I'm a mathematics specialist with interest in general relativity, and would later like to learn quantum field theory and superstring theory. Of course this requires learning mountains of mathematics that I haven't even learned yet because I spend 80% of my studies doing math proofs. Doing math proofs and learning the proofs of all imporant theorems is key for a mathematician, but how much is it for the general relativist or the quantum field theorist? Is it worthwhile for them (and you) to study the proofs of the mathematical theorems that you use in your relativity studies? Do you just memorize the mathematical theorems, accept the results, and just make sure you know how to use them to solve your relativity problems? Or do you actually take the time to learn the proofs of the theorems and understand why the theorems are true. Do you make sure that you can derive the curvature tensor instead of just know how to use it? Do you make sure that you understand why the paracompactness of the manifolds you use in your relativity problems is the necessary condition for the existence of a partition of unity? Or you don't care and just use the results? I ask this because I spend so much time doing math proofs that I cannot learn fast enough the enormous amount of math (and physics) I need to tackle, say, superstrings and supergravity. Yet, I don't feel right accepting new mathematical definitions and theorems without understanding why the theorems are true.