Advice on doing physics under the umbrella of mathematics and the converse 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)?


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*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.
 A: If you're not bothered by the need for rigour, I'd recommend option 1, mathematics. You are going to want to get a job afterwards, and in theoretical areas, physics departments seem to get caught up in fads. There was a great fad for hiring in string theory for quite a while, and people pursuing other theoretical directions were out of luck. Now, there seems to be a fad for phenomenology, and people pursuing other theoretical directions are out of luck.
Mathematics departments are much less susceptible to short-term fads like this. If you're doing substantial mathematics (i.e., some of your papers read Theorem ... Proof ...) that's related to theoretical physics, you should be able to get a job. 
A: Frankly I think Yuji's deleted answer hits the nail on the head, in that concerning yourself with the sociology of various departments is rather a bad idea. "Mathematician"'s answer is essentially the opposite of this advice, making very generic claims about the nature of researchers in various departments, and I believe this is poor advice.
The exact purview of various university departments are not constant across different universities. I know physicists working in at least 5 different departments (physics, mathematics, materials, chemistry, engineering), and mathematicians working in a similar number (mathematics, physics, computer science, biology, engineering). Even talking in generalities, theoretical physics can be found in either its own department, or as part of physics or mathematics departments depending on the university. Making claims about what research papers will look like based on the departmental affiliation of the author is crazy. I myself wrote Theorem...Proof type papers while in a Materials department, and wrote papers without such structure while in a maths department.
When choosing where to do a PhD, you should choose it almost entirely based on the supervisor, not other factors. You'll be shaped far more by your supervisor and their group than by any other factor in grad school. Forget about what department they are in. Many universities don't even include the department on your degree. When asked what their PhD is in, pretty much everyone gives the area not the department. The factors which should really concern you are things like whether a potential supervisor wants to work with you and whether you think they would be good to work with, whether their research is the kind of thing you are interested in, whether they give their students much of their time or whether they are absentee supervisors, the funding situation, etc. None of this is department specific.
