The fundamental issue with AI solving any perceived difficult problem is that we have lost the journey. The sight atop Mount Everest looks much different when you have climbed compared to being dropped from above.
So that raises the question: is mathematics simply a pursuit of passion? Are problems solved "because they're there"? If so, then mathematics can join the ranks of things like mountain climbing, cycling, and weight lifting. But if we are trying to accomplish something important (design better airplanes, find theoretical guarantees about cryptography, factor matrices faster), mathematics needs to become more like a military or search and rescue operation, using the best technology available to secure the outcome we need. Given that the NSF pours billions into scientific research every year, it sure seems like mathematicians want to think of themselves as being in the latter category.
If AI gave us the plane to reach Everest without us having gone through the journey of aviation and flight, what would we have lost without that process?
But the most important problems to be solved are not technological challenges but social ones, involving humans and our relationship to one another. An area AI will forever ill-suited to handle.