> Because in my layperson's eyes that's the difference between math and theoretical physics. Not really. The distinction, to the extent that there even is one,

> Because in my layperson's eyes that's the difference between math and theoretical physics. Not really. The distinction, to the extent that there even is one, is mostly a matter of motivation and methodology. Broadly generalizing: mathematical physicists (i.e. mathematicians) are interested in physical theories that seem like they might need interesting new mathematical tools to understand, while theoretical physicists are interested in theories that seem like they might have something to tell us about the true structure of whatever the object of interest is. There are other differences downstream of this, of course: - mathematical physicists are rigorous while theoretical physicists will let it lapse if that gets them physically correct answers - physicists care less about inconsistencies in theories they know are wrong anyway - mathematicians stay long after all the physical content has been mined out (a significant fraction of just-plain-mathematics is the end result of this process) and so on. But you can find people anywhere between these poles. Witten can (and sometimes does) produce world-class mathematics when he wants to, but most of his work is on the physics side of the spectrum.