Comment by caaqil
10 hours ago
> There seems to be more interest in hitting some arbitrary benchmark (we proved X unsolved problems)
> genuinely contributing to mathematics
What's the difference between the two? Proofs are no longer the goalpost?
10 hours ago
> There seems to be more interest in hitting some arbitrary benchmark (we proved X unsolved problems)
> genuinely contributing to mathematics
What's the difference between the two? Proofs are no longer the goalpost?
Proofs are valuable but I believe the mathematical community values understanding more. Proofs were previously a great way to develop understanding. Now, less so.
Not an expert, but explaining the proof and it being independently verifiable as important as just putting a paper of it. Reminds me of 1000 page proof of Goldbach’s conjecture that a Mathematician reached sometime back. He was told plainly that no one is going to invest time in verifying the proof because there’s a good chance there’s an error somewhere in between.
Proofs of open problems are valuable because we are assuming that proving the problem requires some new method or infrastructure in math to prove it. Basically proving open problems isn't actually useful if it doesn't develop new tooling for mathematics, which can help us create new open problems, solve other ones etc.
I recommend RTFA, it explains exactly that: why proofs should not be considered the goalpost, and why dumping all these AI-generated proofs might be an overall negative for mathematics as a whole.