True, .. and. In this case, the original proof is considered rigorously checked, so finding a bug in the kernel would be nice to know about, but in my opinion would not take away from the accomplishment (FLT in lean using agents) nor the many benefits of getting these mathematical objects formalized and usable in Lean in the future.

Do you have proof of this bug or something? Is this just envy against computers now ?

Well considering the proof is pretty much accepted by mathematicians to be correct (I'll be happy with that!), it would be sort of unnecessary to cheat. Maybe if some aspect is really tricky to formalize it could have done something there? If I had to search for it, I would go for parts of the original proof that are "outsourced" to other mathematical works. Imagine one of the agents struggling to download a paper due to a paywall or whatever and just deciding to cheat lol

This has nothing to do with Lean, e.g.

> The first coordinate of the polynomial X^2 (X^3 + X + 1 ) is equal to the prime factorization of 30 .

We defined polynomials as their coefficient functions in my algebra class, and it makes sense that you'd define a prime factorization as a function from primes to N, which naturally extends to a function N->N. So this junk theorem is part of normal math too. It just says in an obtuse way that they're both the function that's 1 at 2, 3, and 5, and 0 elsewhere.

junk theorems aren't the concern, soundness issues in the lean kernel are the concern.

Notably, junk theorems are true. Nobody would debate that the junk theorem is true. The main thing people would say is that junk theorems, while being true, are sensitive to precisely how you encoded mathematics, so despite being true, they are perhaps not conceptually meaningful.

As an example of a junk theorem, sasy you use the definition of the natural numbers using von neumann ordinals

https://en.wikipedia.org/wiki/Set-theoretic_definition_of_na...

Then for any natural numbers n, m, they're implicitly sets. So n \intersect m = min(n,m). This is the wrong way to think about natural numbers. You should not use this ever in proofs. But this isn't because your proofs would be false, but instead because it is a fundamentally confusing way to think about the natural numbers. It is in this sense it is a "junk theorem".

Isn’t there some theorem that any sufficiently complex mathematical languages will have statements that can’t be proven? :)

Well, there’s actually a very small set of operations that allow all computation, so it doesn’t take much to be a DSL and a GP too; I’d be surprised if a proof language couldn’t swing it.

it is a general-purpose programming language. for example, it's standard library allows you to do file io, networking, etc.