Sunday, July 10, 2016

[rllgtwrb] Elegant theorems, messy proofs

A proof often resembles a Rube Goldberg machine of parts -- lemmas -- strung together in whatever way works to accomplish the task, perhaps leaving doubt: does that actually work?

This is the aesthetics of professional mathematics, an aesthetic which might not appeal to some people.

Even the most beautiful proof is messier than the theorem it proves, because it must necessarily state the theorem as part of the proof.

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