Is AI at the stage that it can also point out all interesting things to study and then solve them? Otherwise humans would still be able and needed for progress.

Good question. I'm not a professional mathematician, but I would be interested in seeing what results the mathematicians get from trying to prompt it to come up with new and interesting problems.

My intuition is that it'll be at 'smart undergrad' levels today, though as the cryptographers say, attacks always get better.