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.)
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
-Same place
Another monthly installment of the rationality quotes thread. The usual rules apply: