Is there any branch in math that is not directly or indirectly used in physics?

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Just out of curiosity.
 
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Probably a few of these. I doubt finite field math (for example integer math modulo some other integer) is related to anything physical.
 
There are many subfields within modern algebra. Some of these that are far away from physics include algebraic geometry - anything that was worked on by Andre Weill or Claude Chevellay or their students.