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.