Math/Physics Bachelors Degree?

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Okay, so right now I'm scheduled to go to University for Aerospace Engineering but I'm having second thoughts. I got into it b/c I love math and physics and I thought that since I also love everything space related this would be the perfect program for me.

Now I'm thinking that I should go directly into a math or physics program. I think that I would enjoy the program itself as well as the possibility of a research career after university. I realize that I would probably have to get a Masters, or more likely a PhD, but I can do that.

My only problem is I don't know how hard or easy it is to get a career in research. I'd much rather be a "mathematician" if they are still around, but being a physicist is not bad at all.

tl;dr what would it take to get into a research career in math or physics. This means what level of degree and how hard would it be after I get it.
 

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