Math envisions and communicates logic-based structures and objects that, as a side effect, may be relevant to certain real world problems decades to centuries after the initial research.

I'd argue your statement is treating this discovery process as an engineering exercise: there exists an unexplored bounded space of logical axioms within which we want to solve the relevant problems and paradoxes. Yes, AI will help under such a framework, by giving mindless and rote repetition to brute force a solution.

But mathematics begins from a different set of primitives - the space of exploration is not guaranteed to be bounded, so the solution context is derived after a lot of trial and error. This is a different philosophical problem being solved.

I'm not sure I'm seeing that the AI solutions offered up by frontier level AI are exploring the same space as mathematics. Overlaps, certainly. But "find new and interesting problems for the sake of fun, beauty, competitive and collaborative prestige" isn't motivational to an AI.