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I love mathematics, but physics is far away from my interest. I see that recent mathematics research is strongly connected to mathematical physics which is something doesn't interest me!

I love mathematical entities and structures, stuff like relativity and quantum mechanics are not even close to my area of interest, so I wonder if I can go any further in mathematics without exposure to those stuff.

My favorite fields so far are complex analysis, PDE and differential geometry but I see them always mentioned with mathematical physics, so my question is

Can I do research in those areas and have any notable achievement without exposure to mathematical physics?

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Absolutely. Studying a mathematical topic for its own sake without a particular "real-world" application (such as a physical model) in mind is what people refer to as "pure mathematics". That said, having at least some idea of the applications of your field can help inspire you to ask fruitful questions. – Austin Mohr Feb 21 '12 at 21:00

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