>> If that's true, if we're really at that level of autonomous mathematical reasoning ability, then we should see hundreds, even thousands, of open problems suddenly solved in a matter of years if not months.
Stressing "hundreds, even thousands".
Google released a paper about solving 9 more Erdos problems for an average of $100 each:
https://arxiv.org/html/2605.22763v1
In a year I think we'll probably have seen hundreds of open problems solved, even if there is some a low hanging fruit exhausiton bottleneck.
I think it is important to temper expectations in light of the fact that these announcements are coming from a startup company with shady values looking to imminently IPO, and thus represent the most biased and misleading take of the situation possible.
And if it isn't, we should find out very soon. If AI has got so good as OpenAI's post implies, then we should soon see a veritable blooming in the production of mathematical results, by lay people no less. No mathematicians needed! OpenAI say that their secret LLM solved the planar unit distance problem "autonomously" and the companion remarks say it one-shotted it; and while the companion remarks make it clear that there was a lot of refinement and improvement work done by humans, everyone seems to agree that the AI did the job by itself.
If that's true, if we're really at that level of autonomous mathematical reasoning ability, then we should see hundreds, even thousands, of open problems suddenly solved in a matter of years if not months. We'll just have to wait and see.