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 :)

  • 1
    $\begingroup$ For the purposes of theoretical physics, I would say that differential geometry is by far the most important subject (you will need a variety here, i.e., Riemmanian, Lorentzian, Symplectic, and the general theory of fiber, principal, and jet bundles). Not only is differential geometry the underlying foundation for GR and large parts of quantum field theory, but it will also serve as a stepping stone for almost everything else you will do. From there, I would look at representation theory of Lie groups and functional analysis. $\endgroup$ – EuYu Dec 6 '17 at 14:27
  • $\begingroup$ Thanks mate :) Better start reading then. $\endgroup$ – user357524 Dec 6 '17 at 14:29
  • $\begingroup$ (cont.) The specific requirements will obviously vary depending on which branch of theoretical physics you ultimately go into, but I would say that most working physicists have good knowledge of at least 2 of the 3 subjects I mentioned above. If you choose to go into something like string theory, well all bets are off. The rabbit hole basically goes as deep as you want. $\endgroup$ – EuYu Dec 6 '17 at 14:29

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