Mathematical beauty

Can mathematics be beautiful? Mathematicians often describe proofs in aesthetic terms – they are elegant, sublime, ineffable; in a word, they are beautiful.

Pythagorean proof
Phildonnia at English Wikipedia [CC BY-SA 3.0], via Wikimedia Commons
Wikipedia cites a couple of famous mathematicians who describe this connection. Bertrand Russell:

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.

Paul Erdős:

I know numbers are beautiful. If they aren’t beautiful, nothing is.

The term elegance is often used here; simple but supremely effective. I know what they mean – while I’m no mathematician, the proof of Pythagoras’ theorum pictured above has a wonderful clean cool beauty to it.


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