Another anecdote. I've got a personal benchmark that I try out on these systems every time there's a new release. It is an academic math question which could be understood by an undergraduate, and which seems easy enough to solve if I were just to hammer it out over a few weeks. My prompt includes a big list of mistakes it is likely to fall into and which it should avoid. The models haven't ever made any useful progress on this question. They usually spin their wheels for a while and then output one of the errors I said to avoid.

My hit/miss rate with using these models for academic questions is low, but non-trivial. I've definitely learned new math because of using them, but it's really just an indulgence because they make stuff up so frequently.