Note: This is a question directly copied from Theoretical Physics SE primarily to get the advice of people indulged in mathematics.
In the current scenario of research in QFT and string theory (and related mathematical topics), which of the following would an undergraduate student, like me, be advised to do and why if s/he is interested in both the foundations and pushing the frontiers of these subjects and doesn't differentiate between them or thinks that different set of skills and attitudes are required (plus the student is not so strict about mathematical rigor and even precise, logical, hand waving arguments suffice to convince him/her)?
Get into a maths department for graduate studies and work under people having similar interests and probably also take advice from people in physics department.
Get into a physics department for graduate studies and work under people having similar interests and probably pick up the mathematics one needs along the way.
Moreover, what would such a student majoring both in mathematics and physics advised to concentrate on during his/her undergraduate education?
It seems to me after reading this post and general experiences of mine that often mathematicians are more willing to accept physical ideas than physicists willing to accept mathematical ideas. Also, the number of people willing also seem to be more in mathematics, at least to me. Also, it seems that some physicists often develop a kind of hatred for mathematics and always remain skeptical that any mathematics can ever do good to physics. On the basis of this, I am inclined towards option 1. Please feel free to correct me.
Best Answer
As someone working in the field of mathematical physics, I believe that for a person with your interests it is somewhat better to be a graduate student in the math department. The reason is while there are quite a few mathematicians which regard physics as an important source of problems and insights, there are far fewer physicists who think that mathematical physics is worth working on. In particular, foundational issues in QFT and strings are not very popular with most physicists.