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I am a second-year physics major, thinking of switching to mathematics. I have always been interested in both, but I could never be sure whether I could become a mathematician. Understanding physics was relatively more straightforward, and I found it fascinating how mathematical concepts could be used to explain the universe. I never was interested in engineering or experiment; in fact, statistical mechanics and general relativity made me decide to study physics.

The math courses I took in college made me question my research interests. I do not like the non-rigorous approach in my linear algebra and differential equations courses which I am required to take as a physics major. On the other hand, I find the rigorous math courses I am taking from the mathematics department, such as the axiomatic set theory and group theory exciting. Even if I change my major to mathematics, I will still be able to take courses like analytical mechanics and quantum mechanics; the only courses I will not take from the physics department will be the experimental ones.

I am almost sure that my future career will revolve around geometry. However, I am still determining whether I want it to be in a more physical setting like relativity, cosmology, particle physics, or pure mathematics.

Could anyone give me some insight into what to expect in terms of mathematics for a career in mathematical physics in the areas I mentioned? Would I need a background in experimental physics to build intuition, or coming from a mathematics background with some theoretical physics courses would be sufficient to understand the physical meanings of the concepts?