Mathematical theory of great beauty | Wikipedia audio article

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00:01:19 1 Beauty in method
00:02:44 2 Beauty in results
00:05:50 3 Beauty in experience
00:09:00 4 Beauty and philosophy
00:11:43 5 Beauty and mathematical information theory
00:13:00 6 Mathematics and the arts
00:13:10 6.1 Music
00:13:43 6.2 Visual arts
00:14:51 7 See also



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"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
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Mathematical beauty describes the notion that some mathematicians may derive aesthetic pleasure from their work, and from mathematics in general. They express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful. Mathematicians describe mathematics as an art form or, at a minimum, as a creative activity. Comparisons are often made with music and poetry.
Bertrand Russell expressed his sense of mathematical beauty in these words:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

Paul Erdős expressed his views on the ineffability of mathematics when he said, "Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is".