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I've just been accepted and will begin as an undergraduate in physics this fall. I'm planning on taking classes, in addition to the required courses, concentrated in particle physics, QM, field theory, etc. Also, I took courses on Set Theory and Topology, and fell in love with what I could garner from the experience.

So my questions are the following: If I were to look into a career in Abstract Math, what sort of options would I have? Academia, education?

Furthermore, I've been told there is a lot of abstract math ideas in many areas of physics. In what ways and areas do abstract math and physics overlap?

What sort of careers could I hope to have that would require knowledge of math and physics in these (theoretical/abstract)ways?

Thank you,