the inquirer should try to attain genuine doubt rather than resting uncritically on common sense.[129] He held that the successful sciences trust not to any single chain of inference (no stronger than its weakest link) but to the cable of multiple and various arguments intimately connected.[130]

Stanovich also asserts that science avoids searching for a "magic bullet"; it avoids the single-cause fallacy. This means a scientist would not ask merely "What is the cause of ...", but rather "What are the most significant causes of ...". This is especially the case in the more macroscopic fields of science (e.g. psychology, physical cosmology).[100]:141–47 Research often analyzes few factors at once, but these are always added to the long list of factors that are most important to consider.[100]:141–47 For example, knowing the details of only a person's genetics, or their history and upbringing, or the current situation may not explain a behavior, but a deep understanding of all these variables combined can be very predictive.

Fringe science, pseudoscience, and junk science An area of study or speculation that masquerades as science in an attempt to claim a legitimacy that it would not otherwise be able to achieve is sometimes referred to as pseudoscience, fringe science, or junk science.[o] Physicist Richard Feynman coined the term "cargo cult science" for cases in which researchers believe they are doing science because their activities have the outward appearance of science but actually lack the "kind of utter honesty" that allows their results to be rigorously evaluated.[131] Various types of commercial advertising, ranging from hype to fraud, may fall into these categories.

There can also be an element of political or ideological bias on all sides of scientific debates. Sometimes, research may be characterized as "bad science," research that may be well-intended but is actually incorrect, obsolete, incomplete, or over-simplified expositions of scientific ideas. The term "scientific misconduct" refers to situations such as where researchers have intentionally misrepresented their published data or have purposely given credit for a discovery to the wrong person.[132]

Scientific literature Main article: Scientific literature

Cover of the first volume of the scientific journal Science in 1880. Scientific research is published in an enormous range of scientific literature.[133] Scientific journals communicate and document the results of research carried out in universities and various other research institutions, serving as an archival record of science. The first scientific journals, Journal des Sçavans followed by the Philosophical Transactions, began publication in 1665. Since that time the total number of active periodicals has steadily increased. In 1981, one estimate for the number of scientific and technical journals in publication was 11,500.[134] The United States National Library of Medicine currently indexes 5,516 journals that contain articles on topics related to the life sciences. Although the journals are in 39 languages, 91 percent of the indexed articles are published in English.[135]

Most scientific journals cover a single scientific field and publish the research within that field; the research is normally expressed in the form of a scientific paper. Science has become so pervasive in modern societies that it is generally considered necessary to communicate the achievements, news, and ambitions of scientists to a wider populace.

Science magazines such as New Scientist, Science & Vie, and Scientific American cater to the needs of a much wider readership and provide a non-technical summary of popular areas of research, including notable discoveries and advances in certain fields of research. Science books engage the interest of many more people. Tangentially, the science fiction genre, primarily fantastic in nature, engages the public imagination and transmits the ideas, if not the methods, of science.

Recent efforts to intensify or develop links between science and non-scientific disciplines such as literature or more specifically, poetry, include the Creative Writing Science resource developed through the Royal Literary Fund.[136]

Practical impacts Discoveries in fundamental science can be world-changing. For example:

Research Impact Static electricity and magnetism (c. 1600) Electric current (18th century) All electric appliances, dynamos, electric power stations, modern electronics, including electric lighting, television, electric heating, transcranial magnetic stimulation, deep brain stimulation, magnetic tape, loudspeaker, and the compass and lightning rod. Diffraction (1665) Optics, hence fiber optic cable (1840s), modern intercontinental communications, and cable TV and internet Germ theory (1700) Hygiene, leading to decreased transmission of infectious diseases; antibodies, leading to techniques for disease diagnosis and targeted anticancer therapies. Vaccination (1798) Leading to the elimination of most infectious diseases from developed countries and the worldwide eradication of smallpox. Photovoltaic effect (1839) Solar cells (1883), hence solar power, solar powered watches, calculators and other devices. The strange orbit of Mercury (1859) and other research leading to special (1905) and general relativity (1916) Satellite-based technology such as GPS (1973), satnav and satellite communications[p] Radio waves (1887) Radio had become used in innumerable ways beyond its better-known areas of telephony, and broadcast television (1927) and radio (1906) entertainment. Other uses included – emergency services, radar (navigation and weather prediction), medicine, astronomy, wireless communications, geophysics, and networking. Radio waves also led researchers to adjacent frequencies such as microwaves, used worldwide for heating and cooking food. Radioactivity (1896) and antimatter (1932) Cancer treatment (1896), Radiometric dating (1905), nuclear reactors (1942) and weapons (1945), mineral exploration, PET scans (1961), and medical research (via isotopic labeling) X-rays (1896) Medical imaging, including computed tomography Crystallography and quantum mechanics (1900) Semiconductor devices (1906), hence modern computing and telecommunications including the integration with wireless devices: the mobile phone,[p] LED lamps and lasers. Plastics (1907) Starting with Bakelite, many types of artificial polymers for numerous applications in industry and daily life Antibiotics (1880s, 1928) Salvarsan, Penicillin, doxycycline etc. Nuclear magnetic resonance (1930s) Nuclear magnetic resonance spectroscopy (1946), magnetic resonance imaging (1971), functional magnetic resonance imaging (1990s). Scientific community Main article: Scientific community The scientific community is a group of all interacting scientists, along with their respective societies and institutions.

Scientists Main article: Scientist

German-born scientist Albert Einstein (1879–1955) developed the theory of relativity. He also won the Nobel Prize in Physics in 1921 for his work in theoretical physics. Scientists are individuals who conduct scientific research to advance knowledge in an area of interest.[137][138] The term scientist was coined by William Whewell in 1833. In modern times, many professional scientists are trained in an academic setting and upon completion, attain an academic degree, with the highest degree being a doctorate such as a Doctor of Philosophy (PhD),[139] Doctor of Medicine (MD), or Doctor of Engineering (DEng). Many scientists pursue careers in various sectors of the economy such as academia, industry, government, and nonprofit environments.[140][141][142]

Scientists exhibit a strong curiosity about reality, with some scientists having a desire to apply scientific knowledge for the benefit of health, nations, environment, or industries. Other motivations include recognition by their peers and prestige. The Nobel Prize, a widely regarded prestigious award,[143] is awarded annually to those who have achieved scientific advances in the fields of medicine, physics, chemistry, and economics.

Women in science Main article: Women in science Further information: Women in STEM fields

Marie Curie was the first person to be awarded two Nobel Prizes: Physics in 1903 and Chemistry in 1911.[144] Science has historically been a male-dominated field, with some notable exceptions.[q] Women faced considerable discrimination in science, much as they did in other areas of male-dominated societies, such as frequently being passed over for job opportunities and denied credit for their work.[r] For example, Christine Ladd (1847–1930) was able to enter a PhD program as "C. Ladd"; Christine "Kitty" Ladd completed the requirements in 1882, but was awarded her degree only in 1926, after a career which spanned the algebra of logic (see truth table), color vision, and psychology. Her work preceded notable researchers like Ludwig Wittgenstein and Charles Sanders Peirce. The achievements of women in science have been attributed to their defiance of their traditional role as laborers within the domestic sphere.[145]

In the late 20th century, active recruitment of women and elimination of institutional discrimination on the basis of sex greatly increased the number of women scientists, but large gender disparities remain in some fields; in the early 21st century over half of new biologists were female, while 80% of PhDs in physics are given to men.[citation needed] In the early part of the 21st century, women in the United States earned 50.3% of bachelor's degrees, 45.6% of master's degrees, and 40.7% of PhDs in science and engineering fields. They earned more than half of the degrees in psychology (about 70%), social sciences (about 50%), and biology (about 50-60%) but earned less than half the degrees in the physical sciences, earth sciences, mathematics, engineering, and computer science.[146] Lifestyle choice also plays a major role in female engagement in science; women with young children are 28% less likely to take tenure-track positions due to work-life balance issues,[147] and female graduate students' interest in careers in research declines dramatically over the course of graduate school, whereas that of their male colleagues remains unchanged.[148]

Learned societies Further information: Learned society

Physicists in front of the Royal Society building in London (1952). Learned societies for the communication and promotion of scientific thought and experimentation have existed since the Renaissance.[149] Many scientists belong to a learned society that promotes their respective scientific discipline, profession, or group of related disciplines.[150] Membership may be open to all, may require possession of some qualifications, or may be an honor conferred by election.[151] Membership often requires possession of some scientific credentials, or may be an honor conferred by election. Most scientific societies are non-profit organizations, and many are professional associations. Their activities typically include holding regular conferences for the presentation and discussion of new research results and publishing or sponsoring academic journals in their discipline. Some also act as professional bodies, regulating the activities of their members in the public interest or the collective interest of the membership. Scholars in the sociology of science[who?] argue that learned societies are of key importance and their formation assists in the emergence and development of new disciplines or professions.

The professionalization of science, begun in the 19th century, was partly enabled by the creation of distinguished academy of sciences in a number of countries such as the Italian Accademia dei Lincei in 1603,[152] the British Royal Society in 1660, the French Académie des Sciences in 1666,[153] the American National Academy of Sciences in 1863, the German Kaiser Wilhelm Institute in 1911, and the Chinese Academy of Sciences in 1928. International scientific organizations, such as the International Council for Science, have since been formed to promote cooperation between the scientific communities of different nations.

Science and the public "Science and society" redirects here. For the academic journal, see Science & Society. Science policy Main articles: Science policy, History of science policy, and Economics of science

The United Nations Global Science-Policy-Business Forum on the Environment in Nairobi, Kenya (2017). Science policy is an area of public policy concerned with the policies that affect the conduct of the scientific enterprise, including research funding, often in pursuance of other national policy goals such as technological innovation to promote commercial product development, weapons development, health care and environmental monitoring. Science policy also refers to the act of applying scientific knowledge and consensus to the development of public policies. Science policy thus deals with the entire domain of issues that involve the natural sciences. In accordance with public policy being concerned about the well-being of its citizens, science policy's goal is to consider how science and technology can best serve the public.

State policy has influenced the funding of public works and science for thousands of years, particularly within civilizations with highly organized governments such as imperial China and the Roman Empire. Prominent historical examples include the Great Wall of China, completed over the course of two millennia through the state support of several dynasties, and the Grand Canal of the Yangtze River, an immense feat of hydraulic engineering begun by Sunshu Ao (孫叔敖 7th c. BCE), Ximen Bao (西門豹 5th c.BCE), and Shi Chi (4th c. BCE). This construction dates from the 6th century BCE under the Sui Dynasty and is still in use today. In China, such state-supported infrastructure and scientific research projects date at least from the time of the Mohists, who inspired the study of logic during the period of the Hundred Schools of Thought and the study of defensive fortifications like the Great Wall of China during the Warring States period.

Public policy can directly affect the funding of capital equipment and intellectual infrastructure for industrial research by providing tax incentives to those organizations that fund research. Vannevar Bush, director of the Office of Scientific Research and Development for the United States government, the forerunner of the National Science Foundation, wrote in July 1945 that "Science is a proper concern of government."[154]

Funding of science Main article: Funding of science

The Commonwealth Scientific and Industrial Research Organisation (CSIRO) Main Entomology Building in Australia Scientific research is often funded through a competitive process in which potential research projects are evaluated and only the most promising receive funding. Such processes, which are run by government, corporations, or foundations, allocate scarce funds. Total research funding in most developed countries is between 1.5% and 3% of GDP.[155] In the OECD, around two-thirds of research and development in scientific and technical fields is carried out by industry, and 20% and 10% respectively by universities and government. The government funding proportion in certain industries is higher, and it dominates research in social science and humanities. Similarly, with some exceptions (e.g. biotechnology) government provides the bulk of the funds for basic scientific research. Many governments have dedicated agencies to support scientific research. Prominent scientific organizations include the National Science Foundation in the United States, the National Scientific and Technical Research Council in Argentina, Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia, Centre national de la recherche scientifique in France, the Max Planck Society and Deutsche Forschungsgemeinschaft in Germany, and CSIC in Spain. In commercial research and development, all but the most research-oriented corporations focus more heavily on near-term commercialisation possibilities rather than "blue-sky" ideas or technologies (such as nuclear fusion).

Public awareness of science Main article: Public awareness of science Further information: Science outreach and Science communication

Dinosaur exhibit in the Houston Museum of Natural Science The public awareness of science relates to the attitudes, behaviors, opinions, and activities that make up the relations between science and the general public. it integrates various themes and activities such as science communication, science museums, science festivals, science fairs, citizen science, and science in popular culture. Social scientists have devised various metrics to measure the public understanding of science such as factual knowledge, self-reported knowledge, and structural knowledge.[156][157]

Science journalism Main article: Science journalism The mass media face a number of pressures that can prevent them from accurately depicting competing scientific claims in terms of their credibility within the scientific community as a whole. Determining how much weight to give different sides in a scientific debate may require considerable expertise regarding the matter.[158] Few journalists have real scientific knowledge, and even beat reporters who know a great deal about certain scientific issues may be ignorant about other scientific issues that they are suddenly asked to cover.[159][160]

Politicization of science Main article: Politicization of science

Results of seven papers from 2004–2015 assessing the overwhelming scientific consensus on man-made global warming (see Surveys of scientists' views on climate change), in contrast to the political controversy over this issue, particularly in the United States. Politicization of science occurs when government, business, or advocacy groups use legal or economic pressure to influence the findings of scientific research or the way it is disseminated, reported, or interpreted. Many factors can act as facets of the politicization of science such as populist anti-intellectualism, perceived threats to religious beliefs, postmodernist subjectivism, and fear for business interests.[161] Politicization of science is usually accomplished when scientific information is presented in a way that emphasizes the uncertainty associated with the scientific evidence.[162] Tactics such as shifting conversation, failing to acknowledge facts, and capitalizing on doubt of scientific consensus have been used to gain more attention for views that have been undermined by scientific evidence.[163] Examples of issues that have involved the politicization of science include the global warming controversy, health effects of pesticides, and health effects of tobacco.[163][164]

See also Antiquarian science books Criticism of science Human timeline Index of branches of science Life timeline List of scientific occupations Normative science Outline of science Pathological science Protoscience Science in popular culture Science wars Scientific dissent Sociology of scientific knowledge Wissenschaft – all areas of scholarly study, including both sciences and non-sciences Notes

"... modern science is a discovery as well as an invention. It was a discovery that nature generally acts regularly enough to be described by laws and even by mathematics; and required invention to devise the techniques, abstractions, apparatus, and organization for exhibiting the regularities and securing their law-like descriptions."— Heilbron 2003, p. vii

"science". Merriam-Webster Online Dictionary. Merriam-Webster, Inc. Retrieved October 16, 2011. 3 a: knowledge or a system of knowledge covering general truths or the operation of general laws especially as obtained and tested through scientific method b: such knowledge or such a system of knowledge concerned with the physical world and its phenomena.

"The historian ... requires a very broad definition of "science" – one that ... will help us to understand the modern scientific enterprise. We need to be broad and inclusive, rather than narrow and exclusive ... and we should expect that the farther back we go [in time] the broader we will need to be."  — (Lindberg 2007, p. 3), which further cites Pingree, David (December 1992). "Hellenophilia versus the History of Science". Isis. 4 (4): 554–63. Bibcode:1992Isis...83..554P. doi:10.1086/356288. JSTOR 234257.
Alhacen had access to the optics books of Euclid and Ptolemy, as is shown by the title of his lost work A Book in which I have Summarized the Science of Optics from the Two Books of Euclid and Ptolemy, to which I have added the Notions of the First Discourse which is Missing from Ptolemy's Book From Ibn Abi Usaibia's catalog, as cited in (Smith 2001):91(vol .1), p. xv
"[Ibn al-Haytham] followed Ptolemy's bridge building ... into a grand synthesis of light and vision. Part of his effort consisted in devising ranges of experiments, of a kind probed before but now undertaken on larger scale."— Cohen 2010, p. 59
The translator, Gerard of Cremona (c. 1114–1187), inspired by his love of the Almagest, came to Toledo, where he knew he could find the Almagest in Arabic. There he found Arabic books of every description, and learned Arabic in order to translate these books into Latin, being aware of 'the poverty of the Latins'. —As cited by Burnett, Charles (2002). "The Coherence of the Arabic-Latin Translation Program in Toledo in the Twelfth Century". Science in Context. 14: 249–88. doi:10.1017/S0269889701000096.
Kepler, Johannes (1604) Ad Vitellionem paralipomena, quibus astronomiae pars opticae traditur (Supplements to Witelo, in which the optical part of astronomy is treated) as cited in Smith, A. Mark (1 January 2004). "What Is the History of Medieval Optics Really about?". Proceedings of the American Philosophical Society. 148 (2): 180–94. JSTOR 1558283. PMID 15338543.

The full title translation is from p. 60 of James R. Voelkel (2001) Johannes Kepler and the New Astronomy Oxford University Press. Kepler was driven to this experiment after observing the partial solar eclipse at Graz, July 10, 1600. He used Tycho Brahe's method of observation, which was to project the image of the Sun on a piece of paper through a pinhole aperture, instead of looking directly at the Sun. He disagreed with Brahe's conclusion that total eclipses of the Sun were impossible, because there were historical accounts of total eclipses. Instead he deduced that the size of the aperture controls the sharpness of the projected image (the larger the aperture, the more accurate the image – this fact is now fundamental for optical system design). Voelkel, p. 61, notes that Kepler's experiments produced the first correct account of vision and the eye, because he realized he could not accurately write about astronomical observation by ignoring the eye.

di Francia 1976, p. 13: "The amazing point is that for the first time since the discovery of mathematics, a method has been introduced, the results of which have an intersubjective value!" (Author's punctuation)
di Francia 1976, pp. 4–5: "One learns in a laboratory; one learns how to make experiments only by experimenting, and one learns how to work with his hands only by using them. The first and fundamental form of experimentation in physics is to teach young people to work with their hands. Then they should be taken into a laboratory and taught to work with measuring instruments – each student carrying out real experiments in physics. This form of teaching is indispensable and cannot be read in a book."
Fara 2009, p. 204: "Whatever their discipline, scientists claimed to share a common scientific method that ... distinguished them from non-scientists."
This realization is the topic of intersubjective verifiability, as recounted, for example, by Max Born (1949, 1965) Natural Philosophy of Cause and Chance, who points out that all knowledge, including natural or social science, is also subjective. p. 162: "Thus it dawned upon me that fundamentally everything is subjective, everything without exception. That was a shock."
In his investigation of the law of falling bodies, Galileo (1638) serves as example for scientific investigation: Two New Sciences "A piece of wooden moulding or scantling, about 12 cubits long, half a cubit wide, and three finger-breadths thick, was taken; on its edge was cut a channel a little more than one finger in breadth; having made this groove very straight, smooth, and polished, and having lined it with parchment, also as smooth and polished as possible, we rolled along it a hard, smooth, and very round bronze ball. Having placed this board in a sloping position, by lifting one end some one or two cubits above the other, we rolled the ball, as I was just saying, along the channel, noting, in a manner presently to be described, the time required to make the descent. We ... now rolled the ball only one-quarter the length of the channel; and having measured the time of its descent, we found it precisely one-half of the former. Next we tried other distances, comparing the time for the whole length with that for the half, or with that for two-thirds, or three-fourths, or indeed for any fraction; in such experiments, repeated many, many, times." Galileo solved the problem of time measurement by weighing a jet of water collected during the descent of the bronze ball, as stated in his Two New Sciences.
Godfrey-Smith 2003, p. 151 credits Willard Van Orman Quine (1969) "Epistemology Naturalized" Ontological Relativity and Other Essays New York: Columbia University Press, as well as John Dewey, with the basic ideas of naturalism – Naturalized Epistemology, but Godfrey-Smith diverges from Quine's position: according to Godfrey-Smith, "A naturalist can think that science can contribute to answers to philosophical questions, without thinking that philosophical questions can be replaced by science questions.".
"No amount of experimentation can ever prove me right; a single experiment can prove me wrong." —Albert Einstein, noted by Alice Calaprice (ed. 2005) The New Quotable Einstein Princeton University Press and Hebrew University of Jerusalem, ISBN 0-691-12074-9 p. 291. Calaprice denotes this not as an exact quotation, but as a paraphrase of a translation of A. Einstein's "Induction and Deduction". Collected Papers of Albert Einstein 7 Document 28. Volume 7 is The Berlin Years: Writings, 1918–1921. A. Einstein; M. Janssen, R. Schulmann, et al., eds.
Fleck, Ludwik (1979). Trenn, Thaddeus J.; Merton, Robert K, eds. Genesis and Development of a Scientific Fact. Chicago: University of Chicago Press. ISBN 978-0-226-25325-1. Claims that before a specific fact "existed", it had to be created as part of a social agreement within a community. Steven Shapin (1980) "A view of scientific thought" Science ccvii (Mar 7, 1980) 1065–66 states "[To Fleck,] facts are invented, not discovered. Moreover, the appearance of scientific facts as discovered things is itself a social construction: a made thing. "
"Pseudoscientific – pretending to be scientific, falsely represented as being scientific", from the Oxford American Dictionary, published by the Oxford English Dictionary; Hansson, Sven Ove (1996)."Defining Pseudoscience", Philosophia Naturalis, 33: 169–76, as cited in "Science and Pseudo-science" (2008) in Stanford Encyclopedia of Philosophy. The Stanford article states: "Many writers on pseudoscience have emphasized that pseudoscience is non-science posing as science. The foremost modern classic on the subject (Gardner 1957) bears the title Fads and Fallacies in the Name of Science. According to Brian Baigrie (1988, 438), "[w]hat is objectionable about these beliefs is that they masquerade as genuinely scientific ones." These and many other authors assume that to be pseudoscientific, an activity or a teaching has to satisfy the following two criteria (Hansson 1996): (1) it is not scientific, and (2) its major proponents try to create the impression that it is scientific".

For example, Hewitt et al. Conceptual Physical Science Addison Wesley; 3 edition (July 18, 2003) ISBN 0-321-05173-4, Bennett et al. The Cosmic Perspective 3e Addison Wesley; 3 edition (July 25, 2003) ISBN 0-8053-8738-2; See also, e.g., Gauch HG Jr. Scientific Method in Practice (2003). A 2006 National Science Foundation report on Science and engineering indicators quoted Michael Shermer's (1997) definition of pseudoscience: '"claims presented so that they appear [to be] scientific even though they lack supporting evidence and plausibility" (p. 33). In contrast, science is "a set of methods designed to describe and interpret observed and inferred phenomena, past or present, and aimed at building a testable body of knowledge open to rejection or confirmation" (p. 17)'.Shermer M. (1997). Why People Believe Weird Things: Pseudoscience, Superstition, and Other Confusions of Our Time. New York: W. H. Freeman and Company. ISBN 978-0-7167-3090-3. as cited by National Science Board. National Science Foundation, Division of Science Resources Statistics (2006). "Science and Technology: Public Attitudes and Understanding". Science and engineering indicators 2006. Archived from the original on February 1, 2013. "A pretended or spurious science; a collection of related beliefs about the world mistakenly regarded as being based on scientific method or as having the status that scientific truths now have," from the Oxford English Dictionary, second edition 1989.

Evicting Einstein, March 26, 2004, NASA. "Both [relativity and quantum mechanics] are extremely successful. The Global Positioning System (GPS), for instance, wouldn't be possible without the theory of relativity. Computers, telecommunications, and the Internet, meanwhile, are spin-offs of quantum mechanics."
Women in science have included:

Hypatia (c. 350–415 CE), of the Library of Alexandria. Trotula of Salerno, a physician c. 1060 CE. Caroline Herschel, one of the first professional astronomers of the 18th and 19th centuries. Christine Ladd-Franklin, a doctoral student of C.S. Peirce, who published Wittgenstein's proposition 5.101 in her dissertation, 40 years before Wittgenstein's publication of Tractatus Logico-Philosophicus. Henrietta Leavitt, a professional human computer and astronomer, who first published the significant relationship between the luminosity of Cepheid variable stars and their distance from Earth. This allowed Hubble to make the discovery of the expanding universe, which led to the Big Bang theory. Emmy Noether, who proved the conservation of energy and other constants of motion in 1915. Marie Curie, who made discoveries relating to radioactivity along with her husband, and for whom Curium is named. Rosalind Franklin, who worked with X-ray diffraction. Jocelyn Bell Burnell, at first not allowed to study science in her preparatory school, persisted, and was the first to observe and precisely analyse the radio pulsars, for which her supervisor was recognized by the 1974 Nobel prize in Physics. (Later awarded a Special Breakthough prize in Physics in 2018, she donated the cash award in order that women, ethnic minority, and refugee students might become physics researchers.) In 2018 Donna Strickland became the third woman (the second being Maria Goeppert-Mayer in 1962) to be awarded the Nobel Prize in Physics, for her work in chirped pulse amplification of lasers. Frances H. Arnold became the fifth woman to be awarded the Nobel Prize in Chemistry for the directed evolution of enzymes. See the project of Jess Wade (Christina Zdanowicz (27 July 2018), CNN A physicist is writing one Wikipedia entry a day to recognize women in science )

Nina Byers, Contributions of 20th Century Women to Physics which provides details on 83 female physicists of the 20th century. By 1976, more women were physicists, and the 83 who were detailed were joined by other women in noticeably larger numbers.

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Sources Crease, Robert P. (2009). The Great Equations. New York: W.W. Norton. ISBN 978-0-393-06204-5. di Francia, Giuliano Toraldo (1976). The Investigation of the Physical World. Originally published in Italian as L'Indagine del Mondo Fisico by Giulio Einaudi editore 1976; first published in English by Cambridge University Press 1981. Cambridge: Cambridge University Press. ISBN 978-0-521-29925-1. Fara, Patricia (2009). Science : a four thousand year history. Oxford: Oxford University Press. p. 408. ISBN 978-0-19-922689-4. Feyerabend, Paul (1993). Against Method (3rd ed.). London: Verso. ISBN 978-0-86091-646-8. Godfrey-Smith, Peter (2003). Theory and Reality. Chicago 60637: University of Chicago. p. 272. ISBN 978-0-226-30062-7. Heilbron, J.L. (editor-in-chief) (2003). The Oxford Companion to the History of Modern Science. New York: Oxford University Press. ISBN 978-0-19-511229-0. Lindberg, David C. (2007). The beginnings of Western science: the European Scientific tradition in philosophical, religious, and institutional context (Second ed.). Chicago: Univ. of Chicago Press. ISBN 978-0-226-48205-7. Nola, Robert; Irzik, Gürol (2005). Philosophy, science, education and culture. Science & technology education library. 28. Springer. ISBN 978-1-4020-3769-6. Polanyi, Michael (1958). Personal Knowledge: Towards a Post-Critical Philosophy. University of Chicago Press. ISBN 978-0-226-67288-5. Popper, Karl Raimund (1996) [1984]. In search of a better world: lectures and essays from thirty years. New York: Routledge. New York, NY. Bibcode:1992sbwl.book.....P. ISBN 978-0-415-13548-1. Popper, Karl R. (2002) [1959]. The Logic of Scientific Discovery. New York, NY: Routledge Classics. ISBN 978-0-415-27844-7. OCLC 59377149. Stanovich, Keith E. (2007). How to Think Straight About Psychology. Boston: Pearson Education. ISBN 978-0-205-68590-5. Ziman, John (1978). Reliable knowledge: An exploration of the grounds for belief in science. Cambridge: Cambridge University Press. p. 197. ISBN 978-0-521-22087-3. Further reading Augros, Robert M., Stanciu, George N., The New Story of Science: mind and the universe, Lake Bluff, Ill.: Regnery Gateway, c1984. ISBN 0-89526-833-7 Becker, Ernest (1968). The structure of evil; an essay on the unification of the science of man. New York: G. Braziller. Burguete, Maria, and Lam, Lui, eds.(2014). All About Science: Philosophy, History, Sociology & Communication. World Scientific: Singapore. ISBN 978-981-4472-92-0 Cole, K.C., Things your teacher never told you about science: Nine shocking revelations Newsday, Long Island, New York, March 23, 1986, pp. 21+ Crease, Robert P. (2011). World in the Balance: the historic quest for an absolute system of measurement. New York: W.W. Norton. p. 317. ISBN 978-0-393-07298-3. Feyerabend, Paul (2005). Science, history of the philosophy, as cited in Honderich, Ted (2005). The Oxford companion to philosophy. Oxford Oxfordshire: Oxford University Press. ISBN 978-0-19-926479-7. OCLC 173262485. Feynman, Richard P. (1999). Robbins, Jeffrey, ed. The pleasure of finding things out the best short works of Richard P. Feynman. Cambridge, Massachusetts: Perseus Books. ISBN 978-0465013128. Feynman, R.P. (1999). The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman. Perseus Books Group. ISBN 978-0-465-02395-0. OCLC 181597764. Feynman, Richard "Cargo Cult Science" Gaukroger, Stephen (2006). The Emergence of a Scientific Culture: Science and the Shaping of Modernity 1210–1685. Oxford: Oxford University Press. ISBN 978-0-19-929644-6. Gopnik, Alison, "Finding Our Inner Scientist", Daedalus, Winter 2004. Krige, John, and Dominique Pestre, eds., Science in the Twentieth Century, Routledge 2003, ISBN 0-415-28606-9 Levin, Yuval (2008). Imagining the Future: Science and American Democracy. New York, Encounter Books. ISBN 1-59403-209-2 Lindberg, D.C. (1976). Theories of Vision from al-Kindi to Kepler. Chicago: University of Chicago Press. Kuhn, Thomas, The Structure of Scientific Revolutions, 1962. William F., McComas (1998). "The principal elements of the nature of science: Dispelling the myths" (PDF). In McComas, William F. The nature of science in science education: rationales and strategies. Springer. ISBN 978-0-7923-6168-8. Needham, Joseph (1954). "Science and Civilisation in China: Introductory Orientations". 1. Cambridge University Press. Obler, Paul C.; Estrin, Herman A. (1962). The New Scientist: Essays on the Methods and Values of Modern Science. Anchor Books, Doubleday. Papineau, David. (2005). Science, problems of the philosophy of., as cited in Honderich, Ted (2005). The Oxford companion to philosophy. Oxford Oxfordshire: Oxford University Press. ISBN 978-0-19-926479-7. OCLC 173262485. Parkin, D. (1991). "Simultaneity and Sequencing in the Oracular Speech of Kenyan Diviners". In Philip M. Peek. African Divination Systems: Ways of Knowing. Indianapolis, IN: Indiana University Press. Russell, Bertrand (1985) [1952]. The Impact of Science on Society. London: Unwin. ISBN 978-0-04-300090-8. Rutherford, F. James; Ahlgren, Andrew (1990). Science for all Americans. New York, NY: American Association for the Advancement of Science, Oxford University Press. ISBN 978-0-19-506771-2. Smith, A. Mark (2001). Written at Philadelphia. Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's De Aspectibus, the Medieval Latin Version of Ibn al-Haytham's Kitāb al-Manāẓir, 2 vols. Transactions of the American Philosophical Society. 91. Philadelphia: American Philosophical Society. ISBN 978-0-87169-914-5. OCLC 47168716. Smith, A. Mark (2001). "Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's "De aspectibus", the Medieval Latin Version of Ibn al-Haytham's "Kitāb al-Manāẓir": Volume One". Transactions of the American Philosophical Society. 91 (4): i–337. JSTOR 3657358. Smith, A. Mark (2001). "Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's "De aspectibus", the Medieval Latin Version of Ibn al-Haytham's "Kitāb al-Manāẓir": Volume Two". Transactions of the American Philosophical Society. 91 (5): 339–819. JSTOR 3657357. Thurs, Daniel Patrick (2007). Science Talk: Changing Notions of Science in American Popular Culture. ISBN 978-0-8135-4073-3. 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Jump to navigationJump to search This article is about the study of topics such as quantity and structure. For other uses, see Mathematics (disambiguation). "Math" redirects here. For other uses, see Math (disambiguation).

Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[a] Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity,[1] structure,[2] space,[1] and change.[3][4][5]

Mathematicians seek and use patterns[6][7] to formulate new conjectures; they resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.[8]

Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake) without having any application in mind, but practical applications for what began as pure mathematics are often discovered later.[9][10]

Contents 1 History 1.1 Etymology 2 Definitions of mathematics 2.1 Mathematics as science 3 Inspiration, pure and applied mathematics, and aesthetics 4 Notation, language, and rigor 5 Fields of mathematics 5.1 Foundations and philosophy 5.2 Pure mathematics 5.3 Applied mathematics 6 Mathematical awards 7 See also 8 Notes 9 Footnotes 10 References 11 Further reading History Main article: History of mathematics

The Babylonian mathematical tablet Plimpton 322, dated to 1800 BC.

Archimedes used the method of exhaustion to approximate the value of pi.

The numerals used in the Bakhshali manuscript, dated between the 2nd century BCE and the 2nd century CE. The history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, which is shared by many animals,[11] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.

As evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also recognized how to count abstract quantities, like time – days, seasons, years.[12]

Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[13] The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. It is in Babylonian mathematics that elementary arithmetic (addition, subtraction, multiplication and division) first appear in the archaeological record. The Babylonians also possessed a place-value system, and used a sexagesimal numeral system, still in use today for measuring angles and time.[14]

Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics.[15] Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof. His textbook Elements is widely considered the most successful and influential textbook of all time.[16] The greatest mathematician of antiquity is often held to be Archimedes (c. 287–212 BC) of Syracuse.[17] He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.[18] Other notable achievements of Greek mathematics are conic sections (Apollonius of Perga, 3rd century BC),[19] trigonometry (Hipparchus of Nicaea (2nd century BC),[20] and the beginnings of algebra (Diophantus, 3rd century AD).[21]

The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, and an early form of infinite series.

A page from al-Khwārizmī's Algebra During the Golden Age of Islam, especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī.

During the early modern period, mathematics began to develop at an accelerating pace in Western Europe. The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries. Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, analysis, differential geometry, matrix theory,number theory, and statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system that is consistent will contain unprovable propositions.

Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."[22]

Etymology The word mathematics comes from Ancient Greek μάθημα (máthēma), meaning "that which is learnt",[23] "what one gets to know", hence also "study" and "science". The word for "mathematics" came to have the narrower and more technical meaning "mathematical study" even in Classical times.[24] Its adjective is μαθηματικός (mathēmatikós), meaning "related to learning" or "studious", which likewise further came to mean "mathematical". In particular, μαθηματικὴ τέχνη (mathēmatikḗ tékhnē), Latin: ars mathematica, meant "the mathematical art".

Similarly, one of the two main schools of thought in Pythagoreanism was known as the mathēmatikoi (μαθηματικοί)—which at the time meant "teachers" rather than "mathematicians" in the modern sense.

In Latin, and in English until around 1700, the term mathematics more commonly meant "astrology" (or sometimes "astronomy") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This has resulted in several mistranslations. For example, Saint Augustine's warning that Christians should beware of mathematici, meaning astrologers, is sometimes mistranslated as a condemnation of mathematicians.[25]

The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural τὰ μαθηματικά (ta mathēmatiká), used by Aristotle (384–322 BC), and meaning roughly "all things mathematical"; although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, which were inherited from Greek.[26] In English, the noun mathematics takes a singular verb. It is often shortened to maths or, in North America, math.[27]

Definitions of mathematics Main article: Definitions of mathematics

Leonardo Fibonacci, the Italian mathematician who introduced the Hindu–Arabic numeral system invented between the 1st and 4th centuries by Indian mathematicians, to the Western World Mathematics has no generally accepted definition.[28][29] Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century.[30] Galileo Galilei (1564–1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth."[31] Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences".[32] Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions".[33] David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise."[34] Albert Einstein (1879–1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[35]

Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions.[36] Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals.[28] There is not even consensus on whether mathematics is an art or a science.[29] A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable.[28] Some just say, "Mathematics is what mathematicians do."[28]

Three leading types of definition of mathematics are called logicist, intuitionist, and formalist, each reflecting a different philosophical school of thought.[37] All have severe problems, none has widespread acceptance, and no reconciliation seems possible.[37]

An early definition of mathematics in terms of logic was Benjamin Peirce's "the science that draws necessary conclusions" (1870).[38] In the Principia Mathematica, Bertrand Russell and Alfred North Whitehead advanced the philosophical program known as logicism, and attempted to prove that all mathematical concepts, statements, and principles can be defined and proved entirely in terms of symbolic logic. A logicist definition of mathematics is Russell's "All Mathematics is Symbolic Logic" (1903).[39]

Intuitionist definitions, developing from the philosophy of mathematician L. E. J. Brouwer, identify mathematics with certain mental phenomena. An example of an intuitionist definition is "Mathematics is the mental activity which consists in carrying out constructs one after the other."[37] A peculiarity of intuitionism is that it rejects some mathematical ideas considered valid according to other definitions. In particular, while other philosophies of mathematics allow objects that can be proved to exist even though they cannot be constructed, intuitionism allows only mathematical objects that one can actually construct.

Formalist definitions identify mathematics with its symbols and the rules for operating on them. Haskell Curry defined mathematics simply as "the science of formal systems".[40] A formal system is a set of symbols, or tokens, and some rules telling how the tokens may be combined into formulas. In formal systems, the word axiom has a special meaning, different from the ordinary meaning of "a self-evident truth". In formal systems, an axiom is a combination of tokens that is included in a given formal system without needing to be derived using the rules of the system.

Mathematics as science

Carl Friedrich Gauss, known as the prince of mathematicians The German mathematician Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences".[32] More recently, Marcus du Sautoy has called mathematics "the Queen of Science ... the main driving force behind scientific discovery".[41] In the original Latin Regina Scientiarum, as well as in German Königin der Wissenschaften, the word corresponding to science means a "field of knowledge", and this was the original meaning of "science" in English, also; mathematics is in this sense a field of knowledge. The specialization restricting the meaning of "science" to natural science follows the rise of Baconian science, which contrasted "natural science" to scholasticism, the Aristotelean method of inquiring from first principles. The role of empirical experimentation and observation is negligible in mathematics, compared to natural sciences such as biology, chemistry, or physics. Albert Einstein stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[35]

Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper.[42] However, in the 1930s Gödel's incompleteness theorems convinced many mathematicians[who?] that mathematics cannot be reduced to logic alone, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."[43] Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself.[44][45]

An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. Mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences. Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics.

The opinions of mathematicians on this matter are varied. Many mathematicians[46] feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts; others[who?] feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering has driven much development in mathematics. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created (as in art) or discovered (as in science). It is common to see universities divided into sections that include a division of Science and Mathematics, indicating that the fields are seen as being allied but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is one of many issues considered in the philosophy of mathematics.[citation needed]

Inspiration, pure and applied mathematics, and aesthetics Main article: Mathematical beauty Isaac Newton Gottfried Wilhelm von Leibniz Isaac Newton (left) and Gottfried Wilhelm Leibniz developed infinitesimal calculus. Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement, architecture and later astronomy; today, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. For example, the physicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.[47]

Some mathematics is relevant only in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. A distinction is often made between pure mathematics and applied mathematics. However pure mathematics topics often turn out to have applications, e.g. number theory in cryptography. This remarkable fact, that even the "purest" mathematics often turns out to have practical applications, is what Eugene Wigner has called "the unreasonable effectiveness of mathematics".[10] As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages.[48] Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science.

For those who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. He identified criteria such as significance, unexpectedness, inevitability, and economy as factors that contribute to a mathematical aesthetic.[49] Mathematical research often seeks critical features of a mathematical object. A theorem expressed as a characterization of the object by these features is the prize. Examples of particularly succinct and revelatory mathematical arguments has been published in Proofs from THE BOOK.

The popularity of recreational mathematics is another sign of the pleasure many find in solving mathematical questions. And at the other social extreme, philosophers continue to find problems in philosophy of mathematics, such as the nature of mathematical proof.[50]

Notation, language, and rigor Main article: Mathematical notation

Leonhard Euler created and popularized much of the mathematical notation used today. Most of the mathematical notation in use today was not invented until the 16th century.[51] Before that, mathematics was written out in words, limiting mathematical discovery.[52] Euler (1707–1783) was responsible for many of the notations in use today. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. According to Barbara Oakley, this can be attributed to the fact that mathematical ideas are both more abstract and more encrypted than those of natural language.[53] Unlike natural language, where people can often equate a word (such as cow) with the physical object it corresponds to, mathematical symbols are abstract, lacking any physical analog.[54] Mathematical symbols are also more highly encrypted than regular words, meaning a single symbol can encode a number of different operations or ideas.[55]

Mathematical language can be difficult to understand for beginners because even common terms, such as or and only, have a more precise meaning than they have in everyday speech, and other terms such as open and field refer to specific mathematical ideas, not covered by their laymen's meanings. Mathematical language also includes many technical terms such as homeomorphism and integrable that have no meaning outside of mathematics. Additionally, shorthand phrases such as iff for "if and only if" belong to mathematical jargon. There is a reason for special notation and technical vocabulary: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".

This is a good article. Follow the link for more information. Page semi-protected English language From Wikipedia, the free encyclopedia Jump to navigationJump to search For other uses, see English (disambiguation). English Pronunciation /ˈɪŋɡlɪʃ/[1] Region Worldwide Native speakers 360–400 million (2006)[2] L2 speakers: 400 million; as a foreign language: 600–700 million[2] Language family Indo-European Germanic West Germanic Anglo-Frisian Anglic English Early forms Old English Middle English Early Modern English Writing system Latin script (English alphabet) Anglo Saxon runes (Historically) English Braille, Unified English Braille Signed forms Manually coded English (multiple systems) Official status Official language in 67 countries 27 non-sovereign entities Various organisations[show] Language codes ISO 639-1 en ISO 639-2 eng ISO 639-3 eng Glottolog stan1293[3] Linguasphere 52-ABA Anglospeak.png

 Areas where English is a majority native language
 Areas where English is official but not a majority native language

This article contains IPA phonetic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Unicode characters. For a guide to IPA symbols, see Help:IPA. Part of a series on The English language Topics English language English-speaking world English as a second language History of English Advanced topics English as a world language English as a lingua franca European language Modern English Phonology Phonological history of English English phonology Dialects English American Anguillan Antiguan Australian Bahamian Bajan Bay Islands Belizean Bermudian Brunei Burmese Cameroonian Canadian Caribbean Guyanese Ghanaian Indian Irish Jamaican Kenyan Liberian Malawian Malaysian Manx Namlish Nepali New Zealand Nigerian Pakistani Philippine San Andrés–Providencia Scottish Singapore South African South Atlantic Sri Lankan Trinidadian Ugandan Welsh see also: List of dialects of English Teaching Teaching English as a second language Category:English words and phrases Higher category: Language vte English is a West Germanic language that was first spoken in early medieval England and eventually became a global lingua franca.[4][5] Named after the Angles, one of the Germanic tribes that migrated to the area of Great Britain that would later take their name, England, both names ultimately deriving from the Anglia peninsula in the Baltic Sea. It is closely related to Frisian and Low Saxon, and its vocabulary has been significantly influenced by other Germanic languages, particularly Norse (a North Germanic language), and to a greater extent Latin and French.[6]

English has developed over the course of more than 1,400 years. The earliest forms of English, a set of West Germanic (Ingvaeonic) dialects brought to Great Britain by Anglo-Saxon settlers in the 5th century, are collectively called Old English. Middle English began in the late 11th century with the Norman conquest of England and was a period in which the language was influenced by French.[7] Early Modern English began in the late 15th century with the introduction of the printing press to London, the printing of the King James Bible and the start of the Great Vowel Shift.[8]

Through the worldwide influence of the British Empire, Modern English spread around the world from the 17th to mid-20th centuries. Through all types of printed and electronic media, and spurred by the emergence of the United States as a global superpower, English has become the leading language of international discourse and the lingua franca in many regions and professional contexts such as science, navigation and law.[9]

English is the third most-spoken native language in the world, after Standard Chinese and Spanish.[10] It is the most widely learned second language and is either the official language or one of the official languages in almost 60 sovereign states. There are more people who have learned it as a second language than there are native speakers. English is the most commonly spoken language in the United Kingdom, the United States, Canada, Australia, Ireland and New Zealand, and it is widely spoken in some areas of the Caribbean, Africa and South Asia.[11] It is a co-official language of the United Nations, the European Union and many other world and regional international organisations. It is the most widely spoken Germanic language, accounting for at least 70% of speakers of this Indo-European branch. English has a vast vocabulary, though counting how many words any language has is impossible.[12][13] English speakers are called "Anglophones".

Modern English grammar is the result of a gradual change from a typical Indo-European dependent marking pattern with a rich inflectional morphology and relatively free word order to a mostly analytic pattern with little inflection, a fairly fixed SVO word order and a complex syntax.[14] Modern English relies more on auxiliary verbs and word order for the expression of complex tenses, aspect and mood, as well as passive constructions, interrogatives and some negation. Despite noticeable variation among the accents and dialects of English used in different countries and regions—in terms of phonetics and phonology, and sometimes also vocabulary, grammar and spelling—English-speakers from around the world are able to communicate with one another with relative ease.

Contents 1 Classification 2 History 2.1 Proto-Germanic to Old English 2.2 Middle English 2.3 Early Modern English 2.4 Spread of Modern English 3 Geographical distribution 3.1 Three circles of English-speaking countries 3.2 Pluricentric English 3.3 English as a global language 4 Phonology 4.1 Consonants 4.2 Vowels 4.3 Phonotactics 4.4 Stress, rhythm and intonation 4.5 Regional variation 5 Grammar 5.1 Nouns and noun phrases 5.1.1 Adjectives 5.1.2 Pronouns, case, and person 5.1.3 Prepositions 5.2 Verbs and verb phrases 5.2.1 Tense, aspect and mood 5.2.2 Phrasal verbs 5.2.3 Adverbs 5.3 Syntax 5.3.1 Basic constituent order 5.3.2 Clause syntax 5.3.3 Auxiliary verb constructions 5.3.4 Questions 5.3.5 Discourse level syntax 6 Vocabulary 6.1 Word formation processes 6.2 Word origins 6.3 English loanwords and calques in other languages 7 Writing system 8 Dialects, accents, and varieties 8.1 United Kingdom and Ireland 8.2 North America 8.3 Australia and New Zealand 8.4 Africa, the Caribbean, and South Asia 9 References 10 Bibliography 11 External links Classification

Anglic languages

 English
 Scots

Anglo-Frisian languages Anglic and

 Frisian

North Sea Germanic languages Anglo-Frisian and

 Low German/Low Saxon

West Germanic languages North Sea Germanic and

 Dutch; in Africa: Afrikaans
 German

The West Germanic languages English is an Indo-European language and belongs to the West Germanic group of the Germanic languages.[15] Old English originated from a Germanic tribal and linguistic continuum along the Frisian North Sea coast, whose languages gradually evolved into the Anglic languages on the British Isles, and into the Frisian languages and Low German/Low Saxon on the continent. The Frisian languages, together with which the Anglic languages form the Anglo-Frisian languages, are the closest living relatives of English. Low German/Low Saxon is also closely related, and sometimes English, the Frisian languages, and Low German are grouped together as the Ingvaeonic (North Sea Germanic) languages, though this grouping remains debated.[16] Old English evolved into Middle English, which in turn evolved into Modern English.[17] Particular dialects of Old and Middle English also developed into a number of other Anglic languages, including Scots[18] and the extinct Fingallian and Forth and Bargy (Yola) dialects of Ireland.[19]

Like Icelandic and Faroese, the development of English on the British Isles isolated it from the continental Germanic languages and influences, and has since undergone substantial evolution. English is thus not mutually intelligible with any continental Germanic language, differing in vocabulary, syntax, and phonology, although some, such as Dutch or Frisian, do show strong affinities with English, especially with its earlier stages.[20]

Unlike Icelandic or Faroese, the long history of invasions of the British Isles by other peoples and languages, particularly Old Norse and Norman French, left a profound mark of their own on the language, such that English shares substantial vocabulary and grammar similarities with many languages outside its linguistic clades, while also being unintelligible with any of those languages. Some scholars have even argued that English can be considered a mixed language or a creole—a theory called the Middle English creole hypothesis. Although the high degree of influence from these languages on the vocabulary and grammar of Modern English is widely acknowledged, most specialists in language contact do not consider English to be a true mixed language.[21][22]

English is classified as a Germanic language because it shares innovations with other Germanic languages such as Dutch, German, and Swedish.[23] These shared innovations show that the languages have descended from a single common ancestor called Proto-Germanic. Some shared features of Germanic languages include the division of verbs into strong and weak classes, the use of modal verbs, and the sound changes affecting Proto-Indo-European consonants, known as Grimm's and Verner's laws. English is classified as an Anglo-Frisian language because Frisian and English share other features, such as the palatalisation of consonants that were velar consonants in Proto-Germanic (see Phonological history of Old English § Palatalization).[24]

English: sing, sang, sung; Low German: singen, sung, sungen; Dutch: zingen, zong, gezongen; German: singen, sang, gesungen (strong verb) English: laugh, laughed, laughed; Low German: lachen, lachte, lacht; Dutch: lachen, lachte, gelachen; German: lachen, lachte, gelacht (weak verb) English: I dream, he dreams; Low German: ik drööm, he dröömt; Dutch: ik droom, hij droomt; German: ich träume, er träumt (non-modal verb) English: I shall, he shall; Low German: ik schall, he schall; Dutch: ik zal, hij zal; German: ich soll, er soll (modal verb) English: foot; Low German: Foot; Dutch: voet; German: Fuß; Norwegian and Swedish: fot ("f" and "v" from Proto-Indo-European "p" through Grimm's law) Latin: pes; Greek: πόδι (pódi); Russian: под (pod); Sanskrit: पद् (pád) English: cheese, church; West Frisian: tsiis, tsjerke; ("ch" and "ts" from palatalization) Low German: Keese, Kark; Dutch: kaas, kerk; German: Käse, Kirche ("k" without palatalization) History Main article: History of English Proto-Germanic to Old English Main article: Old English

The opening to the Old English epic poem Beowulf, handwritten in half-uncial script: Hƿæt ƿē Gārde/na ingēar dagum þēod cyninga / þrym ge frunon... "Listen! We of the Spear-Danes from days of yore have heard of the glory of the folk-kings..." The earliest form of English is called Old English or Anglo-Saxon (c. 550–1066 CE). Old English developed from a set of North Sea Germanic dialects originally spoken along the coasts of Frisia, Lower Saxony, Jutland, and Southern Sweden by Germanic tribes known as the Angles, Saxons, and Jutes. In the fifth century, the Anglo-Saxons settled Britain as the Roman economy and administration collapsed. By the seventh century, the Germanic language of the Anglo-Saxons became dominant in Britain, replacing the languages of Roman Britain (43–409 CE): Common Brittonic, a Celtic language, and Latin, brought to Britain by the Roman occupation.[25][26][27] England and English (originally Ænglaland and Ænglisc) are named after the Angles.[28]

Old English was divided into four dialects: the Anglian dialects, Mercian and Northumbrian, and the Saxon dialects, Kentish and West Saxon.[29] Through the educational reforms of King Alfred in the ninth century and the influence of the kingdom of Wessex, the West Saxon dialect became the standard written variety.[30] The epic poem Beowulf is written in West Saxon, and the earliest English poem, Cædmon's Hymn, is written in Northumbrian.[31] Modern English developed mainly from Mercian, but the Scots language developed from Northumbrian. A few short inscriptions from the early period of Old English were written using a runic script.[32] By the sixth century, a Latin alphabet was adopted, written with half-uncial letterforms. It included the runic letters wynn ⟨ƿ⟩ and thorn ⟨þ⟩, and the modified Latin letters eth ⟨ð⟩, and ash ⟨æ⟩.[32][33]

Old English is very different from Modern English and difficult for 21st-century English speakers to understand. Its grammar was similar to that of modern German, and its closest relative is Old Frisian. Nouns, adjectives, pronouns, and verbs had many more inflectional endings and forms, and word order was much freer than in Modern English. Modern English has case forms in pronouns (he, him, his) and a few verb endings (I have, he has), but Old English had case endings in nouns as well, and verbs had more person and number endings.[34][35][36]

The translation of Matthew 8:20 from 1000 CE shows examples of case endings (nominative plural, accusative plural, genitive singular) and a verb ending (present plural):

Foxas habbað holu and heofonan fuglas nest Fox-as habb-að hol-u and heofon-an fugl-as nest-∅ fox-nom.pl have-prs.pl hole-acc.pl and heaven-gen.sg bird-nom.pl nest-acc.pl "Foxes have holes and the birds of heaven nests"[37] Middle English Main articles: Middle English and Influence of French on English Englischmen þeyz hy hadde fram þe bygynnyng þre manner speche, Souþeron, Northeron, and Myddel speche in þe myddel of þe lond, ... Noþeles by comyxstion and mellyng, furst wiþ Danes, and afterward wiþ Normans, in menye þe contray longage ys asperyed, and som vseþ strange wlaffyng, chyteryng, harryng, and garryng grisbytting.

Although, from the beginning, Englishmen had three manners of speaking, southern, northern and midlands speech in the middle of the country, ... Nevertheless, through intermingling and mixing, first with Danes and then with Normans, amongst many the country language has arisen, and some use strange stammering, chattering, snarling, and grating gnashing. John of Trevisa, ca. 1385[38] In the period from the 8th to the 12th century, Old English gradually transformed through language contact into Middle English. Middle English is often arbitrarily defined as beginning with the conquest of England by William the Conqueror in 1066, but it developed further in the period from 1200–1450.

First, the waves of Norse colonisation of northern parts of the British Isles in the 8th and 9th centuries put Old English into intense contact with Old Norse, a North Germanic language. Norse influence was strongest in the Northeastern varieties of Old English spoken in the Danelaw area around York, which was the centre of Norse colonisation; today these features are still particularly present in Scots and Northern English. However the centre of norsified English seems to have been in the Midlands around Lindsey, and after 920 CE when Lindsey was reincorporated into the Anglo-Saxon polity, Norse features spread from there into English varieties that had not been in intense contact with Norse speakers. Some elements of Norse influence that persist in all English varieties today are the pronouns beginning with th- (they, them, their) which replaced the Anglo-Saxon pronouns with h- (hie, him, hera).[39]

With the Norman conquest of England in 1066, the now norsified Old English language was subject to contact with the Old Norman language, a Romance language closely related to Modern French. The Norman language in England eventually developed into Anglo-Norman. Because Norman was spoken primarily by the elites and nobles, while the lower classes continued speaking Anglo-Saxon, the influence of Norman consisted of introducing a wide range of loanwords related to politics, legislation and prestigious social domains.[40] Middle English also greatly simplified the inflectional system, probably in order to reconcile Old Norse and Old English, which were inflectionally different but morphologically similar. The distinction between nominative and accusative case was lost except in personal pronouns, the instrumental case was dropped, and the use of the genitive case was limited to describing possession. The inflectional system regularised many irregular inflectional forms,[41] and gradually simplified the system of agreement, making word order less flexible.[42] By the Wycliffe Bible of the 1380s, the passage Matthew 8:20 was written

Foxis han dennes, and briddis of heuene han nestis[43] Here the plural suffix -n on the verb have is still retained, but none of the case endings on the nouns are present.

By the 12th century Middle English was fully developed, integrating both Norse and Norman features; it continued to be spoken until the transition to early Modern English around 1500. Middle English literature includes Geoffrey Chaucer's The Canterbury Tales, and Malory's Le Morte d'Arthur. In the Middle English period, the use of regional dialects in writing proliferated, and dialect traits were even used for effect by authors such as Chaucer.

Early Modern English Main article: Early Modern English

Graphic representation of the Great Vowel Shift, showing how the pronunciation of the long vowels gradually shifted, with the high vowels i: and u: breaking into diphthongs and the lower vowels each shifting their pronunciation up one level The next period in the history of English was Early Modern English (1500–1700). Early Modern English was characterised by the Great Vowel Shift (1350–1700), inflectional simplification, and linguistic standardisation.

The Great Vowel Shift affected the stressed long vowels of Middle English. It was a chain shift, meaning that each shift triggered a subsequent shift in the vowel system. Mid and open vowels were raised, and close vowels were broken into diphthongs. For example, the word bite was originally pronounced as the word beet is today, and the second vowel in the word about was pronounced as the word boot is today. The Great Vowel Shift explains many irregularities in spelling since English retains many spellings from Middle English, and it also explains why English vowel letters have very different pronunciations from the same letters in other languages.[44][45]

English began to rise in prestige, relative to Norman French, during the reign of Henry V. Around 1430, the Court of Chancery in Westminster began using English in its official documents, and a new standard form of Middle English, known as Chancery Standard, developed from the dialects of London and the East Midlands. In 1476, William Caxton introduced the printing press to England and began publishing the first printed books in London, expanding the influence of this form of English.[46] Literature from the Early Modern period includes the works of William Shakespeare and the translation of the Bible commissioned by King James I. Even after the vowel shift the language still sounded different from Modern English: for example, the consonant clusters /kn ɡn sw/ in knight, gnat, and sword were still pronounced. Many of the grammatical features that a modern reader of Shakespeare might find quaint or archaic represent the distinct characteristics of Early Modern English.[47]

In the 1611 King James Version of the Bible, written in Early Modern English, Matthew 8:20 says:

The Foxes haue holes and the birds of the ayre haue nests[37] This exemplifies the loss of case and its effects on sentence structure (replacement with Subject-Verb-Object word order, and the use of of instead of the non-possessive genitive), and the introduction of loanwords from French (ayre) and word replacements (bird originally meaning "nestling" had replaced OE fugol).

Spread of Modern English By the late 18th century, the British Empire had facilitated the spread of English through its colonies and geopolitical dominance. Commerce, science and technology, diplomacy, art, and formal education all contributed to English becoming the first truly global language. English also facilitated worldwide international communication.[48][9] As England continued to form new colonies, these, in turn, became independent and developed their own norms for how to speak and write the language. English was adopted in North America, India, parts of Africa, Australasia, and many other regions. In the post-colonial period, some of the newly created nations that had multiple indigenous languages opted to continue using English as the official language to avoid the political difficulties inherent in promoting any one indigenous language above the others.[49][50][51] In the 20th century the growing economic and cultural influence of the United States and its status as a superpower following the Second World War has, along with worldwide broadcasting in English by the BBC[52] and other broadcasters, significantly accelerated the spread of the language across the planet.[53][54] By the 21st century, English was more widely spoken and written than any language has ever been.[55]

A major feature in the early development of Modern English was the codification of explicit norms for standard usage, and their dissemination through official media such as public education and state-sponsored publications. In 1755 Samuel Johnson published his A Dictionary of the English Language which introduced a standard set of spelling conventions and usage norms. In 1828, Noah Webster published the American Dictionary of the English language in an effort to establish a norm for speaking and writing American English that was independent from the British standard. Within Britain, non-standard or lower class dialect features were increasingly stigmatised, leading to the quick spread of the prestige varieties among the middle classes.[56]

In terms of grammatical evolution, Modern English has now reached a stage where the loss of case is almost complete (case is now only found in pronouns, such as he and him, she and her, who and whom), and where SVO word-order is mostly fixed.[56] Some changes, such as the use of do-support have become universalised. (Earlier English did not use the word "do" as a general auxiliary as Modern English does; at first it was only used in question constructions where it was not obligatory.[57] Now, do-support with the verb have is becoming increasingly standardised.) The use of progressive forms in -ing, appears to be spreading to new constructions, and forms such as had been being built are becoming more common. Regularisation of irregular forms also slowly continues (e.g. dreamed instead of dreamt), and analytical alternatives to inflectional forms are becoming more common (e.g. more polite instead of politer). British English is also undergoing change under the influence of American English, fuelled by the strong presence of American English in the media and the prestige associated with the US as a world power. [58][59][60]

Geographical distribution

See also: List of territorial entities where English is an official language, Geographical distribution of English speakers, List of countries by English-speaking population, and English-speaking world

Percentage of English native speakers.

Percentage of English speakers by country.

 80–100%
 60–80%
 40–60%
 20–40%
 0–20%
 Not available

As of 2016, 400 million people spoke English as their first language, and 1.1 billion spoke it as a secondary language.[61] English is probably the third largest language by number of native speakers, after Mandarin and Spanish.[10] However, when combining native and non-native speakers it may, depending on the estimate used, be the most commonly spoken language in the world.[55][62][63][64] English is spoken by communities on every continent and on oceanic islands in all the major oceans.[65]

The countries in which English is spoken can be grouped into different categories by how English is used in each country. The "inner circle"[66] countries with many native speakers of English share an international standard of written English and jointly influence speech norms of English around the world. English does not belong to just one country, and it does not belong solely to descendants of English settlers. English is an official language of countries populated by few descendants of native speakers of English. It has also become by far the most important language of international communication when people who share no native language meet anywhere in the world.

Three circles of English-speaking countries Braj Kachru distinguishes countries where English is spoken with a three circles model.[66] In his model, the "inner circle" countries are countries with large communities of native speakers of English, "outer circle" countries have small communities of native speakers of English but widespread use of English as a second language in education or broadcasting or for local official purposes, and "expanding circle" countries are countries where many learners learn English as a foreign language. Kachru bases his model on the history of how English spread in different countries, how users acquire English, and the range of uses English has in each country. The three circles change membership over time.[67]

Braj Kachru's Three Circles of English Braj Kachru's Three Circles of English. Countries with large communities of native speakers of English (the inner circle) include Britain, the United States, Australia, Canada, Ireland, and New Zealand, where the majority speaks English, and South Africa, where a significant minority speaks English. The countries with the most native English speakers are, in descending order, the United States (at least 231 million),[68] the United Kingdom (60 million),[69][70][71] Canada (19 million),[72] Australia (at least 17 million),[73] South Africa (4.8 million),[74] Ireland (4.2 million), and New Zealand (3.7 million).[75] In these countries, children of native speakers learn English from their parents, and local people who speak other languages or new immigrants learn English to communicate in their neighbourhoods and workplaces.[76] The inner-circle countries provide the base from which English spreads to other countries in the world.[67]

Estimates of the number of English speakers who are second language and foreign-language speakers vary greatly from 470 million to more than 1,000 million depending on how proficiency is defined.[11] Linguist David Crystal estimates that non-native speakers now outnumber native speakers by a ratio of 3 to 1.[62] In Kachru's three-circles model, the "outer circle" countries are countries such as the Philippines,[77] Jamaica,[78] India, Pakistan, Singapore,[79] and Nigeria[80][81] with a much smaller proportion of native speakers of English but much use of English as a second language for education, government, or domestic business, and where English is routinely used for school instruction and official interactions with the government.[82]

Those countries have millions of native speakers of dialect continua ranging from an English-based creole to a more standard version of English. They have many more speakers of English who acquire English in the process of growing up through day by day use and listening to broadcasting, especially if they attend schools where English is the medium of instruction. Varieties of English learned by speakers who are not native speakers born to English-speaking parents may be influenced, especially in their grammar, by the other languages spoken by those learners.[76] Most of those varieties of English include words little used by native speakers of English in the inner-circle countries,[76] and they may have grammatical and phonological differences from inner-circle varieties as well. The standard English of the inner-circle countries is often taken as a norm for use of English in the outer-circle countries.[76]

In the three-circles model, countries such as Poland, China, Brazil, Germany, Japan, Indonesia, Egypt, and other countries where English is taught as a foreign language make up the "expanding circle".[83] The distinctions between English as a first language, as a second language, and as a foreign language are often debatable and may change in particular countries over time.[82] For example, in the Netherlands and some other countries of Europe, knowledge of English as a second language is nearly universal, with over 80 percent of the population able to use it,[84] and thus English is routinely used to communicate with foreigners and often in higher education. In these countries, although English is not used for government business, its widespread use puts them at the boundary between the "outer circle" and "expanding circle". English is unusual among world languages in how many of its users are not native speakers but speakers of English as a second or foreign language.[85]

Many users of English in the expanding circle use it to communicate with other people from the expanding circle, so that interaction with native speakers of English plays no part in their decision to use English.[86] Non-native varieties of English are widely used for international communication, and speakers of one such variety often encounter features of other varieties.[87] Very often today a conversation in English anywhere in the world may include no native speakers of English at all, even while including speakers from several different countries.[88]

Pie chart showing the percentage of native English speakers living in "inner circle" English-speaking countries. Native speakers are now substantially outnumbered worldwide by second-language speakers of English (not counted in this chart).

 US (64.3%)
 UK (16.7%)
 Canada (5.3%)
 Australia (4.7%)
 South Africa (1.3%)
 Ireland (1.1%)
 New Zealand (1%)
 Other (5.6%)

Pluricentric English English is a pluricentric language, which means that no one national authority sets the standard for use of the language.[89][90][91][92] But English is not a divided language,[93] despite a long-standing joke originally attributed to George Bernard Shaw that the United Kingdom and the United States are "two countries separated by a common language".[94] Spoken English, for example English used in broadcasting, generally follows national pronunciation standards that are also established by custom rather than by regulation. International broadcasters are usually identifiable as coming from one country rather than another through their accents,[95] but newsreader scripts are also composed largely in international standard written English. The norms of standard written English are maintained purely by the consensus of educated English-speakers around the world, without any oversight by any government or international organisation.[96]

American listeners generally readily understand most British broadcasting, and British listeners readily understand most American broadcasting. Most English speakers around the world can understand radio programmes, television programmes, and films from many parts of the English-speaking world.[97] Both standard and non-standard varieties of English can include both formal or informal styles, distinguished by word choice and syntax and use both technical and non-technical registers.[98]

The settlement history of the English-speaking inner circle countries outside Britain helped level dialect distinctions and produce koineised forms of English in South Africa, Australia, and New Zealand.[99] The majority of immigrants to the United States without British ancestry rapidly adopted English after arrival. Now the majority of the United States population are monolingual English speakers,[100][68] although English has been given official status by only 30 of the 50 state governments of the US.[101][102]

English as a global language See also: Foreign language influences in English and Study of global communication English has ceased to be an "English language" in the sense of belonging only to people who are ethnically English.[103][104] Use of English is growing country-by-country internally and for international communication. Most people learn English for practical rather than ideological reasons.[105] Many speakers of English in Africa have become part of an "Afro-Saxon" language community that unites Africans from different countries.[106]

As decolonisation proceeded throughout the British Empire in the 1950s and 1960s, former colonies often did not reject English but rather continued to use it as independent countries setting their own language policies.[50][51][107] For example, the view of the English language among many Indians has gone from associating it with colonialism to associating it with economic progress, and English continues to be an official language of India.[108] English is also widely used in media and literature, and the number of English language books published annually in India is the third largest in the world after the US and UK.[109] However English is rarely spoken as a first language, numbering only around a couple hundred-thousand people, and less than 5% of the population speak fluent English in India.[110][111] David Crystal claimed in 2004 that, combining native and non-native speakers, India now has more people who speak or understand English than any other country in the world,[112] but the number of English speakers in India is very uncertain, with most scholars concluding that the United States still has more speakers of English than India.[113]

Modern English, sometimes described as the first global lingua franca,[53][114] is also regarded as the first world language.[115][116] English is the world's most widely used language in newspaper publishing, book publishing, international telecommunications, scientific publishing, international trade, mass entertainment, and diplomacy.[116] English is, by international treaty, the basis for the required controlled natural languages[117] Seaspeak and Airspeak, used as international languages of seafaring[118] and aviation.[119] English used to have parity with French and German in scientific research, but now it dominates that field.[120] It achieved parity with French as a language of diplomacy at the Treaty of Versailles negotiations in 1919.[121] By the time of the foundation of the United Nations at the end of World War II, English had become pre-eminent [122] and is now the main worldwide language of diplomacy and international relations.[123] It is one of six official languages of the United Nations.[124] Many other worldwide international organisations, including the International Olympic Committee, specify English as a working language or official language of the organisation.

Many regional international organisations such as the European Free Trade Association, Association of Southeast Asian Nations (ASEAN),[54] and Asia-Pacific Economic Cooperation (APEC) set English as their organisation's sole working language even though most members are not countries with a majority of native English speakers. While the European Union (EU) allows member states to designate any of the national languages as an official language of the Union, in practice English is the main working language of EU organisations.[125]

Although in most countries English is not an official language, it is currently the language most often taught as a foreign language.[53][54] In the countries of the EU, English is the most widely spoken foreign language in nineteen of the twenty-five member states where it is not an official language (that is, the countries other than the UK, Ireland and Malta). In a 2012 official Eurobarometer poll, 38 percent of the EU respondents outside the countries where English is an official language said they could speak English well enough to have a conversation in that language. The next most commonly mentioned foreign language, French (which is the most widely known foreign language in the UK and Ireland), could be used in conversation by 12 percent of respondents.[126]

A working knowledge of English has become a requirement in a number of occupations and professions such as medicine[127] and computing. English has become so important in scientific publishing that more than 80 percent of all scientific journal articles indexed by Chemical Abstracts in 1998 were written in English, as were 90 percent of all articles in natural science publications by 1996 and 82 percent of articles in humanities publications by 1995.[128]

Specialised subsets of English arise spontaneously in international communities, for example, among international business people, as an auxiliary language. This has led some scholars to develop the study of English as an auxiliary language. Globish uses a relatively small subset of English vocabulary (about 1500 words with highest use in international business English) in combination with the standard English grammar. Other examples include Simple English.

The increased use of the English language globally has had an effect on other languages, leading to some English words being assimilated into the vocabularies of other languages. This influence of English has led to concerns about language death,[129] and to claims of linguistic imperialism,[130] and has provoked resistance to the spread of English; however the number of speakers continues to increase because many people around the world think that English provides them with opportunities for better employment and improved lives.[131]

Although some scholars mention a possibility of future divergence of English dialects into mutually unintelligible languages, most think a more likely outcome is that English will continue to function as a koineised language in which the standard form unifies speakers from around the world.[132] English is used as the language for wider communication in countries around the world.[133] Thus English has grown in worldwide use much more than any constructed language proposed as an international auxiliary language, including Esperanto.[134][135]

Phonology Main article: English phonology The phonetics and phonology of the English language differ from one dialect to another, usually without interfering with mutual communication. Phonological variation affects the inventory of phonemes (i.e. speech sounds that distinguish meaning), and phonetic variation consists in differences in pronunciation of the phonemes. [136] This overview mainly describes the standard pronunciations of the United Kingdom and the United States: Received Pronunciation (RP) and General American (GA). (See § Dialects, accents, and varieties, below.)

The phonetic symbols used below are from the International Phonetic Alphabet (IPA).[137][138][139]

Consonants Main article: English phonology § Consonants Most English dialects share the same 24 consonant phonemes. The consonant inventory shown below is valid for California English,[140] and for RP.[141]

Consonant phonemes Labial Dental Alveolar Post- alveolar Palatal Velar Glottal Nasal m n ŋ Stop p b t d tʃ dʒ k ɡ Fricative f v θ ð s z ʃ ʒ h Approximant l ɹ* j w

• Conventionally transcribed /r/.

In the table, when obstruents (stops, affricates, and fricatives) appear in pairs, such as /p b/, /tʃ dʒ/, and /s z/, the first is fortis (strong) and the second is lenis (weak). Fortis obstruents, such as /p tʃ s/ are pronounced with more muscular tension and breath force than lenis consonants, such as /b dʒ z/, and are always voiceless. Lenis consonants are partly voiced at the beginning and end of utterances, and fully voiced between vowels. Fortis stops such as /p/ have additional articulatory or acoustic features in most dialects: they are aspirated [pʰ] when they occur alone at the beginning of a stressed syllable, often unaspirated in other cases, and often unreleased [p̚] or pre-glottalised [ʔp] at the end of a syllable. In a single-syllable word, a vowel before a fortis stop is shortened: thus nip has a noticeably shorter vowel (phonetically, but not phonemically) than nib [nɪˑb̥] (see below).[142]

lenis stops: bin [b̥ɪˑn], about [əˈbaʊt], nib [nɪˑb̥] fortis stops: pin [pʰɪn]; spin [spɪn]; happy [ˈhæpi]; nip [nɪp̚] or [nɪʔp] In RP, the lateral approximant /l/, has two main allophones (pronunciation variants): the clear or plain [l], as in light, and the dark or velarised [ɫ], as in full.[143] GA has dark l in most cases.[144]

clear l: RP light [laɪt] dark l: RP and GA full [fʊɫ], GA light [ɫaɪt] All sonorants (liquids /l, r/ and nasals /m, n, ŋ/) devoice when following a voiceless obstruent, and they are syllabic when following a consonant at the end of a word.[145]

voiceless sonorants: clay [kl̥eɪ̯]; snow RP [sn̥əʊ̯], GA [sn̥oʊ̯] syllabic sonorants: paddle [ˈpad.l̩], button [ˈbʌt.n̩] Vowels Main article: English phonology § Vowels The pronunciation of vowels varies a great deal between dialects and is one of the most detectable aspects of a speaker's accent. The table below lists the vowel phonemes in Received Pronunciation (RP) and General American (GA), with examples of words in which they occur from lexical sets compiled by linguists. The vowels are represented with symbols from the International Phonetic Alphabet; those given for RP are standard in British dictionaries and other publications.[146]

Monophthongs RP GA Word iː i need ɪ bid e ɛ bed æ back ɑː ɑ bra ɒ box ɔ, ɑ cloth ɔː paw uː u food ʊ good ʌ but ɜː ɜr bird ə comma Closing diphthongs RP GA Word eɪ bay əʊ oʊ road aɪ cry aʊ cow ɔɪ boy Centering diphthongs RP GA word ɪə ɪɹ peer eə ɛɹ pair ʊə ʊɹ poor In RP, vowel length is phonemic; long vowels are marked with a triangular colon ⟨ː⟩ in the table above, such as the vowel of need [niːd] as opposed to bid [bɪd]. In GA, vowel length is non-distinctive.

In both RP and GA, vowels are phonetically shortened before fortis consonants in the same syllable, like /t tʃ f/, but not before lenis consonants like /d dʒ v/ or in open syllables: thus, the vowels of rich [rɪtʃ], neat [nit], and safe [seɪ̯f] are noticeably shorter than the vowels of ridge [rɪˑdʒ], need [niˑd], and save [seˑɪ̯v], and the vowel of light [laɪ̯t] is shorter than that of lie [laˑɪ̯]. Because lenis consonants are frequently voiceless at the end of a syllable, vowel length is an important cue as to whether the following consonant is lenis or fortis.[147]

The vowel /ə/ only occurs in unstressed syllables and is more open in quality in stem-final positions.[148][149] Some dialects do not contrast /ɪ/ and /ə/ in unstressed positions, so that rabbit and abbot rhyme and Lenin and Lennon are homophonous, a dialect feature called weak vowel merger.[150] GA /ɜr/ and /ər/ are realised as an r-coloured vowel [ɚ], as in further [ˈfɚðɚ] (phonemically /ˈfɜrðər/), which in RP is realised as [ˈfəːðə] (phonemically /ˈfɜːðə/).[151]

Phonotactics An English syllable includes a syllable nucleus consisting of a vowel sound. Syllable onset and coda (start and end) are optional. A syllable can start with up to three consonant sounds, as in sprint /sprɪnt/, and end with up to four, as in texts /teksts/. This gives an English syllable the following structure, (CCC)V(CCCC) where C represents a consonant and V a vowel; the word strengths /strɛŋkθs/ is thus an example of the most complex syllable possible in English. The consonants that may appear together in onsets or codas are restricted, as is the order in which they may appear. Onsets can only have four types of consonant clusters: a stop and approximant, as in play; a voiceless fricative and approximant, as in fly or sly; s and a voiceless stop, as in stay; and s, a voiceless stop, and an approximant, as in string.[152] Clusters of nasal and stop are only allowed in codas. Clusters of obstruents always agree invoicing, and clusters of sibilants and of plosives with the same point of articulation are prohibited. Furthermore, several consonants have limited distributions: /h/ can only occur in syllable-initial position, and /ŋ/ only in syllable-final position.[153]

Stress, rhythm and intonation See also: Stress and vowel reduction in English and Intonation in English Stress plays an important role in English. Certain syllables are stressed, while others are unstressed. Stress is a combination of duration, intensity, vowel quality, and sometimes changes in pitch. Stressed syllables are pronounced longer and louder than unstressed syllables, and vowels in unstressed syllables are frequently reduced while vowels in stressed syllables are not.[154] Some words, primarily short function words but also some modal verbs such as can, have weak and strong forms depending on whether they occur in stressed or non-stressed position within a sentence.

Stress in English is phonemic, and some pairs of words are distinguished by stress. For instance, the word contract is stressed on the first syllable (/ˈkɒntrækt/ KON-trakt) when used as a noun, but on the last syllable (/kənˈtrækt/ kən-TRAKT) for most meanings (for example, "reduce in size") when used as a verb.[155][156][157] Here stress is connected to vowel reduction: in the noun "contract" the first syllable is stressed and has the unreduced vowel /ɒ/, but in the verb "contract" the first syllable is unstressed and its vowel is reduced to /ə/. Stress is also used to distinguish between words and phrases, so that a compound word receives a single stress unit, but the corresponding phrase has two: e.g. a burnout (/ˈbɜːrnaʊt/) versus to burn out (/ˈbɜːrn ˈaʊt/), and a hotdog (/ˈhɒtdɒɡ/) versus a hot dog (/ˈhɒt ˈdɒɡ/).[158]

In terms of rhythm, English is generally described as a stress-timed language, meaning that the amount of time between stressed syllables tends to be equal. Stressed syllables are pronounced longer, but unstressed syllables (syllables between stresses) are shortened. Vowels in unstressed syllables are shortened as well, and vowel shortening causes changes in vowel quality: vowel reduction.

Regional variation Varieties of Standard English and their features[159] Dialects and low vowels Lexical set RP GA Can Sound change THOUGHT /ɔː/ /ɔ/ or /ɑ/ /ɑ/ cot–caught merger CLOTH /ɒ/ lot–cloth split LOT /ɑ/ father–bother merger PALM /ɑː/ BATH /æ/ /æ/ trap–bath split TRAP /æ/ Varieties of English vary the most in pronunciation of vowels. The best known national varieties used as standards for education in non English-speaking countries are British (BrE) and American (AmE). Countries such as Canada, Australia, Ireland, New Zealand and South Africa have their own standard varieties which are less often used as standards for education internationally. Some differences between the various dialects are shown in the table "Varieties of Standard English and their features".[159]

English has undergone many historical sound changes, some of them affecting all varieties, and others affecting only a few. Most standard varieties are affected by the Great Vowel Shift, which changed the pronunciation of long vowels, but a few dialects have slightly different results. In North America, a number of chain shifts such as the Northern Cities Vowel Shift and Canadian Shift have produced very different vowel landscapes in some regional accents.

Some dialects have fewer or more consonant phonemes and phones than the standard varieties. Some conservative varieties like Scottish English have a voiceless [ʍ] sound in whine that contrasts with the voiced [w] in wine, but most other dialects pronounce both words with voiced [w], a dialect feature called wine–whine merger. The unvoiced velar fricative sound /x/ is found in Scottish English, which distinguishes loch /lɔx/ from lock /lɔk/. Accents like Cockney with "h-dropping" lack the glottal fricative /h/, and dialects with th-stopping and th-fronting like African American Vernacular and Estuary English do not have the dental fricatives /θ, ð/, but replace them with dental or alveolar stops /t, d/ or labiodental fricatives /f, v/.[160][161] Other changes affecting the phonology of local varieties are processes such as yod-dropping, yod-coalescence, and reduction of consonant clusters.

General American and Received Pronunciation vary in their pronunciation of historical /r/ after a vowel at the end of a syllable (in the syllable coda). GA is a rhotic dialect, meaning that it pronounces /r/ at the end of a syllable, but RP is non-rhotic, meaning that it loses /r/ in that position. English dialects are classified as rhotic or non-rhotic depending on whether they elide /r/ like RP or keep it like GA.[162]

There is complex dialectal variation in words with the open front and open back vowels /æ ɑː ɒ ɔː/. These four vowels are only distinguished in RP, Australia, New Zealand and South Africa. In GA, these vowels merge to three /æ ɑ ɔ/,[163] and in Canadian English, they merge to two /æ ɑ/.[164] In addition, the words that have each vowel vary by dialect. The table "Dialects and open vowels" shows this variation with lexical sets in which these sounds occur.

Grammar Main article: English grammar As is typical of an Indo-European language, English follows accusative morphosyntactic alignment. Unlike other Indo-European languages though, English has largely abandoned the inflectional case system in favor of analytic constructions. Only the personal pronouns retain morphological case more strongly than any other word class. English distinguishes at least seven major word classes: verbs, nouns, adjectives, adverbs, determiners (including articles), prepositions, and conjunctions. Some analyses add pronouns as a class separate from nouns, and subdivide conjunctions into subordinators and coordinators, and add the class of interjections.[165] English also has a rich set of auxiliary verbs, such as have and do, expressing the categories of mood and aspect. Questions are marked by do-support, wh-movement (fronting of question words beginning with wh-) and word order inversion with some verbs.

Some traits typical of Germanic languages persist in English, such as the distinction between irregularly inflected strong stems inflected through ablaut (i.e. changing the vowel of the stem, as in the pairs speak/spoke and foot/feet) and weak stems inflected through affixation (such as love/loved, hand/hands). Vestiges of the case and gender system are found in the pronoun system (he/him, who/whom) and in the inflection of the copula verb to be.

The seven word classes are exemplified in this sample sentence:[166]

The chairman of the committee and the loquacious politician clashed violently when the meeting started. Det. Noun Prep. Det. Noun Conj. Det. Adj. Noun Verb Advb. Conj. Det. Noun Verb Nouns and noun phrases English nouns are only inflected for number and possession. New nouns can be formed through derivation or compounding. They are semantically divided into proper nouns (names) and common nouns. Common nouns are in turn divided into concrete and abstract nouns, and grammatically into count nouns and mass nouns.[167]

Most count nouns are inflected for plural number through the use of the plural suffix -s, but a few nouns have irregular plural forms. Mass nouns can only be pluralised through the use of a count noun classifier, e.g. one loaf of bread, two loaves of bread.[168]

Regular plural formation:

Singular: cat, dog Plural: cats, dogs Irregular plural formation:

Singular: man, woman, foot, fish, ox, knife, mouse Plural: men, women, feet, fish, oxen, knives, mice Possession can be expressed either by the possessive enclitic -s (also traditionally called a genitive suffix), or by the preposition of. Historically the -s possessive has been used for animate nouns, whereas the of possessive has been reserved for inanimate nouns. Today this distinction is less clear, and many speakers use -s also with inanimates. Orthographically the possessive -s is separated from the noun root with an apostrophe.

Possessive constructions:

With -s: The woman's husband's child With of: The child of the husband of the woman Nouns can form noun phrases (NPs) where they are the syntactic head of the words that depend on them such as determiners, quantifiers, conjunctions or adjectives.[169] Noun phrases can be short, such as the man, composed only of a determiner and a noun. They can also include modifiers such as adjectives (e.g. red, tall, all) and specifiers such as determiners (e.g. the, that). But they can also tie together several nouns into a single long NP, using conjunctions such as and, or prepositions such as with, e.g. the tall man with the long red trousers and his skinny wife with the spectacles (this NP uses conjunctions, prepositions, specifiers, and modifiers). Regardless of length, an NP functions as a syntactic unit. For example, the possessive enclitic can, in cases which do not lead to ambiguity, follow the entire noun phrase, as in The President of India's wife, where the enclitic follows India and not President.

The class of determiners is used to specify the noun they precede in terms of definiteness, where the marks a definite noun and a or an an indefinite one. A definite noun is assumed by the speaker to be already known by the interlocutor, whereas an indefinite noun is not specified as being previously known. Quantifiers, which include one, many, some and all, are used to specify the noun in terms of quantity or number. The noun must agree with the number of the determiner, e.g. one man (sg.) but all men (pl.). Determiners are the first constituents in a noun phrase.[170]

Adjectives Adjectives modify a noun by providing additional information about their referents. In English, adjectives come before the nouns they modify and after determiners.[171] In Modern English, adjectives are not inflected, and they do not agree in form with the noun they modify, as adjectives in most other Indo-European languages do. For example, in the phrases the slender boy, and many slender girls, the adjective slender does not change form to agree with either the number or gender of the noun.

Some adjectives are inflected for degree of comparison, with the positive degree unmarked, the suffix -er marking the comparative, and -est marking the superlative: a small boy, the boy is smaller than the girl, that boy is the smallest. Some adjectives have irregular comparative and superlative forms, such as good, better, and best. Other adjectives have comparatives formed by periphrastic constructions, with the adverb more marking the comparative, and most marking the superlative: happier or more happy, the happiest or most happy.[172] There is some variation among speakers regarding which adjectives use inflected or periphrastic comparison, and some studies have shown a tendency for the periphrastic forms to become more common at the expense of the inflected form.[173]

Pronouns, case, and person English pronouns conserve many traits of case and gender inflection. The personal pronouns retain a difference between subjective and objective case in most persons (I/me, he/him, she/her, we/us, they/them) as well as a gender and animateness distinction in the third person singular (distinguishing he/she/it). The subjective case corresponds to the Old English nominative case, and the objective case is used both in the sense of the previous accusative case (in the role of patient, or direct object of a transitive verb), and in the sense of the Old English dative case (in the role of a recipient or indirect object of a transitive verb).[174][175] Subjective case is used when the pronoun is the subject of a finite clause, and otherwise, the objective case is used.[176] While grammarians such as Henry Sweet[177] and Otto Jespersen[178] noted that the English cases did not correspond to the traditional Latin based system, some contemporary grammars, for example Huddleston & Pullum (2002), retain traditional labels for the cases, calling them nominative and accusative cases respectively.

Possessive pronouns exist in dependent and independent forms; the dependent form functions as a determiner specifying a noun (as in my chair), while the independent form can stand alone as if it were a noun (e.g. the chair is mine).[179] The English system of grammatical person no longer has a distinction between formal and informal pronouns of address (the old 2nd person singular familiar pronoun thou acquired a pejorative or inferior tinge of meaning and was abandoned), and the forms for 2nd person plural and singular are identical except in the reflexive form. Some dialects have introduced innovative 2nd person plural pronouns such as y'all found in Southern American English and African American (Vernacular) English or youse and ye found in Irish English.

English personal pronouns Person Subjective case Objective case Dependent possessive Independent possessive Reflexive 1st p. sg. I me my mine myself 2nd p. sg. you you your yours yourself 3rd p. sg. he/she/it him/her/it his/her/its his/hers/its himself/herself/itself 1st p. pl. we us our ours ourselves 2nd p. pl. you you your yours yourselves 3rd p. pl. they them their theirs themselves Pronouns are used to refer to entities deictically or anaphorically. A deictic pronoun points to some person or object by identifying it relative to the speech situation—for example, the pronoun I identifies the speaker, and the pronoun you, the addressee. Anaphorical pronouns such as that refer back to an entity already mentioned or assumed by the speaker to be known by the audience, for example in the sentence I already told you that. The reflexive pronouns are used when the oblique argument is identical to the subject of a phrase (e.g. "he sent it to himself" or "she braced herself for impact").[180]

Prepositions Prepositional phrases (PP) are phrases composed of a preposition and one or more nouns, e.g. with the dog, for my friend, to school, in England. Prepositions have a wide range of uses in English. They are used to describe movement, place, and other relations between different entities, but they also have many syntactic uses such as introducing complement clauses and oblique arguments of verbs. For example, in the phrase I gave it to him, the preposition to marks the recipient, or Indirect Object of the verb to give. Traditionally words were only considered prepositions if they governed the case of the noun they preceded, for example causing the pronouns to use the objective rather than subjective form, "with her", "to me", "for us". But some contemporary grammars such as that of Huddleston & Pullum (2002:598–600) no longer consider government of case to be the defining feature of the class of prepositions, rather defining prepositions as words that can function as the heads of prepositional phrases.

Verbs and verb phrases English verbs are inflected for tense and aspect and marked for agreement with present-tense third-person singular subject. Only the copula verb to be is still inflected for agreement with the plural and first and second person subjects.[172] Auxiliary verbs such as have and be are paired with verbs in the infinitive, past, or progressive forms. They form complex tenses, aspects, and moods. Auxiliary verbs differ from other verbs in that they can be followed by the negation, and in that they can occur as the first constituent in a question sentence.[181][182]

Most verbs have six inflectional forms. The primary forms are a plain present, a third-person singular present, and a preterite (past) form. The secondary forms are a plain form used for the infinitive, a gerund-participle and a past participle.[183] The copula verb to be is the only verb to retain some of its original conjugation, and takes different inflectional forms depending on the subject. The first-person present-tense form is am, the third person singular form is and the form are is used second-person singular and all three plurals. The only verb past participle is been and its gerund-participle is being.

English inflectional forms Inflection Strong Regular Plain present take love 3rd person sg. present takes loves Preterite took loved Plain (infinitive) take love Gerund–participle taking loving Past participle taken loved Tense, aspect and mood English has two primary tenses, past (preterit) and non-past. The preterit is inflected by using the preterit form of the verb, which for the regular verbs includes the suffix -ed, and for the strong verbs either the suffix -t or a change in the stem vowel. The non-past form is unmarked except in the third person singular, which takes the suffix -s.[181]

Present Preterite First person I run I ran Second person You run You ran Third person John runs John ran English does not have a morphologised future tense.[184] Futurity of action is expressed periphrastically with one of the auxiliary verbs will or shall.[185] Many varieties also use a near future constructed with the phrasal verb be going to.[186]

Future First person I will run Second person You will run Third person John will run Further aspectual distinctions are encoded by the use of auxiliary verbs, primarily have and be, which encode the contrast between a perfect and non-perfect past tense (I have run vs. I was running), and compound tenses such as preterite perfect (I had been running) and present perfect (I have been running).[187]

For the expression of mood, English uses a number of modal auxiliaries, such as can, may, will, shall and the past tense forms could, might, would, should. There is also a subjunctive and an imperative mood, both based on the plain form of the verb (i.e. without the third person singular -s), and which is used in subordinate clauses (e.g. subjunctive: It is important that he run every day; imperative Run!).[185]

An infinitive form, that uses the plain form of the verb and the preposition to, is used for verbal clauses that are syntactically subordinate to a finite verbal clause. Finite verbal clauses are those that are formed around a verb in the present or preterit form. In clauses with auxiliary verbs, they are the finite verbs and the main verb is treated as a subordinate clause. For example, he has to go where only the auxiliary verb have is inflected for time and the main verb to go is in the infinitive, or in a complement clause such as I saw him leave, where the main verb is to see which is in a preterite form, and leave is in the infinitive.

Phrasal verbs English also makes frequent use of constructions traditionally called phrasal verbs, verb phrases that are made up of a verb root and a preposition or particle which follows the verb. The phrase then functions as a single predicate. In terms of intonation the preposition is fused to the verb, but in writing it is written as a separate word. Examples of phrasal verbs are to get up, to ask out, to back up, to give up, to get together, to hang out, to put up with, etc. The phrasal verb frequently has a highly idiomatic meaning that is more specialised and restricted than what can be simply extrapolated from the combination of verb and preposition complement (e.g. lay off meaning terminate someone's employment).[188] In spite of the idiomatic meaning, some grammarians, including Huddleston & Pullum (2002:274), do not consider this type of construction to form a syntactic constituent and hence refrain from using the term "phrasal verb". Instead, they consider the construction simply to be a verb with a prepositional phrase as its syntactic complement, i.e. he woke up in the morning and he ran up in the mountains are syntactically equivalent.

Adverbs The function of adverbs is to modify the action or event described by the verb by providing additional information about the manner in which it occurs. Many adverbs are derived from adjectives with the suffix -ly, but not all, and many speakers tend to omit the suffix in the most commonly used adverbs. For example, in the phrase the woman walked quickly the adverb quickly derived from the adjective quick describes the woman's way of walking. Some commonly used adjectives have irregular adverbial forms, such as good which has the adverbial form well.

Syntax

In the English sentence The cat sat on the mat, the subject is the cat (a NP), the verb is sat, and on the mat is a prepositional phrase (composed of an NP the mat, and headed by the preposition on). The tree describes the structure of the sentence. Modern English syntax language is moderately analytic.[189] It has developed features such as modal verbs and word order as resources for conveying meaning. Auxiliary verbs mark constructions such as questions, negative polarity, the passive voice and progressive aspect.

Basic constituent order English word order has moved from the Germanic verb-second (V2) word order to being almost exclusively subject–verb–object (SVO).[190] The combination of SVO order and use of auxiliary verbs often creates clusters of two or more verbs at the centre of the sentence, such as he had hoped to try to open it.

In most sentences, English only marks grammatical relations through word order.[191] The subject constituent precedes the verb and the object constituent follows it. The example below demonstrates how the grammatical roles of each constituent is marked only by the position relative to the verb:

The dog bites the man S V O The man bites the dog S V O An exception is found in sentences where one of the constituents is a pronoun, in which case it is doubly marked, both by word order and by case inflection, where the subject pronoun precedes the verb and takes the subjective case form, and the object pronoun follows the verb and takes the objective case form. The example below demonstrates this double marking in a sentence where both object and subject is represented with a third person singular masculine pronoun:

He hit him S V O Indirect objects (IO) of ditransitive verbs can be placed either as the first object in a double object construction (S V IO O), such as I gave Jane the book or in a prepositional phrase, such as I gave the book to Jane [192]

Clause syntax Main article: English clause syntax In English a sentence may be composed of one or more clauses, that may, in turn, be composed of one or more phrases (e.g. Noun Phrases, Verb Phrases, and Prepositional Phrases). A clause is built around a verb and includes its constituents, such as any NPs and PPs. Within a sentence, one clause is always the main clause (or matrix clause) whereas other clauses are subordinate to it. Subordinate clauses may function as arguments of the verb in the main clause. For example, in the phrase I think (that) you are lying, the main clause is headed by the verb think, the subject is I, but the object of the phrase is the subordinate clause (that) you are lying. The subordinating conjunction that shows that the clause that follows is a subordinate clause, but it is often omitted.[193] Relative clauses are clauses that function as a modifier or specifier to some constituent in the main clause: For example, in the sentence I saw the letter that you received today, the relative clause that you received today specifies the meaning of the word letter, the object of the main clause. Relative clauses can be introduced by the pronouns who, whose, whom and which as well as by that (which can also be omitted.)[194] In contrast to many other Germanic languages there is no major differences between word order in main and subordinate clauses.[195]

Auxiliary verb constructions Main articles: Do-support and Subject–auxiliary inversion English syntax relies on auxiliary verbs for many functions including the expression of tense, aspect, and mood. Auxiliary verbs form main clauses, and the main verbs function as heads of a subordinate clause of the auxiliary verb. For example, in the sentence the dog did not find its bone, the clause find its bone is the complement of the negated verb did not. Subject–auxiliary inversion is used in many constructions, including focus, negation, and interrogative constructions.

The verb do can be used as an auxiliary even in simple declarative sentences, where it usually serves to add emphasis, as in "I did shut the fridge." However, in the negated and inverted clauses referred to above, it is used because the rules of English syntax permit these constructions only when an auxiliary is present. Modern English does not allow the addition of the negating adverb not to an ordinary finite lexical verb, as in *I know not—it can only be added to an auxiliary (or copular) verb, hence if there is no other auxiliary present when negation is required, the auxiliary do is used, to produce a form like I do not (don't) know. The same applies in clauses requiring inversion, including most questions—inversion must involve the subject and an auxiliary verb, so it is not possible to say *Know you him?; grammatical rules require Do you know him?[196]

Negation is done with the adverb not, which precedes the main verb and follows an auxiliary verb. A contracted form of not -n't can be used as an enclitic attaching to auxiliary verbs and to the copula verb to be. Just as with questions, many negative constructions require the negation to occur with do-support, thus in Modern English I don't know him is the correct answer to the question Do you know him?, but not *I know him not, although this construction may be found in older English.[197]

Passive constructions also use auxiliary verbs. A passive construction rephrases an active construction in such a way that the object of the active phrase becomes the subject of the passive phrase, and the subject of the active phrase is either omitted or demoted to a role as an oblique argument introduced in a prepositional phrase. They are formed by using the past participle either with the auxiliary verb to be or to get, although not all varieties of English allow the use of passives with get. For example, putting the sentence she sees him into the passive becomes he is seen (by her), or he gets seen (by her).[198]

Questions Both yes–no questions and wh-questions in English are mostly formed using subject–auxiliary inversion (Am I going tomorrow?, Where can we eat?), which may require do-support (Do you like her?, Where did he go?). In most cases, interrogative words (wh-words; e.g. what, who, where, when, why, how) appear in a fronted position. For example, in the question What did you see?, the word what appears as the first constituent despite being the grammatical object of the sentence. (When the wh-word is the subject or forms part of the subject, no inversion occurs: Who saw the cat?.) Prepositional phrases can also be fronted when they are the question's theme, e.g. To whose house did you go last night?. The personal interrogative pronoun who is the only interrogative pronoun to still show inflection for case, with the variant whom serving as the objective case form, although this form may be going out of use in many contexts.[199]

Discourse level syntax While English is a subject-prominent language, at the discourse level it tends to use a topic-comment structure, where the known information (topic) precedes the new information (comment). Because of the strict SVO syntax, the topic of a sentence generally has to be the grammatical subject of the sentence. In cases where the topic is not the grammatical subject of the sentence, frequently the topic is promoted to subject position through syntactic means. One way of doing this is through a passive construction, the girl was stung by the bee. Another way is through a cleft sentence where the main clause is demoted to be a complement clause of a copula sentence with a dummy subject such as it or there, e.g. it was the girl that the bee stung, there was a girl who was stung by a bee.[200] Dummy subjects are also used in constructions where there is no grammatical subject such as with impersonal verbs (e.g., it is raining) or in existential clauses (there are many cars on the street). Through the use of these complex sentence constructions with informationally vacuous subjects, English is able to maintain both a topic-comment sentence structure and a SVO syntax.

Focus constructions emphasise a particular piece of new or salient information within a sentence, generally through allocating the main sentence level stress on the focal constituent. For example, the girl was stung by a bee (emphasising it was a bee and not, for example, a wasp that stung her), or The girl was stung by a bee (contrasting with another possibility, for example that it was the boy).[201] Topic and focus can also be established through syntactic dislocation, either preposing or postposing the item to be focused on relative to the main clause. For example, That girl over there, she was stung by a bee, emphasises the girl by preposition, but a similar effect could be achieved by postposition, she was stung by a bee, that girl over there, where reference to the girl is established as an "afterthought".[202]

Cohesion between sentences is achieved through the use of deictic pronouns as anaphora (e.g. that is exactly what I mean where that refers to some fact known to both interlocutors, or then used to locate the time of a narrated event relative to the time of a previously narrated event).[203] Discourse markers such as oh, so or well, also signal the progression of ideas between sentences and help to create cohesion. Discourse markers are often the first constituents in sentences. Discourse markers are also used for stance taking in which speakers position themselves in a specific attitude towards what is being said, for example, no way is that true! (the idiomatic marker no way! expressing disbelief), or boy! I'm hungry (the marker boy expressing emphasis). While discourse markers are particularly characteristic of informal and spoken registers of English, they are also used in written and formal registers.[204]

Vocabulary See also: Foreign language influences in English English is a rich language in terms of vocabulary, containing more synonyms than any other language.[130] There are words which appear on the surface to mean exactly the same thing but which, in fact, have slightly different shades of meaning and must be chosen appropriately if a speaker wants to convey precisely the message intended. It is generally stated that English has around 170,000 words, or 220,000 if obsolete words are counted; this estimate is based on the last full edition of the Oxford English Dictionary from 1989.[205] Over half of these words are nouns, a quarter adjectives, and a seventh verbs. There is one count that puts the English vocabulary at about 1 million words—but that count presumably includes words such as Latin species names, scientific terminology, botanical terms, prefixed and suffixed words, jargon, foreign words of extremely limited English use, and technical acronyms.[13]

Due to its status as an international language, English adopts foreign words quickly, and borrows vocabulary from many other sources. Early studies of English vocabulary by lexicographers, the scholars who formally study vocabulary, compile dictionaries, or both, were impeded by a lack of comprehensive data on actual vocabulary in use from good-quality linguistic corpora,[206] collections of actual written texts and spoken passages. Many statements published before the end of the 20th century about the growth of English vocabulary over time, the dates of first use of various words in English, and the sources of English vocabulary will have to be corrected as new computerised analysis of linguistic corpus data becomes available.[13][207]

Word formation processes English forms new words from existing words or roots in its vocabulary through a variety of processes. One of the most productive processes in English is conversion,[208] using a word with a different grammatical role, for example using a noun as a verb or a verb as a noun. Another productive word-formation process is nominal compounding,[13][207] producing compound words such as babysitter or ice cream or homesick.[208] A process more common in Old English than in Modern English, but still productive in Modern English, is the use of derivational suffixes (-hood, -ness, -ing, -ility) to derive new words from existing words (especially those of Germanic origin) or stems (especially for words of Latin or Greek origin).

Formation of new words, called neologisms, based on Greek and/or Latin roots (for example television or optometry) is a highly productive process in English and in most modern European languages, so much so that it is often difficult to determine in which language a neologism originated. For this reason, lexicographer Philip Gove attributed many such words to the "international scientific vocabulary" (ISV) when compiling Webster's Third New International Dictionary (1961). Another active word-formation process in English is acronyms,[209] words formed by pronouncing as a single word abbreviations of longer phrases (e.g. NATO, laser).

Word origins Main article: Lists of English loanwords by country or language of origin

Source languages of English vocabulary[6][210] English, besides forming new words from existing words and their roots, also borrows words from other languages. This adoption of words from other languages is commonplace in many world languages, but English has been especially open to borrowing of foreign words throughout the last 1,000 years.[211] The most commonly used words in English are West Germanic.[212] The words in English learned first by children as they learn to speak, particularly the grammatical words that dominate the word count of both spoken and written texts, are mainly the Germanic words inherited from the earliest periods of the development of Old English.[13]

But one of the consequences of long language contact between French and English in all stages of their development is that the vocabulary of English has a very high percentage of "Latinate" words (derived from French, especially, and also from Latin and other Romance languages). French words from various periods of the development of French now make up one-third of the vocabulary of English.[213] Words of Old Norse origin have entered the English language primarily from the contact between Old Norse and Old English during colonisation of eastern and northern England. Many of these words are part of English core vocabulary, such as egg and knife.[214]

English has also borrowed many words directly from Latin, the ancestor of the Romance languages, during all stages of its development.[207][13] Many of these words had earlier been borrowed into Latin from Greek. Latin or Greek are still highly productive sources of stems used to form vocabulary of subjects learned in higher education such as the sciences, philosophy, and mathematics.[215] English continues to gain new loanwords and calques ("loan translations") from languages all over the world, and words from languages other than the ancestral Anglo-Saxon language make up about 60% of the vocabulary of English.[216]

English has formal and informal speech registers; informal registers, including child-directed speech, tend to be made up predominantly of words of Anglo-Saxon origin, while the percentage of vocabulary that is of Latinate origin is higher in legal, scientific, and academic texts.[217][218]

English loanwords and calques in other languages English has a strong influence on the vocabulary of other languages.[213][219] The influence of English comes from such factors as opinion leaders in other countries knowing the English language, the role of English as a world lingua franca, and the large number of books and films that are translated from English into other languages.[220] That pervasive use of English leads to a conclusion in many places that English is an especially suitable language for expressing new ideas or describing new technologies. Among varieties of English, it is especially American English that influences other languages.[221] Some languages, such as Chinese, write words borrowed from English mostly as calques, while others, such as Japanese, readily take in English loanwords written in sound-indicating script.[222] Dubbed films and television programmes are an especially fruitful source of English influence on languages in Europe.[222]

Writing system See also: English alphabet, English braille, and English orthography Since the ninth century, English has been written in a Latin alphabet (also called Roman alphabet). Earlier Old English texts in Anglo-Saxon runes are only short inscriptions. The great majority of literary works in Old English that survive to today are written in the Roman alphabet.[32] The modern English alphabet contains 26 letters of the Latin script: a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z (which also have capital forms: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z).

The spelling system, or orthography, of English is multi-layered, with elements of French, Latin, and Greek spelling on top of the native Germanic system.[223] Further complications have arisen through sound changes with which the orthography has not kept pace.[44] Compared to European languages for which official organisations have promoted spelling reforms, English has spelling that is a less consistent indicator of pronunciation, and standard spellings of words that are more difficult to guess from knowing how a word is pronounced.[224] There are also systematic spelling differences between British and American English. These situations have prompted proposals for spelling reform in English.[225]

Although letters and speech sounds do not have a one-to-one correspondence in standard English spelling, spelling rules that take into account syllable structure, phonetic changes in derived words, and word accent are reliable for most English words.[226] Moreover, standard English spelling shows etymological relationships between related words that would be obscured by a closer correspondence between pronunciation and spelling, for example the words photograph, photography, and photographic,[226] or the words electricity and electrical. While few scholars agree with Chomsky and Halle (1968) that conventional English orthography is "near-optimal",[223] there is a rationale for current English spelling patterns.[227] The standard orthography of English is the most widely used writing system in the world.[228] Standard English spelling is based on a graphomorphemic segmentation of words into written clues of what meaningful units make up each word.[229]

Readers of English can generally rely on the correspondence between spelling and pronunciation to be fairly regular for letters or digraphs used to spell consonant sounds. The letters b, d, f, h, j, k, l, m, n, p, r, s, t, v, w, y, z represent, respectively, the phonemes /b, d, f, h, dʒ, k, l, m, n, p, r, s, t, v, w, j, z/. The letters c and g normally represent /k/ and /ɡ/, but there is also a soft c pronounced /s/, and a soft g pronounced /dʒ/. The differences in the pronunciations of the letters c and g are often signalled by the following letters in standard English spelling. Digraphs used to represent phonemes and phoneme sequences include ch for /tʃ/, sh for /ʃ/, th for /θ/ or /ð/, ng for /ŋ/, qu for /kw/, and ph for /f/ in Greek-derived words. The single letter x is generally pronounced as /z/ in word-initial position and as /ks/ otherwise. There are exceptions to these generalisations, often the result of loanwords being spelled according to the spelling patterns of their languages of origin[226] or proposals by pedantic scholars in the early period of Modern English to mistakenly follow the spelling patterns of Latin for English words of Germanic origin.[230]

For the vowel sounds of the English language, however, correspondences between spelling and pronunciation are more irregular. There are many more vowel phonemes in English than there are single vowel letters (a, e, i, o, u, w, y). As a result, some "long vowels" are often indicated by combinations of letters (like the oa in boat, the ow in how, and the ay in stay), or the historically based silent e (as in note and cake).[227]

The consequence of this complex orthographic history is that learning to read can be challenging in English. It can take longer for school pupils to become independently fluent readers of English than of many other languages, including Italian, Spanish, and German.[231] Nonetheless, there is an advantage for learners of English reading in learning the specific sound-symbol regularities that occur in the standard English spellings of commonly used words.[226] Such instruction greatly reduces the risk of children experiencing reading difficulties in English.[232][233] Making primary school teachers more aware of the primacy of morpheme representation in English may help learners learn more efficiently to read and write English.[234]

English writing also includes a system of punctuation marks that is similar to those used in most alphabetic languages around the world. The purpose of punctuation is to mark meaningful grammatical relationships in sentences to aid readers in understanding a text and to indicate features important for reading a text aloud.[235]

Dialects, accents, and varieties Main articles: List of dialects of the English language, World Englishes, and regional accents of English Dialectologists identify many English dialects, which usually refer to regional varieties that differ from each other in terms of patterns of grammar, vocabulary, and pronunciation. The pronunciation of particular areas distinguishes dialects as separate regional accents. The major native dialects of English are often divided by linguists into the two extremely general categories of British English (BrE) and North American English (NAE).[236] There also exists a third common major grouping of English varieties: Southern Hemisphere English, the most prominent being Australian and New Zealand English.

United Kingdom and Ireland See also: English language in England, Northern England English, Scots language, Scottish English, Welsh English, Estuary English, Ulster English, and Hiberno-English

Map showing the main dialect regions in the UK and Ireland As the place where English first evolved, the British Isles, and particularly England, are home to the most diverse dialects. Within the United Kingdom, the Received Pronunciation (RP), an educated dialect of South East England, is traditionally used as the broadcast standard and is considered the most prestigious of the British dialects. The spread of RP (also known as BBC English) through the media has caused many traditional dialects of rural England to recede, as youths adopt the traits of the prestige variety instead of traits from local dialects. At the time of the Survey of English Dialects, grammar and vocabulary differed across the country, but a process of lexical attrition has led most of this variation to disappear.[237]

Nonetheless this attrition has mostly affected dialectal variation in grammar and vocabulary, and in fact, only 3 percent of the English population actually speak RP, the remainder speaking regional accents and dialects with varying degrees of RP influence.[238] There is also variability within RP, particularly along class lines between Upper and Middle-class RP speakers and between native RP speakers and speakers who adopt RP later in life.[239] Within Britain, there is also considerable variation along lines of social class, and some traits though exceedingly common are considered "non-standard" and are associated with lower class speakers and identities. An example of this is H-dropping, which was historically a feature of lower-class London English, particularly Cockney, and can now be heard in the local accents of most parts of England—yet it remains largely absent in broadcasting and among the upper crust of British society.[240]

Speech example MENU0:00 An example of an Essex male with a working-class Estuary accent of the region around London (Russell Brand). Problems playing this file? See media help.

Speech example MENU0:00 An example of an English female with a Received Pronunciation or "Standard British" accent. Problems playing this file? See media help.

Speech example MENU0:00 An example of a Renfrewshire male with a Scottish accent. Problems playing this file? See media help.

Speech example MENU0:00 An example of a woman with a supraregional Irish accent (Mary Robinson). Problems playing this file? See media help. English in England can be divided into four major dialect regions, Southwest English, South East English, Midlands English, and Northern English. Within each of these regions several local subdialects exist: Within the Northern region, there is a division between the Yorkshire dialects, and the Geordie dialect spoken in Northumbria around Newcastle, and the Lancashire dialects with local urban dialects in Liverpool (Scouse) and Manchester (Mancunian). Having been the centre of Danish occupation during the Viking Invasions, Northern English dialects, particularly the Yorkshire dialect, retain Norse features not found in other English varieties.[241]

Since the 15th century, southeastern England varieties centred around London, which has been the centre from which dialectal innovations have spread to other dialects. In London, the Cockney dialect was traditionally used by the lower classes, and it was long a socially stigmatised variety. The spread of Cockney features across the south-east led the media to talk of Estuary English as a new dialect, but the notion was criticised by many linguists on the grounds that London had influencing neighbouring regions throughout history.[242][243][244] Traits that have spread from London in recent decades include the use of intrusive R (drawing is pronounced drawring /ˈdrɔːrɪŋ/), t-glottalisation (Potter is pronounced with a glottal stop as Po'er /poʔʌ/), and the pronunciation of th- as /f/ (thanks pronounced fanks) or /v/ (bother pronounced bover).[245]

Scots is today considered a separate language from English, but it has its origins in early Northern Middle English[246] and developed and changed during its history with influence from other sources, particularly Scots Gaelic and Old Norse. Scots itself has a number of regional dialects. And in addition to Scots, Scottish English are the varieties of Standard English spoken in Scotland, most varieties are Northern English accents, with some influence from Scots.[247]

In Ireland, various forms of English have been spoken since the Norman invasions of the 11th century. In County Wexford, in the area surrounding Dublin, two extinct dialects known as Forth and Bargy and Fingallian developed as offshoots from Early Middle English, and were spoken until the 19th century. Modern Irish English, however, has its roots in English colonisation in the 17th century. Today Irish English is divided into Ulster English, the Northern Ireland dialect with strong influence from Scots, as well as various dialects of the Republic of Ireland. Like Scottish and most North American accents, almost all Irish accents preserve the rhoticity which has been lost in the dialects influenced by RP.[19][248]

North America Main articles: American English, General American, African American Vernacular English, Southern American English, and Canadian English

Speech example MENU0:00 An example of a Midwestern U.S. male with a general American accent (Emery Emery). Problems playing this file? See media help.

Speech example MENU0:00 An example of a Texan male with a Southern U.S. accent (George W. Bush). Problems playing this file? See media help.

Speech example MENU0:00 An example of an Ontario woman with a standard Canadian accent (Margaret Atwood) Problems playing this file? See media help.

Rhoticity dominates in North American English. The Atlas of North American English found over 50% non-rhoticity, though, in at least one local white speaker in each U.S. metropolitan area designated here by a red dot. Non-rhotic African American Vernacular English pronunciations may be found among African Americans regardless of location. North American English is fairly homogeneous compared to British English. Today, American accent variation is often increasing at the regional level and decreasing at the very local level,[249] though most Americans still speak within a phonological continuum of similar accents,[250] known collectively as General American (GA), with differences hardly noticed even among Americans themselves (such as Midland and Western American English).[251][252][253] In most American and Canadian English dialects, rhoticity (or r-fulness) is dominant, with non-rhoticity (r-dropping) becoming associated with lower prestige and social class especially after World War II; this contrasts with the situation in England, where non-rhoticity has become the standard.[254]

Separate from GA are American dialects with clearly distinct sound systems, historically including Southern American English, English of the coastal Northeast (famously including Eastern New England English and New York City English), and African American Vernacular English, all of which are historically non-rhotic. Canadian English, except for the Atlantic provinces and perhaps Quebec, may be classified under GA as well, but it often shows the raising of the vowels /aɪ/ and /aʊ/ before voiceless consonants, as well as distinct norms for written and pronunciation standards.[255]

In Southern American English, the most populous American "accent group" outside of GA,[256] rhoticity now strongly prevails, replacing the region's historical non-rhotic prestige.[257][258][259] Southern accents are colloquially described as a "drawl" or "twang,"[260] being recognised most readily by the Southern Vowel Shift initiated by glide-deleting in the /aɪ/ vowel (e.g. pronouncing spy almost like spa), the "Southern breaking" of several front pure vowels into a gliding vowel or even two syllables (e.g. pronouncing the word "press" almost like "pray-us"),[261] the pin–pen merger, and other distinctive phonological, grammatical, and lexical features, many of which are actually recent developments of the 19th century or later.[262]

Today spoken primarily by working- and middle-class African Americans, African-American Vernacular English (AAVE) is also largely non-rhotic and likely originated among enslaved Africans and African Americans influenced primarily by the non-rhotic, non-standard older Southern dialects. A minority of linguists,[263] contrarily, propose that AAVE mostly traces back to African languages spoken by the slaves who had to develop a pidgin or Creole English to communicate with slaves of other ethnic and linguistic origins.[264] AAVE's important commonalities with Southern accents suggests it developed into a highly coherent and homogeneous variety in the 19th or early 20th century. AAVE is commonly stigmatised in North America as a form of "broken" or "uneducated" English, as are white Southern accents, but linguists today recognise both as fully developed varieties of English with their own norms shared by a large speech community.[265][266]

Australia and New Zealand Main articles: Australian English and New Zealand English

Speech example MENU0:00 An example of a male with a general Australian accent. Problems playing this file? See media help. Since 1788, English has been spoken in Oceania, and Australian English has developed as a first language of the vast majority of the inhabitants of the Australian continent, its standard accent being General Australian. The English of neighbouring New Zealand has to a lesser degree become an influential standard variety of the language.[267] Australian and New Zealand English are each other's closest relatives with few differentiating characteristics, followed by South African English and the English of southeastern England, all of which have similarly non-rhotic accents, aside from some accents in the South Island of New Zealand. Australian and New Zealand English stand out for their innovative vowels: many short vowels are fronted or raised, whereas many long vowels have diphthongised. Australian English also has a contrast between long and short vowels, not found in most other varieties. Australian English grammar aligns closely to British and American English; like American English, collective plural subjects take on a singular verb (as in the government is rather than are).[268][269] New Zealand English uses front vowels that are often even higher than in Australian English.[270][271][272]

Africa, the Caribbean, and South Asia See also: South African English, Nigerian English, Caribbean English, and Indian English

Speech example MENU0:00 An example of a black male with a South African accent. Problems playing this file? See media help. English is spoken widely in South Africa and is an official or co-official language in several countries. In South Africa, English has been spoken since 1820, co-existing with Afrikaans and various African languages such as the Khoe and Bantu languages. Today, about 9 percent of the South African population speaks South African English (SAE) as a first language. SAE is a non-rhotic variety, which tends to follow RP as a norm. It is alone among non-rhotic varieties in lacking intrusive r. There are different L2 varieties that differ based on the native language of the speakers.[273] Most phonological differences from RP are in the vowels.[274] Consonant differences include the tendency to pronounce /p, t, t͡ʃ, k/ without aspiration (e.g. pin pronounced [pɪn] rather than as [pʰɪn] as in most other varieties), while r is often pronounced as a flap [ɾ] instead of as the more common fricative.[275]

Speech example MENU0:00 An example of a woman with an educated Nigerian accent (Chimamanda Adichie) Problems playing this file? See media help. Nigerian English is a dialect of English spoken in Nigeria.[276] It is based on British English, but in recent years, because of influence from the United States, some words of American English origin have made it into Nigerian English. Additionally, some new words and collocations have emerged from the language, which come from the need to express concepts specific to the culture of the nation (e.g. senior wife). Over 150 million population of Nigerians speak English.[277]

Several varieties of English are also spoken in the Caribbean Islands that were colonial possessions of Britain, including Jamaica, and the Leeward and Windward Islands and Trinidad and Tobago, Barbados, the Cayman Islands, and Belize. Each of these areas are home both to a local variety of English and a local English based creole, combining English and African languages. The most prominent varieties are Jamaican English and Jamaican Creole. In Central America, English based creoles are spoken in on the Caribbean coasts of Nicaragua and Panama.[278] Locals are often fluent both in the local English variety and the local creole languages and code-switching between them is frequent, indeed another way to conceptualise the relationship between Creole and Standard varieties is to see a spectrum of social registers with the Creole forms serving as "basilect" and the more RP-like forms serving as the "acrolect", the most formal register.[279]

Most Caribbean varieties are based on British English and consequently, most are non-rhotic, except for formal styles of Jamaican English which are often rhotic. Jamaican English differs from RP in its vowel inventory, which has a distinction between long and short vowels rather than tense and lax vowels as in Standard English. The diphthongs /ei/ and /ou/ are monophthongs [eː] and [oː] or even the reverse diphthongs [ie] and [uo] (e.g. bay and boat pronounced [bʲeː] and [bʷoːt]). Often word-final consonant clusters are simplified so that "child" is pronounced [t͡ʃail] and "wind" [win].[280][281][282]

Speech example MENU0:00 An example of a North Indian woman with an Indian accent (Vandana Shiva) Problems playing this file? See media help. As a historical legacy, Indian English tends to take RP as its ideal, and how well this ideal is realised in an individual's speech reflects class distinctions among Indian English speakers. Indian English accents are marked by the pronunciation of phonemes such as /t/ and /d/ (often pronounced with retroflex articulation as [ʈ] and [ɖ]) and the replacement of /θ/ and /ð/ with dentals [t̪] and [d̪]. Sometimes Indian English speakers may also use spelling based pronunciations where the silent ⟨h⟩ found in words such as ghost is pronounced as an Indian voiced aspirated stop [ɡʱ].[283]

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Mathematical proof is fundamentally a matter of rigor. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.[b] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Misunderstanding the rigor is a cause for some of the common misconceptions of mathematics. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous.[56]

Axioms in traditional thought were "self-evident truths", but that conception is problematic.[57] At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.[58]

Fields of mathematics See also: Areas of mathematics and Glossary of areas of mathematics

The abacus is a simple calculating tool used since ancient times. Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty. While some areas might seem unrelated, the Langlands program has found connections between areas previously thought unconnected, such as Galois groups, Riemann surfaces and number theory.

Foundations and philosophy In order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic includes the mathematical study of logic and the applications of formal logic to other areas of mathematics; set theory is the branch of mathematics that studies sets or collections of objects. Category theory, which deals in an abstract way with mathematical structures and relationships between them, is still in development. The phrase "crisis of foundations" describes the search for a rigorous foundation for mathematics that took place from approximately 1900 to 1930.[59] Some disagreement about the foundations of mathematics continues to the present day. The crisis of foundations was stimulated by a number of controversies at the time, including the controversy over Cantor's set theory and the Brouwer–Hilbert controversy.

Mathematical logic is concerned with setting mathematics within a rigorous axiomatic framework, and studying the implications of such a framework. As such, it is home to Gödel's incompleteness theorems which (informally) imply that any effective formal system that contains basic arithmetic, if sound (meaning that all theorems that can be proved are true), is necessarily incomplete (meaning that there are true theorems which cannot be proved in that system). Whatever finite collection of number-theoretical axioms is taken as a foundation, Gödel showed how to construct a formal statement that is a true number-theoretical fact, but which does not follow from those axioms. Therefore, no formal system is a complete axiomatization of full number theory. Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science,[citation needed] as well as to category theory. In the context of recursion theory, the impossibility of a full axiomatization of number theory can also be formally demonstrated as a consequence of the MRDP theorem.

Theoretical computer science includes computability theory, computational complexity theory, and information theory. Computability theory examines the limitations of various theoretical models of the computer, including the most well-known model – the Turing machine. Complexity theory is the study of tractability by computer; some problems, although theoretically solvable by computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with the rapid advancement of computer hardware. A famous problem is the "P = NP?" problem, one of the Millennium Prize Problems.[60] Finally, information theory is concerned with the amount of data that can be stored on a given medium, and hence deals with concepts such as compression and entropy.

{p\Rightarrow q} {p\Rightarrow q} Venn A intersect B.svg Commutative diagram for morphism.svg DFAexample.svg Mathematical logic Set theory Category theory Theory of computation Pure mathematics Quantity Main article: Arithmetic The study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic. The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem. The twin prime conjecture and Goldbach's conjecture are two unsolved problems in number theory.

As the number system is further developed, the integers are recognized as a subset of the rational numbers ("fractions"). These, in turn, are contained within the real numbers, which are used to represent continuous quantities. Real numbers are generalized to complex numbers. These are the first steps of a hierarchy of numbers that goes on to include quaternions and octonions. Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of "infinity". According to the fundamental theorem of algebra all solutions of equations in one unknown with complex coefficients are complex numbers, regardless of degree. Another area of study is the size of sets, which is described with the cardinal numbers. These include the aleph numbers, which allow meaningful comparison of the size of infinitely large sets.

{(0),1,2,3,\ldots } {(0),1,2,3,\ldots } {\ldots ,-2,-1,0,1,2\,\ldots } {\ldots ,-2,-1,0,1,2\,\ldots } {-2,{\frac {2}{3}},1.21} {-2,{\frac {2}{3}},1.21} {-e,{\sqrt {2}},3,\pi } {-e,{\sqrt {2}},3,\pi } {2,i,-2+3i,2e^{i{\frac {4\pi }{3}}}} {2,i,-2+3i,2e^{i{\frac {4\pi }{3}}}} Natural numbers Integers Rational numbers Real numbers Complex numbers Structure Main article: Algebra Many mathematical objects, such as sets of numbers and functions, exhibit internal structure as a consequence of operations or relations that are defined on the set. Mathematics then studies properties of those sets that can be expressed in terms of that structure; for instance number theory studies properties of the set of integers that can be expressed in terms of arithmetic operations. Moreover, it frequently happens that different such structured sets (or structures) exhibit similar properties, which makes it possible, by a further step of abstraction, to state axioms for a class of structures, and then study at once the whole class of structures satisfying these axioms. Thus one can study groups, rings, fields and other abstract systems; together such studies (for structures defined by algebraic operations) constitute the domain of abstract algebra.

By its great generality, abstract algebra can often be applied to seemingly unrelated problems; for instance a number of ancient problems concerning compass and straightedge constructions were finally solved using Galois theory, which involves field theory and group theory. Another example of an algebraic theory is linear algebra, which is the general study of vector spaces, whose elements called vectors have both quantity and direction, and can be used to model (relations between) points in space. This is one example of the phenomenon that the originally unrelated areas of geometry and algebra have very strong interactions in modern mathematics. Combinatorics studies ways of enumerating the number of objects that fit a given structure.

{{\begin{matrix}(1,2,3)&(1,3,2)\\(2,1,3)&(2,3,1)\\(3,1,2)&(3,2,1)\end{matrix}}} {\begin{matrix}(1,2,3)&(1,3,2)\\(2,1,3)&(2,3,1)\\(3,1,2)&(3,2,1)\end{matrix}} Elliptic curve simple.svg Rubik's cube.svg Group diagdram D6.svg Lattice of the divisibility of 60.svg Braid-modular-group-cover.svg Combinatorics Number theory Group theory Graph theory Order theory Algebra Space Main article: Geometry The study of space originates with geometry – in particular, Euclidean geometry, which combines space and numbers, and encompasses the well-known Pythagorean theorem. Trigonometry is the branch of mathematics that deals with relationships between the sides and the angles of triangles and with the trigonometric functions. The modern study of space generalizes these ideas to include higher-dimensional geometry, non-Euclidean geometries (which play a central role in general relativity) and topology. Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry. Convex and discrete geometry were developed to solve problems in number theory and functional analysis but now are pursued with an eye on applications in optimization and computer science. Within differential geometry are the concepts of fiber bundles and calculus on manifolds, in particular, vector and tensor calculus. Within algebraic geometry is the description of geometric objects as solution sets of polynomial equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Topology in all its many ramifications may have been the greatest growth area in 20th-century mathematics; it includes point-set topology, set-theoretic topology, algebraic topology and differential topology. In particular, instances of modern-day topology are metrizability theory, axiomatic set theory, homotopy theory, and Morse theory. Topology also includes the now solved Poincaré conjecture, and the still unsolved areas of the Hodge conjecture. Other results in geometry and topology, including the four color theorem and Kepler conjecture, have been proved only with the help of computers.

Illustration to Euclid's proof of the Pythagorean theorem.svg Sinusvåg 400px.png Hyperbolic triangle.svg Torus.svg Mandel zoom 07 satellite.jpg Measure illustration (Vector).svg Geometry Trigonometry Differential geometry Topology Fractal geometry Measure theory Change Main article: Calculus Understanding and describing change is a common theme in the natural sciences, and calculus was developed as a powerful tool to investigate it. Functions arise here, as a central concept describing a changing quantity. The rigorous study of real numbers and functions of a real variable is known as real analysis, with complex analysis the equivalent field for the complex numbers. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many problems lead naturally to relationships between a quantity and its rate of change, and these are studied as differential equations. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior.

Integral as region under curve.svg Vector field.svg Navier Stokes Laminar.svg Limitcycle.svg Lorenz attractor.svg Conformal grid after Möbius transformation.svg Calculus Vector calculus Differential equations Dynamical systems Chaos theory Complex analysis Applied mathematics Main article: Applied mathematics Applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge. The term applied mathematics also describes the professional specialty in which mathematicians work on practical problems; as a profession focused on practical problems, applied mathematics focuses on the "formulation, study, and use of mathematical models" in science, engineering, and other areas of mathematical practice.

In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics, where mathematics is developed primarily for its own sake. Thus, the activity of applied mathematics is vitally connected with research in pure mathematics.

Statistics and other decision sciences Main article: Statistics Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially with probability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments;[61] the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.[c]

Statistical theory studies decision problems such as minimizing the risk (expected loss) of a statistical action, such as using a procedure in, for example, parameter estimation, hypothesis testing, and selecting the best. In these traditional areas of mathematical statistics, a statistical-decision problem is formulated by minimizing an objective function, like expected loss or cost, under specific constraints: For example, designing a survey often involves minimizing the cost of estimating a population mean with a given level of confidence.[62] Because of its use of optimization, the mathematical theory of statistics shares concerns with other decision sciences, such as operations research, control theory, and mathematical economics.[63]

Computational mathematics Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic matrix and graph theory. Other areas of computational mathematics include computer algebra and symbolic computation.

Arbitrary-gametree-solved.svg BernoullisLawDerivationDiagram.svg Composite trapezoidal rule illustration small.svg Maximum boxed.png Two red dice 01.svg Oldfaithful3.png Caesar3.svg Game theory Fluid dynamics Numerical analysis Optimization Probability theory Statistics Cryptography Market Data Index NYA on 20050726 202628 UTC.png Gravitation space source.svg CH4-structure.svg Signal transduction pathways.svg GDP PPP Per Capita IMF 2008.svg Simple feedback control loop2.svg Mathematical finance Mathematical physics Mathematical chemistry Mathematical biology Mathematical economics Control theory Mathematical awards Arguably the most prestigious award in mathematics is the Fields Medal,[64][65] established in 1936 and awarded every four years (except around World War II) to as many as four individuals. The Fields Medal is often considered a mathematical equivalent to the Nobel Prize.

The Wolf Prize in Mathematics, instituted in 1978, recognizes lifetime achievement, and another major international award, the Abel Prize, was instituted in 2003. The Chern Medal was introduced in 2010 to recognize lifetime achievement. These accolades are awarded in recognition of a particular body of work, which may be innovational, or provide a solution to an outstanding problem in an established field.

A famous list of 23 open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Only one of them, the Riemann hypothesis, duplicates one of Hilbert's problems. A solution to any of these problems carries a$ (Error compiling LaTeX. Unknown error_msg)1 million reward.

See also icon Mathematics portal Mathematics at Wikipedia's sister projects Definitions from Wiktionary Media from Wikimedia Commons News from Wikinews Quotations from Wikiquote Texts from Wikisource Textbooks from Wikibooks Resources from Wikiversity Wikiversity At Wikiversity, you can learn more and teach others about Mathematics at the School of Mathematics. Library resources about Mathematics Resources in your library International Mathematical Olympiad Lists of mathematics topics Mathematical sciences Mathematics and art Mathematics education National Museum of Mathematics Philosophy of mathematics Relationship between mathematics and physics Science, Technology, Engineering, and Mathematics Notes

No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art depends on the artist's imagination (see Euclid).
See false proof for simple examples of what can go wrong in a formal proof.
Like other mathematical sciences such as physics and computer science, statistics is an autonomous discipline rather than a branch of applied mathematics. Like research physicists and computer scientists, research statisticians are mathematical scientists. Many statisticians have a degree in mathematics, and some statisticians are also mathematicians.

Footnotes

"mathematics, n.". Oxford English Dictionary. Oxford University Press. 2012. Retrieved June 16, 2012. The science of space, number, quantity, and arrangement, whose methods involve logical reasoning and usually the use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis.
Kneebone, G.T. (1963). Mathematical Logic and the Foundations of Mathematics: An Introductory Survey. Dover. p. 4. ISBN 978-0-486-41712-7. Mathematics ... is simply the study of abstract structures, or formal patterns of connectedness.
LaTorre, Donald R.; Kenelly, John W.; Biggers, Sherry S.; Carpenter, Laurel R.; Reed, Iris B.; Harris, Cynthia R. (2011). Calculus Concepts: An Informal Approach to the Mathematics of Change. Cengage Learning. p. 2. ISBN 978-1-4390-4957-0. Calculus is the study of change—how things change, and how quickly they change.
Ramana (2007). Applied Mathematics. Tata McGraw–Hill Education. p. 2.10. ISBN 978-0-07-066753-2. The mathematical study of change, motion, growth or decay is calculus.
Ziegler, Günter M. (2011). "What Is Mathematics?". An Invitation to Mathematics: From Competitions to Research. Springer. p. vii. ISBN 978-3-642-19532-7.
Steen, L.A. (April 29, 1988). The Science of Patterns Science, 240: 611–16. And summarized at Association for Supervision and Curriculum Development Archived October 28, 2010, at the Wayback Machine, www.ascd.org.
Devlin, Keith, Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe (Scientific American Paperback Library) 1996, ISBN 978-0-7167-5047-5
Eves, p. 306
Peterson, p. 12
Wigner, Eugene (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Communications on Pure and Applied Mathematics. 13 (1): 1–14. Bibcode:1960CPAM...13....1W. doi:10.1002/cpa.3160130102. Archived from the original on February 28, 2011.
Dehaene, Stanislas; Dehaene-Lambertz, Ghislaine; Cohen, Laurent (Aug 1998). "Abstract representations of numbers in the animal and human brain". Trends in Neurosciences. 21 (8): 355–61. doi:10.1016/S0166-2236(98)01263-6. PMID 9720604.
See, for example, Raymond L. Wilder, Evolution of Mathematical Concepts; an Elementary Study, passim
Kline 1990, Chapter 1.
Boyer 1991, "Mesopotamia"