> In any research phd course you're actively told to bite off something small and likely to be provable so that you can prove it (and publish it).

But that's the start of math research, not the end.

The point is to get practice and experience doing research.

Did ChatGPT learn anything from these proofs, that it can build on?

Part of what's annoying people is that ChatGPT is churning though problems that are meant to be motivating. They are problems that aren't worth the effort of human professionals (usually because they are incredibly computation-hevy, so better suited for a computer than a human), so they are good for students to work on.