I did my undergrad in mathematics, and I really enjoyed studying that subject. After graduating, I've been continuing my study in Real Analysis with one of my undergrad professors, and I really feel like I'm blooming into a decent analysis student. This week I'm going to start learning functional analysis and lebesgue integration as a directed study over Skype, and I'm really looking forward to it. It's almost as if math is the only "pure" subject out there, i.e. rigorous in the sense that every thing you say must have a precise meaning and there is no tolerance for hand-waviness or ambiguity (at least that's the way I like to do it and some of my best professors did). That is the one thing that I do not like about physics, physicists are too imprecise about what they say, and they introduce variables and formulas without even naming or defining them half the time. At the same time, I also studied plasma physics and E&M and classical mechanics as an undergrad, and my goal throughout college has been to end up working in the nuclear fusion research field someday. I even did a summer internship in a plasma physics lab in a nuclear engineering department last year, and thoroughly enjoyed it. I was accepted into a M.Sc. in Fusion Energy at the University of York in the UK, and I'm going to go there to do my Master's this year. I also really think I will enjoy that course and it pertains more directly to what I'd like to do as my future career. So basically, I'm kind of at a crossroads as to whether I should continue to pursue plasma physics as a Ph.D. option, or if I should go into a Math Ph.D. instead. Last year, when I was applying to grad schools, I got into the Uni. of Wisconsin among others for nuclear engineering, and I was offered a spot in a computational/theory group where they do a lot of work in numerical analysis for plasma simulations and also pure theory. It seemed like a really good fit, but I got a fellowship to go to the UK so I'm taking a year to go and do that. Sometimes I just feel as if I would be "selling out" by not doing a Math Ph.D. I really enjoy analysis and I want to know everything about it that I can learn, but honestly I don't really want to be a professional mathematician. I'm just afraid my knowledge of analysis and other relevant subjects would be less if I didn't do a Math Ph.D. I've always wanted to work in plasma physics and nuclear fusion research, though. My ideal future career would probably be to be a full-time researcher at a national lab or NASA. At Wisconsin, they have an MA in Math intended for Ph.D. students in other subjects, which is only course-based. Also, St. Andrews University in Scotland has a Ph.D. in Math, but there is an active group studying solar plasma physics in the math department. I'm just a little confused as to what is the best path for me to take. Right now I'm feeling Wisconsin, but who knows? What if I end up falling in love with analysis/math even more than physics? edit* The other dilemma is that, if I go into math, I could probably only get into a rank 30-50 school at best with my credentials (i'm guessing, I haven't taken the math GRE yet), but I could get into a top 5 school in Nuc. Eng., since I already have once.