I'm majoring physics, but really interested in mathematics.
I liked physics since it was really beautiful to have an analysis on a nature with mathematical tool. However, the more i study, the more it seems like physics is not like what i thought it was. It's not because physics don't use mathematics, but because professors don't teach mathematics. Mathematical physics is an example. One can check that it's not precise at all.
Many physicists say that "Physics is totally different from mathematics" and don't like to treat physics as an application of mathematics. (Mathematicians too don't like people treating mathematics as a tool for physics. Aren't you?) I agree both, but i believe one could influence on another. Who is the inventor of calculus? and Who thinks Lorentz is nothing compared to Einstein? Hilbert said, "Physics is too hard for physicists".
Anyway, I haven't decided yet, but i think I'm going to major theoretical physics (I even have some mind to change my major to mathematics) and i have a great interest in set theory. However, i see there are only few set theoriest relative to other branches of mathematics professors. One day, i visit a topology professor and asked some questions about set theory. I was so surprised that he doesn't even know what is ZFC, and he suggested me to study another mathematics rather than set theory which is 'tedious' to do. Well, I think it's not tedious at all, but it's something fundamental.
However, there is a problem. It's going to take a really long time to study proper set theory. To make it clear, 'I'm not interested in sets, but interested in precisely studying mathematic starting from ZF or ZFC'. It's almost impossible for me to study both physics and mathematics..(Maybe possible! If i study really hard.. Any experience?). Should i change my major to mathematics to be a mathematical theoretic physicist?