Comment by pinkmuffinere
16 hours ago
> think proof of Riemann Hypothesis autonomously generated (end to end) formally proven - is it allowed or not?
Sorry to be rude, but this seems like a dumb question. I want science to progress. A primary purpose of these journals is to progress science. A full proof of the Riemann Hypothesis progresses science. I don't care how it was produced, if Hitler is coauthor, etc, I just care that it is correct. Whether the authors should be rewarded for whatever methods they used can be a separate question.
Terence Tao had a nice talk from the Future of Mathematics conference posted yesterday [0] that shapes a lot of my own feelings on this matter.
The short of it is he argues how first to correctness shouldn't be the only goal / isn't a great optimisation incentive. Presentation and digestibility of correct results is a missing 1/3 when you've finished generation and verification. I completely agree with him. You don't just need an AI generated proof of the Reimann Hypothesis. You would really like it to be intentional and structured for others to understand.
A really beautiful quote I learned of in the talk is this:
> "We are not trying to meet some abstract production quota of definitions, theorems, and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about math." - William Thurston
[0] https://www.youtube.com/watch?v=Uc2zt198U_U
Ya, I think this totally makes sense. Just to be clear though, I don’t think we’re actually disagreeing. A proof of the Riemann hypothesis that’s obtuse and basically unreadable is a great step on the path to a proof that is enlightening and clear. If ai provides correct-but-annoying results, I’m confident humans can still learn benefit from that marginal result.
He would say that now he’s got tenure though.