So, I am currently doing a bachelor in mathematics, as I have found out that math is one of my great passions. However, as time has passed after graduating from upper secondary school (~High school) I have started missing physics lessons (I want to do physics again). The thing is, I am a littlebit uncertain to what directions to choose, especially when thinking that I want to be an expert in at least one field (some day), and the required workload. After my Bachelor I have been thinking about immersing my self in : Diophantine Analysis(with focus on diophantine equations) and/or Complex Analysis, but I also want to learn the math behind General relativity and Quantum Mechanics, so that I can be part of the train towards the Theory of everything (ToE).
So, i Wonder:
-How much work is expected in order to have an impact level of expertice in any of these fields? Are any more difficult than the others?
Would the transition between math and theoretical physics require me to have a lot of knowledge on practical physics first? (As i see it, theoretical physics is just another approach to creating a mathematical system). For example, would all this require me to take like two masters degrees?
I have also heard from physicist at my university that many who major in theoretical physics struggle because of the dificult math, and that they are better off doing math first. Is this correct?
Where do I start on studying these fields? I mean, I have had real analysis in multiple variables, linear algebra, number theory and the latest i was doing in physics was a basic course in various fields of physics(GR,QM, astronomy and thermodynamics.) Is the next thing vector fields?
Do you have any books to highly reccomend on any of these fields?
Any thoughts or career advice?
Sincerely, Robin :)