This is a very philosophical question, so i understand the answer is going to be very arbitrary and subject to opinion. I am interested in both Pure mathematics and Theoretical Physics. The time is soon approaching, where i must decide upon which path to take. I love proofs, and i love rigor, yet sometimes i find myself sitting in a number theory class and wondering, why? What is the point? Sure its beautiful and i enjoy it, but there is still a nagging feeling of doubt, like i am missing something. When i am learning physics I experience the reverse, i wonder "Is this too applicable, Am i just being a glorified engineer?" My goal in entering science is to understand the universe. So of course Physics makes sense, but some mathematicians claim that if you understand mathematics, you understand all possible universes, and thus it sounds much more important and interesting then theoretical physics. My worry is, that if i take a PHD in mathematics, i would not understand say Quantum Field theory or Advanced Relativity as well as a Physics Grad student. This leaves me at a loss! I wish i could somehow combine the mathematical proof with the physical understanding. Alot of people mention mathematical physicists, but from my research they seem to be primarily interested in mathematical technique over understanding, say how a certain partial differential equation works, rather then how quarks interacted at the beginning of time (just an example). My dilemma is that either path i choose i will lose something, either rigor, or real world understanding. It all depends on the nature of theoretical physics. Is physics just mathematics, that we choose to apply to an experiment or is there something more? Am i confusing the map with the landscape?