Is Number Theory Worth Studying for Physicists?

[manlyman62]

Hello! I am a sophmore physics/math major who will probably be going into Mathematical or Theoretical Physics. My question is should I take Number Theory at some point during my undergrad years? On the one hand, it looks like an interesting/fun class (and I love math :) ) , but I've heard it's just pure math and doesn't have many practical applications. Advice on this matter would be appreciated. Thank you!

 

[Newtime]

If you're taking math classes to further your physics education, then it isn't too important IMO. But otherwise, take it if you're interested in it.

 

[deRham]

Number theory is explicitly about the numbers, and it's born of algebra, and in an undergrad class, it should have absolutely no connection to the physics you are doing (which should involve global and local techniques in classical geometry).

 

[VeeEight]

You may find it more interesting and useful for your physics education to take a course in abstract algebra. An introduction to groups and rings will cover some of the very basic aspects of elementary number theory and is very relevant to physics. Additionally, I found it was much easier to go through basic number theory concepts after having basic knowledge of group/ring/field theory.

 

[TMM]

If you go into quantum gravity, things like infinite Galois theory, cohomology, and algebraic geometry are very important tools from algebraic number theory that one wouldn't necessarily learn in an abstract algebra course.

There's also that cool connection between calculating Etale motives and residues of Feynman integrals, if you're into that.

 

[manlyman62]

Ok thanks for the advice guys! There are several slots for electives in my schedule, so one of them is definitely going to be used for number theory! Also, abstract algebra is required for my math major, so ill be taking that as well.

 

[Chris11]

Number theory is amazing. Take it for the math.