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this post was submitted on 26 Jul 2026
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As an interesting follow-up to the ai-does-maths-using lean4 stubstack comments on Sunday, an llm accidentally uncovers a bug in the lean4 kernel.
Summary by Meven Lennon-Bertrand:
https://lipn.info/@mevenlennonbertrand/116997917683191056
Eta: “sorry-free” in this case means a complete proof with no trust-me-bro steps or TODOs… the
sorrytactic in lean “proves” a theorem to be correct even if it is garbage or incomplete. More programming languages should make developers apologise for half-arsing their work.How bad this is, is unclear just yet… probably not the sky actually falling, but not great. Interesting though.
A little bit of plot thickening spotted by abadidea: https://infosec.exchange/@0xabad1dea/117002106099986943
tl;dr, the timeline looks like this:
There was only a day between the first two events, and the non-proof was not where the bugs were discovered. So maybe it was just a coincidence that the chatbot found the bug at the same time, or maybe it’s training data included previous investigations into those bugs which it then built upon and that would be a bad thing for other llm generated proofs.
The collatz conjecture is sufficiently famous that enough third-party checking was done to spot the problem. I wonder how much checking would have been done on proofs of less famous and interesting things.
And a follow-up by talia ringer, who observes that there have always been gaps between the type-theoretic underpinnings of things like the lean prover and their actual implementation, and this hasn’t been so much of an issue til now because theorem provers haven’t had the attention of people in high places, and the type-theoreticians have been able to catch up in due course.
https://mathstodon.xyz/@TaliaRinger/117005740997367321
Anyone want to place any bets on whether or nor the big llm companies are going to fund academic research that isn’t obviously mechanisable right now and won’t yield any clickbait headlines?
See also a question asked today on Math Overflow, "Are we stuck with Lean?". The proposed alternative, Metamath, isn't type-theoretic and thus skips the entire dialogue between type theory and proof assistants.
Lean was already known to be untrustworthy and bad, although people refuse to internalize the situation because they're caught up in Buzzard's hype machine. This is extremely funny but I don't see any signs of people waking up and realizing that Lean sucks.