OpenAI should be allowed to produce whatever it wants but it just can't claim that it has actually solved without the due process like peer review. If for example OpenAI solves a new conjecture, OpenAI should be free to publish it in their blog or arxiv in whatever way they desire. It can be slop, it can be non-slop. No one should police it.
Mathematicians are free to use it or discard it. They shouldn't externalise their concerns and restrict labs.
Mathematics is seen today as the noblest and most aristocratic of professions. Turns out, AI disrupts it because access to capital/compute now decides the results. Mathematicians don't like this corruption - understandable.
Its like guild of accountants opposing the calculator and require a responsible release. haha