Mathematics PhD after M.Sc. Physics

Question

I am an Indian physics student, studying mathematical aspects of quantum field theory and such. Over the years, I have realised that I do not enjoy the mathematical hand waviness that goes into theoretical physics. I often find myself asking about the validity of theorems stated by authors in general. Looking at myself now, I think I care more about the abstract mathematical structures built on very strong foundations (I loved taking a proper mathematics course in Linear Algebra a few years ago). My grades are excellent and my research profile (in theoretical phys.) is decent. Given that I am currently in physics, is it a practical idea to transition into a graduate program in mathematics? Of course, I am not as good as someone who actually studied pure math as an undergrad, but with some hard work, I think I can catch up.

Any help is appreciated.

Answer 1

What is "practical" is a judgement call that only you can make. But it is possible. The road might be longer than you like, however.

It's not a good life choice to make a career out of things that you don't enjoy.

I suggest that you go to the maths department at your current institution and ask them what they think it would take for you to switch fields based on your prior education. If that seems reasonable to you, even if hard, then you can apply to some programs that might accept you. You might have a lot to make up, however, depending on which math courses you have already taken. The exploration can be easily done.

Answer 2

Yes, people do go from other fields into PhD study in mathematics. Doing this may mean some "remedial" course work: writing proofs, or learning parts of mathematics that you didn't cover before. If the math program is large, then there would likely be other new PhD students doing this also.

Answer 3

If the question is whether it's possible, the answer is yes because I can cite a concrete example: myself. In my case, I had a personal connection to the math research group in which I ended up being a PhD student (I had been a student worker there for a while) and the math department made me take some pure math courses as a condition for ultimately being allowed to defend my PhD thesis, but other than that there were no conditions: Apparently they believed that I was good enough mathematically.

Answer 4

There are theoretical physicists who do mathematical physics, i.e. develop theories rigorously. This is also the case in quantum field theory. Maybe that is middle way that would suit you. It is then just a matter of finding such groups and get accepted there.