@P3ng1z@SdBachman@koshercockney@Mish_K_ I think he just misspoke. He should probably slow down his speech so he has more time to think before he blurts out with his usual rapid fire style.
@BobMcElrath I don't understand why they didn't get *everything* Lean formalised and verified, or at least only release the stuff that had been?
The whole sell of formal verification is: a machine verified it and that's better than any meatbag (meatbags just need to check the formalisation)
@epyoncf You *can*, in principle, but as you well know, basically nobody does, historically because
1. it takes a few orders of magnitude more effort
2. specs are terrible/non-existent
3. it requires specialist knowledge and most programmers suck even at maths
@epyoncf That's their incompetence, frankly. First rule of formal verification is that humans verify carefully audit the formalisation. You should also sanity check the formalisation: e.g. prove expected corollaries.
@thinkingheights Right. The Lean proof should be the source of truth, and you can use whatever tools you want to understand it, including a Lean -> NL pass.
Incidentally, you do get these same issue with hand written formal verifications, where someone's write-up isn't completely faithful.
@acanthari@semiDL Hopefully.
I got chewed out by my external examiner because I restated my formally verified theorem in simplified natural language that was technically inconsistent.
@uubzu@ElliotGlazer No. What needs to happen is that mathematicians need to audit the formalised theorem statements and confirm that Lean verified the proofs. This is relatively easy to do.
If OpenAI didn't bother, it's because of their basic incompetence at formal verification.
@neocentrist Possibly a big deal.
The philosophy of formal verification is that humans carefully audit the formalisations. The proofs can then be whatever slop you like.
If you are getting the LLM to do the formalisation and not auditing that, you are being f**king retarded.
@uubzu@ElliotGlazer Mathematicians have no reason to bother with slop unless they're confident it is correct. That's the whole point of getting Lean verifications *first*.
This applies to humans too. Famously, mathematicians couldn't be bothered with Deolalikar's purported proof that P != NP.
@Ognifedefingo The line I was fed studying history of maths is that the problem solving begets problems, and so the whole thing keeps churning. Alignment here is making sure that the LLMs are begetting good problems.
@reset_by_peer Implementation is definitely a bottleneck. There's a load of stuff now in my daily workflow I would never have remotely considered in a billion years were it not for the LLMs being able to hack it up in a few minutes.
@Noahpinion I think Daemon is definitely worth a reread in light of AI doom discourse. The stuff in that novel is extremely far-fetched but less so now with LLMs, and the broader point is that you should worry about narrow AI before AGI.