Should I opt for physics as minor for better mathematical intuition? Context: I intend to study mathematics and do research as a career. I am studying analysis and abstract algebra now and I shall begin my undergraduate studies shortly.


  Should I opt for physics as minor for better mathematical intuition?


I have been told my friend that physics may lend one intuition into a few mathematical structures though I am not sure. I can only think of differential equations as an example. In particular, please tell me if physics can serve as a source of motivation and if it is crucial enough.
There's a range of applications for mathematics around many disciplines. In the XX century, physics was definitely the biggest consumer of mathematics, from the photoelectric effect and the black body spectrum in the early century through nuclear bombs and space exploration of the second half. The XXI century looks to shape around biology and life sciences.


Physics leans heavily on PDE, real and complex analysis. Some areas may require abstract algebra, but they could turn out to be somewhat exotic (quantum Hall effect and other solid state physics stuff), and you would need to study physics for about 5 years to get to understand what it is if you are starting from ground zero. (School physics IS ground zero, in my books.) Until you know what Green's function is, there may be little point approaching physics for you.
Economics leans heavily on real analysis and optimization. There's some use of abstract algebra, although again to get to the areas where it is really needed (welfare economics, may be some very abstract macro), you need to get very deep into grad school in economics.
There's quantitative biology, in which separate fields may require way separate math tools: ecology uses some PDEs, while protein structure is computation that could be using abstract algebra, too, to describe the spatial structures (where it overlaps somewhat with material science).
Computer science is another big obvious consumer of mathematics, and abstract algebra is very immediately used in various codes. If you want to have an immediate gratification from having learned simple groups, you can go ahead and figure out how the PGP algorithm works.