Beautiful/Elegant Mathematics in String Theory

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Discussion Overview

The discussion revolves around the mathematical foundations of string theory, particularly focusing on the elegance and complexity of the mathematics involved. Participants share their experiences and knowledge regarding the mathematical prerequisites for understanding string theory, as well as their personal journeys in learning these concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses a desire to understand the elegant mathematics of string theory, noting that it is often criticized for lacking empirical evidence.
  • Another participant provides a comprehensive list of mathematical topics relevant to string theory, including advanced subjects like K-theory and noncommutative geometry, while expressing uncertainty about their necessity.
  • A different participant welcomes the original poster and suggests that their current mathematical background may not be sufficient for a rigorous understanding of string theory, but offers a resource for further learning.
  • One participant mentions their self-study of complex analysis and reflects on the daunting nature of the mathematical requirements for string theory, indicating a personal connection to the topic.
  • Another participant shares their background in electrical engineering and doubts they will encounter much of the advanced mathematics listed, preferring more accessible resources.

Areas of Agreement / Disagreement

Participants express varying levels of confidence regarding their mathematical backgrounds and the complexity of string theory. There is no consensus on the necessity of certain advanced mathematical topics, and the discussion reflects differing opinions on the accessibility of string theory to those with limited mathematical experience.

Contextual Notes

Some participants acknowledge the challenges posed by the advanced mathematics required for string theory, while others emphasize the importance of foundational knowledge in areas like algebraic geometry and topology. The discussion highlights the varying levels of familiarity with the mathematical concepts among participants.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of physics and mathematics, particularly those curious about the mathematical underpinnings of string theory and its perceived elegance.

RisingSun
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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).
 
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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 :eek:

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.
 
Last edited by a moderator:
RisingSun said:
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 :smile:

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 :biggrin:

@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 :-)
 
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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 :rolleyes:

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 :eek:

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 :)
 

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