If they aren't "smart enough" to know if it work they most likely are also unable to verify if the Lean formalization is indeed the one that matches the problem they were trying to solve.
Verifying that every step in a (potentially long) proof is sound can of course be much, much harder than verifying that a definition is correct. That's kind of the whole point.
That's not what the parent comment meant. They meant checking the Lean-language definitions actually match the mathematical English ones, and that the Lean theorems match the ones in the paper. If that's true then you don't actually need to check the proofs. But you absolutely need to check the definitions, and you can't really do that without sufficient mathematical maturity.
That's great if it works. But it's way harder to produce a formal proof. So my expectation is that this will fail for most difficult problems, even when the non-formal proof is correct.
If they aren't "smart enough" to know if it work they most likely are also unable to verify if the Lean formalization is indeed the one that matches the problem they were trying to solve.
Verifying that every step in a (potentially long) proof is sound can of course be much, much harder than verifying that a definition is correct. That's kind of the whole point.
That's not what the parent comment meant. They meant checking the Lean-language definitions actually match the mathematical English ones, and that the Lean theorems match the ones in the paper. If that's true then you don't actually need to check the proofs. But you absolutely need to check the definitions, and you can't really do that without sufficient mathematical maturity.
3 replies →
That's great if it works. But it's way harder to produce a formal proof. So my expectation is that this will fail for most difficult problems, even when the non-formal proof is correct.
Formalize this in the form of a Iranian Lego Trump Dis Rap video.