More specifically, one thing I learned from Terry that I was not taught in school is the importance of bad proofs. I would say “I think this is true”, work on it, see that there was no nice proof, and give up. Terry would say “Here’s a criterion that eliminates most of the problem. Then in what’s left, here’s a worse one that handles most of the detritus. One or two more epicycles. At that point it comes down to fourteen cases, and I checked them.” Yuck. But we would know it was true, and we would move on. (Usually these would get cleaned up a fair bit before publication.)
At that point I’d start wondering why there doesn’t appear to be a simple proof. For example, maybe some kind of generalization of the result is false and you need the complexity to “break the correspondence” with the generalization.
Or else I would say “I wonder if this is true” and Terry would say “Oh, it is for a while, but it starts to fail in six dimensions” where I hadn’t hardly exhausted the 3-dim
-Allen Knutson on collaborating with Terence Tao
At that point I’d start wondering why there doesn’t appear to be a simple proof. For example, maybe some kind of generalization of the result is false and you need the complexity to “break the correspondence” with the generalization.
(meta)
Saith the linked site: “You must sign in to read answers past the first one.”
Well, that’s obnoxious.
If it’s any consolation, none of the answers past the first one on this question are very good.
Well, there are only 2
-Same place