This is a good point, and there’s some deep philosophical questions there about the extent to which mathematics is invented or discovered. I personally hedge: it’s a bit of both.
That said. I think it’s worth saying that “LLMs just interpolate their training data” is usually framed as a rhetorical statement motivated by emotion and the speaker’s hostility to LLMs. What they usually mean is some stronger version, which is “LLMs are just stochastically spouting stuff from their training data without having any internal model of concepts or meaning or logic.” I think that idea was already refuted by LLMs getting quite good at mathematics about a year ago (Gold on the IMO), combined with the mechanistic interpretatabilty research that was actually able to point to small sections of the network that model higher concepts, counting, etc. LLMs actually proving and disproving novel mathematical results is just the final nail in the coffin. At this point I’m not even sure how to engage with people who still deny all this. The debate has moved on and it’s not even interesting anymore.
So yes, I agree with you, and I’m even happy to say that what I say and do in life myself is in some broad sense and interpolation of the sum of my experiences and my genetic legacy. What else would it be? Creativity is maybe just fortunate remixing of existing ideas and experiences and skills with a bit of randomness and good luck thrown in (“Great artists steal”, and all that.) But that’s not usually what people mean when they say similar-sounding things about LLMs.