[pfdietz]

They're finding them very effective at literature search, and at autoformalization of human-written proofs.

Pretty soon, this is going to mean the entire historical math literature will be formalized (or, in some cases, found to be in error). Consider the implications of that for training theorem provers.

[mlpoknbji]

I think "pretty soon" is a serious overstatement. This does not take into account the difficulty in formalizing definitions and theorem statements. This cannot be done autonomously (or, it can, but there will be serious errors) since there is no way to formalize the "text to lean" process.

What's more, there's almost surely going to turn out to be a large amount of human generated mathematics that's "basically" correct, in the sense that there exists a formal proof that morally fits the arc of the human proof, but there's informal/vague reasoning used (e.g. diagram arguments, etc) that are hard to really formalize, but an expert can use consistently without making a mistake. This will take a long time to formalize, and I expect will require a large amount of human and AI effort.

[pfdietz]

It's all up for debate, but personally I feel you're being too pessimistic there. The advances being made are faster than I had expected. The area is one where success will build upon and accelerate success, so I expect the rate of advance to increase and continue increasing.

This particular field seems ideal for AI, since verification enables identification of failure at all levels. If the definitions are wrong the theorems won't work and applications elsewhere won't work.