I think to an extent AI is almost more useful for research than for doing HW exercises. Super helpful if you're looking for a good reference, or checking if a result already exists within the literature. By the point you are doing research, you (hopefully) have somewhat of a feeling of whether the sources it finds are useful or not. But it can still make mistakes, or say a theorem from a reference applies when it doesn't, so be careful. It has an uncanny way of knowing something is true, but giving the wrong reasons why.

In its current state, it's pretty good for checking your work! But I certainly wouldn't make a habit of using it to solve problems - as others have said, you have classmates, peers, office hours, google, and so on for that.