Comment by rtpg

I don't know if we can really be clear about the order of things, but I think even without AI maths is filled with "someone provides a proof of X, and the proof itself is wrong/incomplete but X itself is true".

"Incomplete" proofs might be a way of viewing this. You have a NL argument to prove X. It turns out the NL proof has holes you can drive a truck through. So... you go around and patch the holes.

The resulting proof is different! You can start off with a bad proof and find a correct proof. Sometimes.

EDIT: for French speakers (maybe autodub gets you there) I saw a very nice simple case of this recently. A commonly stated proof for a relatively simple theory. The proof has a giant hole in it, and completing it requires some work [0])

[0] https://www.youtube.com/watch?v=kQBu6NH1u3I