> Are you implying the machine taught itself the mathematics to do all this?

Are you asking me how LLMs work?

The theory proposed by the original commenter was that there could have been some secret training data the model was trained on that made it possible to solve this problem set. So the only conclusion is they are implying it's a conspiracy by OpenAI to hide some novel math research they funded merely to do marketing about solving math problems (then convincing multiple math experts to verify and support it with papers). That is the definition of a conspiracy.