A book that covers all the math a physicist will ever need?

[Kalvino]

What is a good book, after mastering calculus, that covers all the mathematics a theoretical physicist will ever need?

 

[micromass]

Different theoretical physicists use different kinds of math. So there isn't really such a book. But you can probably start with Boas: https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20 or Kreyszig: https://www.amazon.com/dp/0470458364/?tag=pfamazon01-20

 

[vanhees71]

Indeed, usually when starting some new project, you realize that there still is some math you don't know. That's research! It's important to have the standard repository of mathematical skills. As a theorist I'd say the following topics should be covered: vector/linear algebra, tensor algebra, vector (+tensor) calculus, analysis, elements of functional analysis (theory of distributions), probability theory, the Hilbert space, elementary Lie-group and -algebra theory including representation theory on Hilbert space.

From this basis you can learn any special math topic pretty easily when needed. So it's more impotant to learn the way (applied) mathematicians express their results and how to make them useful for your own research in physics than to just try to learn "all the math a physicist will ever need". E.g., an experimental physicist will need a lot of practical statistics for analyzing the results of his or her measurements, while a theorist interested in General Relativity will need a lot of differential geometry, which is (almost) useless for an experimentalist and vice versa.