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> Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of
by zahlman 1mo ago
> Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize, etc).
This also sounds like a vector for trolling the community with complex putative proofs hiding a known flaw.
- amelius 1mo agoNot if it's lean-verified.
- bayindirh 1mo agoDidn't some of the recent proofs exploited a couple of blind spots of lean, and they were invalidated? Edit: Yup. A bug report to Lean was disguised as a "Collatz" proof in a humorous way. Links below. - https://x.com/gro_tsen/status/2082483878480977959 https://x.com/gro_tsen/status/2082483878480977959 - https://infosec.exchange/@0xabad1dea/117002106099986943 https://infosec.exchange/@0xabad1dea/117002106099986943
- amelius 1mo agoI don't know ... do you have a reference?
- bayindirh 1mo agoYup, found it: https://news.ycombinator.com/item?id=49101465 https://news.ycombinator.com/item?id=49101465
- Ethan_Barry 1mo agoThere was a hash collision bug in the main Lean kernel that was patched, but AFAIK nothing relied on it. You'd have to know what you were doing to accidentally get there...
- bayindirh 1mo agoThe incident in the links I posted exploited several bugs AFAICS, so it's a different story than a single hash collision bug, it seems.
- evenhash 1mo ago"Lean-verified" is not some magical incantation that makes a supposed proof irrefutable. Even disregarding potential bugs in the kernel as others have said. Say that AI gives you a Lean proof and says it proves Theorem X. It could just as easily give you the same proof but claim that it proves (not X). How would you know the difference? Nothing can really be considered proven unless a human expert can read the Lean proof and determine that (X as defined in the Lean proof) corresponds to X. The proof (at least the statement of the theorem) must be intelligible to humans to have value. It's possible people will just start taking AI at its word. Maybe AI says "Here is a Lean proof of X" and we all just shrug and go "Okay, X is proven." But that's not how it works right now for human mathematicians. Why would we apply that standard for AI?
- tmhn2 1mo agoI'm not totally sure what you mean. You can validate the proof using lean, which is what it's for--the whole magic of it is you don't have to just trust what AI says. That said, to your larger point, there are loopholes, and we'd certainly better be able to read the statement in lean, etc.
- evenhash 1mo agoWhat I’m saying is that you can’t just trust what the AI says because it produces a Lean artifact. The statement of the theorem has to be correctly translated from English into Lean code. It’s like translating user requirements into code. The code could run without bugs but not do what the users want. The only way to know the AI did it correctly is to check. You can’t just take it at face value.
- tmhn2 1mo agoYes, everyone is aware that the statement needs to be checked. No one has suggested otherwise. It goes without saying. The "magic" of lean is that (in principle, assuming lean is sound and the proof is verified) that is all you have to check by hand. That is a big deal.
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