I don't accept that premise. It took a while to verify the predictions of General Relativity. It certainly wasn't driven by experimental evidence. Einstein star

I don't accept that premise. It took a while to verify the predictions of General Relativity. It certainly wasn't driven by experimental evidence. Einstein started work on GR with a thought experiment (according to Wikipedia) and of course there's Minkowski's famous observation that SR could have been inferred before Einstein from Galilean Relativity, spatial isotropy and the probable existence of a geometric invariant. In other words, pure math didn't get there, but once they all arrived it could really give insight. Check out Minkowski's famous "staircase wit" comment. Another example from physics is the extent to which Schrodinger was influenced by Eastern philosophy in his formulation of quantum mechanics.