Math is likely moving into a big science era, much like experimental particle physics and astronomy did before it.
Once AI mines the easy unsolved problems, it will take large token budgets to make meaningful advances. That will need to be funded and planned at a societal level, like the great facilities of the other big sciences.
Mathematics will become more like an observational science, with some mathematicians specialized in interpreting the results that come out of the big AIs.
Progress is fundamentally limited not by finances (which are a human abstraction) but by the energy budget and how much can be extracted from it. This has always been the case, really, although it's unusually blunt in case of AI since compute mostly needs cheap power.
There's a separate question of who controls how much energy, and can therefore decide where it's spent. This isn't an inherent limitation to progress, though - it's an imaginary limitation that exists in our minds, a collective delusion, if you will. There's no law of physics that says Sam Altman gets to decide; we as a society choose to respect the property rights that translate to his economic (and attendant political) power to do so. We could choose to stop respecting them, and if we do so collectively, there's nothing they can do about it.
But it’s not like someone is going to expend massive energy without any financial return
These problems are just for marketing for the time being
Maybe the worries of the field of math being “over” are a bit overblown since a lot of pure math these things may discover has no return to the company
Once AI mines the easy unsolved problems, it will take large token budgets to make meaningful advances. That will need to be funded and planned at a societal level, like the great facilities of the other big sciences.
Mathematics will become more like an observational science, with some mathematicians specialized in interpreting the results that come out of the big AIs.