To the “LLMs just interpolate their training data” crowd:
Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules.
I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries.
So either “recombining existing material” isn’t disqualifying, or a lot of Fields Medals need to be returned.
Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules.
I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries.
So either “recombining existing material” isn’t disqualifying, or a lot of Fields Medals need to be returned.