My intuition is that a regular LLM is better att coming up with a correct task description from a fuzzy description than it is at actually solving tasks.

There's a lot of automated proof checkers out there. Presumably you would just run any solution from an AI through those.

And most applied maths doesn't seem to worry about proofs much. They have techniques that either work pretty well or blow up.

Bridge collapses are a form of proof validation.