On Understanding

by rrusczyk, Dec 27, 2011, 8:56 PM

Here is a series of answers to the question of what it is like to have an understanding of higher mathematics. I don't think I have the understanding referred to by the questioner, but several of the people here at AoPS do, and I see glimmers of their insights in the responses. Perhaps more interesting to me is that many of the answers are broadly applicable to descriptions of understanding many other areas or skills.

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That is the nice thing about learning math the AOPS way since it teaches you how to learn which I use to help me in other subjects that I pursue such as science and even english which brings up an interesting point of how despite on the outside all these different subjects seem so different, but if you take a look at the main ideas then they are really not. I honestly think that math, science, language, and any other subject can all be about understanding beauty, just with a different template which is why learning how to learn with one you enjoy the most can help you learn how to do the others. Also, I think that it is mind bending how many connections there are between these subjects for example between math and music there is pascal's triangle and the fibonacci numbers and between math and art there is symmetry. People far too often draw artificial boundaries between various studies of discipline with the belief that mine has all these attributes where as your study has all of these which I think can be attributed some what by just human nature itself with the natural desire to divide.

by humzaiqbal, Dec 31, 2011, 6:34 AM

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About Owner
  • Posts: 16194
  • Joined: Mar 28, 2003
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  • Blog created: Jan 28, 2005
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