Well, the rest mass notion in special relativity is just a natural derivation. It appears once you have the "real" ideas in place. And those aren't really "existing math" at all. It was a pure physics idea at root: "the universe's laws don't change if you are in motion" (or alternate framings like "you can't tell if you're moving from inside a moving box").

Well, it turns out that if you try to construct such a theory, you end up needing some different (pre-existing) math to help describe it. But the idea isn't math at all.

Then the question is "Can LLMs propose new well-framed, evocative theories like relativity", and the answer is sort of open. In point of fact human beings, to first approximation, can't do this either!