Ok, i have come to a realisation that my interests revolve not around pure mathematics (as i once thought) and more around theoretical physics, some people would claim that they merge into one at times, and that leads on to my question. If i wanted to be a theoretical physicist (rather than an experimental physicist), but am not keen on string theory, are there any other fields of theoretical physicis which i could focus on in grad school? Why am i not keen on string theory? well the answer is twofold, one i doubt i could match the contributions of the likes of witten and greene and secondly, i am slightly dubious of the credibility and goals of string theory. My second Question is, how much mathematics must i complete to become a theoretical physicist? (i use this parameter loosly as i am aware you never stop learning mathematics) say i want to learn quantum field theory or Paticle theory in grad school, will mathematics up to complex analysis/fluid dynamics/advanced PDEs (the applied side) suffice, or will i need to learn topology, representation theory, functional analyisis (the pure side) as well?