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Well, mathematical physics is fine, but I think it's better to either start as physics or math and then move to it. To do research in mathematical physics means you should be able to do research level work in both physics and math. You'd be better off just doing research in whatever subject you master first. Trying to master both will obviously take longer, and your goal is getting to research asap. Having said that, I have no idea what the competition is like for this field.
By mathematical physics I mean rigorous stuff like axiomatic quantum field theory.
By mathematical physics I mean rigorous stuff like axiomatic quantum field theory.