Pierre de Fermat

This is an AoPSWiki Word of the Week for July 25-July 31

Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French magistrate and government official. He, however, is most famous for being an amateur mathematician. His name is attached to several results in number theory, though he worked in many other areas of mathematics as well.

Fermat had a respectable background, and had a formal education, rare for the time. He became a civil servant in both the executive and judicial branches of his provincial government, and rose rapidly in the ranks of his peers due to his prowess at the job and an illness that was taking the life of many of his colleagues. He continued serving in these positions until he died.

The work Fermat produced spanned many different areas of mathematics; however, he worked most and was most famous for his accomplishments in number theory. The best-known problem he posed is known as Fermat's Last Theorem, which remained unsolved for hundreds of years. Fermat claimed to have a proof for this problem, but this is doubtful. Other notable areas which Fermat worked in were analytic geometry and laying the foundations of calculus

Biography

Pierre de Fermat was born in the town of Beaumont-deLomagne, in the southerwestern portion of France. His father (named Dominique) was a rich merchant who dealt in leather, and thus Fermat was able to enjoy a formal education. He attended the Franciscan monastery in Grandselve, and then the University of Toulouse. No record shows that he was particularly adept with numbers.

His family urged him to take a career in the civil service, and he complied; being appointed conseiller au Parlement de Toulouse (councilor of the Chamber of Petitions of Toulouse) in 1631. This job entailed hearing locals who wished to petition the king and either approving or declining their requests. Fermat's duties also included enforcing royal decrees; in one sense he was the link between the royal government and the province of Toulouse. He was very efficient in this job, as well as another judiciary career as a magistrate in the side.

This efficiency, as well as a plague that was killing off his superior colleagues (Fermat himself fell ill in 1652; and in fact one of his colleagues announced his death prematurely) enabled him to be promoted rapidly; and he became a minor sort of nobility; permitting him to add "de" to his name. Fermat survived both the plague and the political intrigues common of the era, particularly those relating to Cardinal Richelieu.

Fermat signed his last judicial notice on January 9, 1665, in the town of Castres. He died three days later.

Work

While serving in his civil duties, Fermat was inspired to mathematics by a copy of Diophantus's Arithmetica. Fermat henceforth became fascinated with number theory and mathematics in general.

Fermat's was rather secretive, and enjoyed taunting other mathematicians in correspondence (which he sent quite a lot of) about a theorem which he had discovered the proof to without actually providing the proof. He would often write tantalizing notes in the margins of works, giving a conjecture without proof. Sometimes he would claim that he had discovered a proof to the theorem or even give a few hints as to the proof; sometimes he would do no such thing.

While Fermat mostly worked in number theory, he also invented analytic geometry independently and prior to Rene Descartes (though he did not publish his work, which is why Descartes receives most of the credit). Furthermore, he found a method of drawing tangents to parabolas in the form (or parabolas of Fermat) and hyperbolas in the form (or hyperbolas of Fermat), thus laying the foundations for calculus.

All of Fermat's theorems were either proven or shown to be false by Leonhard Euler years later, except for one. This theorem came to be known as Fermat's Last Theorem, not because it was the last problem he posed (far from it; he first wrote about it in 1637, relatively early in his career), but because it was the last remaining problem that was unsolved. Fermat had written in the margin of the Arithmetica, "I have discovered a truly marvelous proof, which this margin is too narrow to contain". Many failed attempts and advances were made over the next few hundred years towards it, yet no one solved it. A prize of 100,000 German marks was offered for the problem (though this became laughably devalued during the German hyperinflation following World War I), and many pseudo-mathematicians sent in obviously flawed problems.

Eventually, in 1993, Andrew Wiles furnished a proof , after eight years of work, which relied on many modern techniques. However, a flaw was discovered soon after. Wiles managed to correct the proof by October 1994, thus solving the last of Fermat's problems. It is doubtful that Fermat managed to furnish a proof due to the many concepts of modern mathematics in Wile's proof, and many mathematicians now believe that Fermat only had a flawed proof.

See Also

• Fermat point
• Fermat's Little Theorem

References

• Singh, Simon (1997). Walker and Company; New York. Fermat's Enigma. ISBN 0-8027-1331-9.