What's your basis for assuming LLM is capable of doing this?

I honestly don't know personally either way. Based on my limited understanding of how LLMs work, I don't see them be making the next great song or next great book and based on that reasoning I'm betting that it probably wont be able to do whatever next "Descartes, Newton, Leibnitz, Gauss, Euler, Ramanujan, Galois" are going to do.

Of course AI as a wider field comes up with something more powerful than LLM that would be different.

> what basis do you have for assuming an LLM is fundamentally incapable of doing this?

because I have no basis for assuming an LLM is fundamentally capable of doing this.

Because by definition LLMs are permutation machines, not creativity machines. (My premise, which you may disagree with, is that creativity/imagination/artistry is not merely permutation.)