Theoretical Physics: Is Proving Theorems Essential?

[nolanp2]

i'm currently in my 2nd yr in a course in theo phys, but my college hasn't put a course aside for the sublject so instead we sit in on maths and physics courses. I'm having a problem with real and complex analysis as while i find the principles dealt with in them useful the only areas we're tested on in the subjects is our ability to prove theorems and lemmas, which i find very tedious.

what I'm wondering is is this ability crucial to a theoretical physicist, or are we only being tested on it because we are being taught as mathematicians?

 

[arunma]

I've had some research experience in theoretical physics (numerical modeling of electromagnetic waves with specific boundary conditions). In my experience, theoretical physics usually means coding and computer modeling. But mathematical methods are useful to both theoretical and experimental physicists, since we need to properly the theory in order to do any kind of research. If you're currently a second year undergraduate, you'll see that starting next year, mathematical methods will become exceedingly important to your studies. Separable differential equations, Legendre polynomials, spherical harmonics, perturbation theory, and various other things will start popping up all over the place. And these are things that are important whether you go into the theoretical or experimental side of physics.

Of course, any time the word "lemma" is used, that usually refers to mathematical rigor. There's a big difference between the math that you encounter in physics, and the kind that comes up in mathematics classes. Believe it or not, physics math tends to be more difficult than math math. In physics, you need to use math to get some sort of practical result. In mathematics, the rigor is used to build a logical framework so that theorems can be built upon axioms and other theorems. Proving theorems and lemmas is certainly a worthwhile exercise, but I never found it particularly useful in my undergraduate physics classes, nor was I ever required to employ mathematical rigor.

So I guess the short answer to your question is: no, proving theorems and lemmas isn't all to useful in physics. If you're planning on going into theoretical physics, then based on my personal research experience, I'd say that you should focus more on learning computer languages and modeling techniques.