I'll be precise: how much mathematics (in terms of courses in a university mathematics department or mathematics textbooks) can a very good theoretical physicist be expected to know? If this depends on the field, please specify. I am particularly interested in those working in areas of physics amenable to geometrical methods, e.g., general relativity, gauge theory, and quantum gravity.
I've seen similar questions but no concrete answers from physicists.
Edit: By "mathematics" I mean what physicists probably call "pure mathematics". Of course any physicist can solve all kinds of ordinary and partial differential equations, is competent in vector calculus and complex variables, etc. Perhaps other ways to phrase it are "rigorous mathematics" or "mathematics that isn't in Arfken".
Another Edit: To be more specific, how much differential geometry do physicists working in general relativity, gauge theory, etc. know?