Alice: Does Carol's proof solve your big open problem?
Bob: Yes, but it's an ugly proof so it doesn't count.
A beautiful proof—a proof from "The Book"—is a piece of art. You take a look at it and just say "Wow!"
But what about the ugly proof. A boring case analysis that doesn't generalize and gives little to no insight as to why the theorem is true. A colleague, who for some reason wants to remain anonymous on this issue, has strong opinions about ugly proofs.
I guess the question is if there is a nicer proof or not. If there turns out to be, well and good. If not, probably it wasn't a very nice question. Nice questions have pretty answers.I'm all for pretty proofs but if you have an open problem you care about, a need to get from point A to point B, while it is nicer to fly first class, getting to point B by driving a bumpy road still gets you to point B.
I'm all for banning ugly proofs, except that there's likely to be a lack of agreement on what constitutes ugliness. The one positive aspect of an ugly proof is that it might lead to a nicer one. If not, it's worse than no proof at all.
An ugly proof has the same logically correctness as a pretty one. Does the truth lack interest just because we had to take a painful path to get there?