5 ms·

but i don't understand... isn't Wiles's proof and its numerous rewritings already in the training set?

• QuesnayJr 12d ago
  Of course it is. The interesting thing is that it was able to produce a Lean proof in 11 days, when there's been an ongoing project for several years to do the same thing (though a somewhat different proof) that is nowhere near done.
  • tatjam 12d ago
    I think there's a big misunderstanding going on here, translating the proof to Lean is, well... a translation task. Formalizing the proof in a way that's useful (breaks the proof down into relatively independent blocks that can be used for other maths and, importantly, understood individually) is a quite bigger, more creative endeavor. Not sure if LLMs would be able to do it, maybe yes?
    • mswphd 12d ago
      note that this is exactly analogous to an LLM being able to slop code some demo, but not build something more generally useful/maintainable (say something suitable for inclusion in a standard library).
    • QuesnayJr 12d ago
      It wasn't clear that LLMs were up to a Lean translation task of this scale until now. The background required to formalize the FLT proof was tremendous, so many people assumed we would have to wait until all of that was formalized in Lean before we could ask it to formalize Wiles' proof. Now it seems like almost any mathematics paper we can ask an LLM to formalize, including all necessary background, and it can just do it.
• deleted 12d ago
  [deleted]
• ngruhn 12d ago
  Yes. The point was not coming up with the proof from scratch. The point was writing it all down in Lean to make it fully machine checkable.