> The prompt for the Jacobian conjecture was obviously not random. the search space is too big to just try all the combinations of 3 variable polynomials.

Maybe the prompt contained a part like this: "the search space is too big to just try all the combinations of 3 variable polynomials, so be clever about it". Or maybe this part was omitted from the prompt, because modern LLMs are smart enough to figure this out without us having to mention it.

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jknoepfler 20 hours ago | parent [-]

If someone has written that in a paper or article they've ingested, as they no doubt have, then sure.

	▲	jameshart 18 hours ago \| parent [-]
		The ability of LLMs to solve problems is not confined to the training data they ingested. Claude knows how to read mathematical papers because of its training data, but it can and will pull in literature relevant to a specific problem into its context. We really need to stop thinking about LLM training data as the knowledgebase they build from and instead consider it more the skillset they start with.