From my naive standpoint, LLMs like this seem to have some big strengths. One: possession of a superhuman expanse of knowledge. Two: making connections. Three: tireless trial and error.

If you put those three things together, you end up with some cool stuff from time to time. Perhaps the proof of P!=NP is tied to an obscure connection that humans don't easily see due to individual lack of knowledge or predisposition of bias.