Beautiful/Elegant Mathematics in String Theory

[RisingSun]

Hello! First time poster on physicsforums, and I've had a question that I thought would be best addressed here. I'm going to be entering college as a freshman come fall, and I have a pretty decent background in math as well as a strong appreciation for elegant proofs and solutions. So when I read and learned about string theory, it was very interesting and appealing conceptually, but people always lambasted it for being based purely on elegant mathematics instead of empirical evidence, like science was supposed to be (in fact, that's the reason why Richard Feynman wouldn't endorse it). However, the books I read never demonstrated any examples of these beautiful and elegant mathematics. Is there anyone here who can provide some elegant equations or examples that could shed light on the beauty of string theory? Thanks a lot!

P.S. My level is only solid up through all of single variable calc, with some dabbling in random fields, but feel free to put in higher level examples if need be (I hear the math in string theory is exceptionally difficult).

 

[FrogPad]

I am not qualified to make a statement about this, but hey it's late, and I just feel like posting stuff. When you asked about the math that is used in string theory, I became curious. Well after some digging, here is a rundown of the math courses:

Linear Algebra
Euclidean Geometry
Trigonometry
Single Variable Calculus
Multivariable Calculus
Ordinay Differential Equations
Partial Differential Equations
Numerical Methods and Approximations
Probability and Statistics
Real Analysis
Complex Analysis
Group Theory
Differential Geometry
Lie Groups
Differential Forms
Homology
Cohomology
Homotopy
Fiber Bundles
Characteristic Classes
Index Theorems
Supersymmetry and Supergravity
K-theory
Noncommutative Geometry

Looks like a lot of fun stuff

By the way, I got the list from:
https://nrich.maths.org/discus/messages/8577/7608.html?1082032185

I have no idea how qualified the person is that posted it.

 

[Kalimaa23]

Hello! First time poster on physicsforums, and I've had a question that I thought would be best addressed here. I'm going to be entering college as a freshman come fall, and I have a pretty decent background in math as well as a strong appreciation for elegant proofs and solutions. So when I read and learned about string theory, it was very interesting and appealing conceptually, but people always lambasted it for being based purely on elegant mathematics instead of empirical evidence, like science was supposed to be (in fact, that's the reason why Richard Feynman wouldn't endorse it). However, the books I read never demonstrated any examples of these beautiful and elegant mathematics. Is there anyone here who can provide some elegant equations or examples that could shed light on the beauty of string theory? Thanks a lot!

P.S. My level is only solid up through all of single variable calc, with some dabbling in random fields, but feel free to put in higher level examples if need be (I hear the math in string theory is exceptionally difficult).

First of all, welcome the physics forums!

With all due respect, you don't even come close to the level required to understand even the most simple concepts rigorously. Which is normal for a freshman I might add

If you really want a shot at it, I'm posting a sort of introduction to string theory on my blog

http://stringschool.blogspot.com

Look for the posting "String Theory Primer".

If you've got any questions, I'll be happy to answer them

@Frogpad : The list looks ok to me. I'm not sure that K-theory and non-commutative geometry is essential, but it is certainly useful. A lot of the "harder" subjects you noted can be easily summed up by the fact that you'd better have an idea about Algebraic Geometry, Topology and Differential Geometry :-)

 

[FrogPad]

I just started self studying complex analysis, so I'm a little bit more than a 1/3 of the way down that list. I know what some of the other math is vaugely, but still not really

I knew string theory required some crazy mathematics, I just wasn't sure how crazy it was... well, you guys take the cake with a list like that

Anyways, I'm studying electrical engineering so I doubt I'll ever see the majority of that math :) I'll stick with the baby novels, like elegant universe :)