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It seems that a lot of folks misunderstand the guarantees that lean provides.

I just want to state that having "lean proofs" that build (checks) does not mean the actual real theorems we care about hold. Ignoring lean kernel bugs, ultimately a human (not an agent) has to verify the lean encoded theorem statements (specs/specifications), that the lean proofs are checked against, indeed correctly encode the real theorems. For non-trivial theorems such as these, this is an arduous and tricky task where even a little mistake could be fatal. AI generated lean encoded theorems can be huge and difficult to understand. I wonder if anyone reputable has audited these specifications.

by DroneBetter2 days ago|

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well, a bug in the Lean kernel was discovered last week by way of an LLM tricking itself and its handler into believing it had found a non-constructive proof of the existence of a nontrivial Collatz cycle, see https://infosec.exchange/@0xabad1dea/117002106099986943 and https://lipn.info/@mevenlennonbertrand/116997917683191056

by traes2 days ago|

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That seems to have been more of a sensationalized joke. Even your link has a disclaimer in it now. Read this chat from the researcher who did this:

https://leanprover.zulipchat.com/#narrow/channel/270676-lean...

by jibal2 days ago|

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It's not at all a joke ... that's a severe misunderstanding of the context.

by traes2 days ago|

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There is no evidence that I can find for the claim "a bug in the Lean kernel was discovered last week by way of an LLM tricking itself and its handler into believing it had found a non-constructive proof of the existence of a nontrivial Collatz cycle."

As I currently understand it, all we know is that:

- a mathematician produced a Lean-verified counterexample to the Collatz conjecture, demonstrating a bug in the kernel

- he claims that LLMs were involved somehow but pointedly refuses to specify how

- he admits that he knew about the bug before publishing the counterexample to his repository.

Perhaps not a joke (although it sure seems to me like they discovered a bug and thought falsely disproving the Collatz conjecture would be a flashy way to announce it), but at best extremely sensationalized by the above description. If you have additional context I would be happy to hear it!

by zahlman24 minutes ago|

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Indeed. It seems to me much more likely that the AI was directed to look for bugs in Lean, found one, and then it was directed to write a proof specifically targeting the bug.

by danielrmay2 days ago|

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Fascinating, and arguably an illustration of why the bifurcation of responsibility is interesting in the first place.

by traes2 days ago|

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I'm not an expert at it myself, but my understanding is there are numerous ways to "cheat" in a Lean proof (via `sorry` and similar). They're taking responsibility for fully verifying that none of these cheats were used (and that the theorem statements themselves were all correctly formalized.)

by emil-lp2 days ago|

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No, the correctness isn't for the "inside the Lean proofs", but for the translation of "human language math" and its formal Lean variant.

by danielrmay2 days ago|

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I see. It still feels like a bit of an oddly solemn way of saying "this is the part we admit responsibility for"

by jhanschoo1 days ago|

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Traditionally, a mathematician would be implicitly responsible for all that (if they were to publish Lean code) and also the intellectual work that led to the artifact of the mathematical paper (and code, if part of the contribution). This statement should rather be read as an acknowledgement of limitation of authorship from the implicit, traditional understanding.

by emil-lp2 days ago|

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Well, to be fair, with Lean proofs, that's the only thing there is (unless I'm missing something).

by baq2 days ago|

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It’s more than you get from free software - you get no proofs, no warranties and any responsibility of its authors are their pure good will. Reminder lean proofs are software!