Certainly it'll result in a boom for hobby mathematics, and it'll be a hobby at a much more advanced level than before. Whether those hobbyists can continue to push the actual frontier, particularly if AI models operating along that frontier are not made accessible to hobbyists (either via corporate/AI lab gatekeeping, via pricing, or via significant time lags) is a different question. I'm a little more confident in a future where hobbyists push the frontier in applied mathematics than in pure mathematics.

There's probably a loose and deeply imperfect analogy with computing: via democratization hobbyists have made a big impact in applied operating systems development (Linux/OpenBSD) but have been less successful/impactful in OS research (whither Hurd...) or in cost-heavy fields like microprocessor design.