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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.

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2 Answers 2

I think that in a borderline case like this, the math department is indeed the better choice.

At least according to my experience, the math community seems to be more flexible, give you a nicer environment and more freedom on what to work on. Also, it's a bit less competitive and the job options are better.

Read also the excellent advice of John Baez, http://math.ucr.edu/home/baez/advice.html .

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However, "the student is not so strict about mathematical rigor" might not like it in a mathematics department. –  Gerald Edgar Apr 13 '12 at 12:09
    
Fair enough. In general it seems to be more pleasant to be at the intuitive boundary of a rigorous community (if the student is not so interested in the details of something he can just skip that), than to be at the rigorous boundary of an intuitive community (e.g. if he wants to understand something precisely after all, but there is only vague hand-waving available). Of course, it depends on the specific situation of the student, so people who know him personally can give better advice... –  Robert Haslhofer Apr 13 '12 at 12:30
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I would like to clarify that the student likes rigor and prefers it over just hand waving but doesn't let rigor hinder his progress of things that he can directly see from intuition. That was the essence of that statement. Sorry for confusion. –  Lakshya Bhardwaj Apr 13 '12 at 12:39

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.

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