Being a grad student in math, and a rather pedantic one indeed, I was unable to accept many of the things taught to me in undergrad physics courses. I am now trying to learn the applications of geometry to string theory and the applications of probability theory, my main field, to statistical physics. Are there other prominent interfaces between abstract math and theoretical physics?
Where can I find these topics explored in a way that would be accepted by a mathematician? (I.e. every object mentioned is a legitimate object or logical statement in ZFC, and every nontrivial claim is proven, no use of unproven conjectures for anything but motivation, and wherever necessary to actually talk about physics of the real world, assumptions that link mathematical ideas (which are merely logical symbols and sets) to what they intend to model are stated in logically precise ways.)
In other words I am looking for a "Bourbaki" approach to physics, and wouldn't mind if the book started even as pedantically as to say, for instance, what a physical unit represents in set theory.
