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I am a highschool student and my fields of interest are physics and mathematics. I've been advised to apply for the mathematical physics undergraduate program but I don't want to rush so that I won't have to regret my decision afterwards. I have a few questions about the paths I can take later after the Bachelor's degree.

From what I have understood while researching, I will be able to enroll into graduate studies either into physics or mathematics later. But does this mean that I won't be able to begin a career as an experimental physicist if I wish to? (Because mathematical physics is more heavily focused on theory). Also will I be disadvantaged compared to other applicants when applying for either maths or physics graduate studies because ( I guess) they will have completed more maths or physics courses if they chose only maths or physics for their undergraduate studies?

I want to keep all the doors related to maths and physics (I mean the careers) open for me. So I was thinking of double majoring in maths and physics instead. But i don't know which one will be better. Please help me; I don't want to regret afterwards.