I do condensed matter physics modeling in my phd and I was struck up learning quite an amount of physics. But while having done lot of physics courses, I see that if I learn pure math I would understand lot of things better and also probably my modeling skills also might get better. A math prof asked me to do all courses from basic analysis to differential geometry. But that would take time as I see I am taking time studying Walter Rudin's Principles of mathematical analysis. So I am little confused whether am going the right way. Any suggestions?
Without knowing more about your research interests it is difficult to offer an informed opinion. That said, here is my take on your question:
Before I did my Ph.D. work (in condensed matter physics) one of my undergraduate majors was pure mathematics. I took a year of analysis and in particular studied some of the same texts you are. I don't regret this. It was worthwhile.
That said, I suspect studying e.g. analysis will offer you little insight into your work in physics. It is certainly not something a condensed matter physicist is expected to know. It also seems unlikely to improve your "modeling skills", although it's not entirely clear what you mean by that.
Doing all the courses from "basic analysis to differential geometry" is a huge undertaking. In my experience, studying outside your field is valuable because drawing from a different set of influences (as compared to your peers) tends to foster original work. But that was not your stated motivation, and if it is, there is no reason to limit yourself to mathematics.
I totally agree with previous comments . But if the new study makes your research more improved you should learn it and understand it completely. The book you are telling will take at-least two month in my opinion to go through and understand its concept completely because i took 3-4 month to go through it.