I'm currently studying physics in an undegraduate program. It's fascinating and all, but my real interest lies in mathematics. My goal is to get a master's and eventually a PhD in math, but, in the words of my professor, "you will need to go pretty far before you can make a contribution to math." My question is, "how far?" I don't want to spend 10 years getting my PhD. Maybe I should stick with physics or switch to something more applied, like computer science, as a master's?