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I'm a non-mathematician who is self-studying mathematics. Although I'm very interested in mathematics, my main purpose is to apply math in theoretical physics. The problem is that when I read a mathematics books, I can't see a clear way to apply these math in a concrete setting. I want to apply higher math in my study of theoretical physics (not mathematical physics). I'm not looking to put physics on a rigourous basis (e.g axiomatic field theory). I want to use math (e.g. category theory and algebraic geometry) in order to discover new ways of thinking about physics, generalizing concepts and to calculate stuff. I'm completely self taught in math. Should I read pure mathematics textbooks aimed at mathematicians? What's your advice on this?

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    How is physics "not mathematical"?2012-07-24
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    @PeterTamaroff: "Mathematical physics" is a specific subfield of physics. That doesn't mean the rest of physics is "not mathematial". The statement is "not (mathematical physics)", not "(not mathematical) physics".2012-07-24
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    @celtschk I interpret "mathematical physics" as a subset of mathematics rather than of physics, but maybe this is a mathematician's perspective. ArXiv has both math-ph under Physics and MP under Math. By the way, [ArXiv bookworm](http://arxiv.culturomics.org/) divides all of math into 2 areas: *Mathematical Physics* and *Other*. :)2012-07-29
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    @LeonidKovalev: Actually I've never really thought about whether it is considered part of mathematics or part of physics, but just assumed the latter because of the name (usually if something is named "XXX physics" it is considered part of physics). However I don't think it really matters too much; it's more of an example that our desire to put each field under exactly one term doesn't fit reality very well. Real world terms have fuzzy borders, and even the term "mathematics" isn't exempt from this.2012-07-29

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