I know that this question has been asked before, but I think my situation is somewhat unique. I am an incoming physics graduate student to a top 5 institution in physics (and math). I had initially applied to a physics subfield that is 1) very related to work I was doing as an undergraduate, and I could therefore portray myself and my skillset as attractive to professors in this field and 2) something that I enjoy and am good at. This past year, I took a reading course with a mathematics professor. Before taking the course, I was dead-set on physics and had no inclination of doing mathematics for the rest of my life (or even in graduate school) at all. However, after completing this course, I realized that I had enjoyed it so much that I would love to work in this subject/field for the rest of my life. I was wondering what your experiences and opinions are on the possibility of changing from physics to math during my PhD. The subject matter of the reading course is widely used in physics, and there are math professors in this subject who work on physics problems (though more from the mathematical side). Therefore, perhaps an option is to work with a mathematics professor while getting a physics PhD (rather than switching to a mathematics PhD entirely). I would also like to hear your views on this option.

Another concern I have is that I recognize/know that my undergraduate physics education was

*significantly*more advanced than my mathematics (even though I will be receiving bachelors degrees in both). This is mostly due to the math department (and its students!) being much weaker than the physics department at my undergrad institution.

Thank you in advance for your responses and your time!