as physics student you quickly come to figure out that physical intuition is not the same as mathematical intuition. there are many hacks (for lack of a better term) in physics that a mathematician would've never been able to come up with because they're physically intuitive but not mathematically (a famous example is the Feynman path integral)

Right, we know that much of mathematics grew from physics, but the question remains: what is there in the known theoretical physics that is not (applied) math? (Well, I think I may already know the answer: nothing; but it does not matter, because science is not about what is known...)

There is the entire half of physics that is the empirical verification of the hypotheses left, for example. Theoretical physics cannot be separated from that, in my view.

> Theoretical physics cannot be separated from that

Sure, but books on theoretical physics seem to rarely mention empirical verification. It's mostly math, and I am not sure what is left if you remove it (as known).