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by Koshkin 1521 days ago
A proof that no one would understand in not a good proof. The ideal approach to proving theorems, at least according to how Grothendieck did it, is to build a beautiful theory in which the proof becomes elementary.
1 comments

It's quite a big assumption to think truth can always be bent so as to satisfy our ridiculously limited cognition. And math has been used instrumentally from the very beginning, so results are often much more important than the process. Theoreticians may still value elegance because that gives them pleasure or whatever, but few other people care about that as long as they can use the results.
The results aren’t often nearly as useful as the techniques used to find them. For example, a completely opaque proof resolving P vs NP is completely useless to theoretical CS.