AI models and in particular LLMs are not capable of logic reasoning. See for example this paper:

https://arxiv.org/abs/2506.06941

Ergo, they can't prove any theorem whatsoever. How do people at OpenAI expect that we believe in claims like that? This is yet another before-the-IPO stunt in my opinion..

Personally, I won't believe any of these claims until the community of mathematicians says otherwise.