I will expand this question with more specific points when I have my own internet connection and more time (we're moving in, so I'm at a friend's house).

This question is broad, involved, and to some degree subjective.

I started out as a physics-only student, but eventually decided to add a mathematics major. I am greatly interested in mathematics; the typical curriculum required for physics students is not deep or thorough enough; mathematics is more general (that means work!); and it only requires a few more classes. Naturally, I enjoy mathematics immensely.

This question asks mainly of undergraduate-level study, but feel free to discuss graduate-level study if you like.

Please do not rush your answer or try to be comprehensive. I realize the StackOverflow model rewards quick answers, but I would rather wait for a thoughtful, thorough (on a point) answer than get a fast, cluttered one. (As you probably know, revision produces clear, useful writing; and a properly-done comprehensive answer would take more than a reasonable amount of time and effort.) If you think an overview is necessary, that is fine.

For a question this large, I think the best thing to do is focus on a specific area in each answer.