Mathematics cannot be "solved", that's a consequence of Gödel's First Incompleteness Theorem.
It can already be "cheaply verified" in the sense that if you write a proof in, say, Lean, the compiler will tell if you if it's valid. The hard part is coming up with the proof.
It may be possible that some sort of AI at some stage becomes as good, or even better than, research mathematicians in coming up with novel proofs. But so far it doesn't look like it - LLMs seem to be able to help a little bit with finding theorems (e.g. stuff like https://leansearch.net/), but to my understanding they are rather poor beyond that.