Hi, I'm a graduate engineering student, and as an undergrad I had all the typical engineering math courses: Cal I - III, linear algebra, and differential equations. I am curious. What else is out there? You hear about the top theoretical physicists of the day trying to prove string theory or find "the theory of everything," also recently the problem involving poincare's conjecture that was solved (I'm guessing this was solved with differential equations and some complex geometry?). What branch(s) of mathematics are involved with these kinds of proofs? This is not my field particularly as I am not a physicist (I do have a minor in physics however), but I very much want to improve my skills as a mathematician. Can anyone provide any guidance, references, sources, or books that I may look into? Thank you!