Now, I think AI will solve some, but we'll find out that some are just either unsolvable or wildly huge that nothing is solving them any time soon.
And a whole lot of these problems have been around quite some time, when even knowing how to do advanced math meant you were a landed gentry or someone of high wealth. If those problems fall, they fall. They aren't pets we keep around forever. And new problems will crop up over time for both AI and men to scratch their brains over.