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Questions tagged [mathematics]

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

Do not use just because your question involves math!

1364 questions
127
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4 answers

The Role of Rigor

The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into five specific questions. Update February, 12,…
Gil Kalai
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104
votes
13 answers

Best books for mathematical background?

What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory? Some subjects off the top of my head that probably need covering: Differential geometry, Manifolds, etc. Lie groups, Lie…
ahh
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92
votes
11 answers

Quantum Field Theory from a mathematical point of view

I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view. Are there any good books or other reference material which can help in learning about quantum field…
user774025
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91
votes
11 answers

What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?

I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean? More specifically, Why is it that dot product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB\cos\theta$? Why is it…
claws
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77
votes
7 answers

Number theory in Physics

As a Graduate Mathematics student, my interest lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications of Number theory to physics. I have heard…
C.S.
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62
votes
3 answers

How is the Saddle point approximation used in physics?

I am trying to understand the saddle point approximation and apply it to a problem I have but the treatments I have seen online are all very mathematical and are not giving me a good qualitative description of the method and why it's used and for…
BeauGeste
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60
votes
7 answers

Why does Taylor’s series “work”?

I am an undergraduate Physics student completing my first year shortly. The following question is based on the physical systems I’ve encountered so far. (We mostly did Newtonian mechanics.) In all of our analyses of the physical systems (up till…
Atom
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59
votes
11 answers

What is the logarithm of a kilometer? Is it a dimensionless number?

In log-plots a quantity is plotted on a logarithmic scale. This got me thinking about what the logarithm of a unit actually is. Suppose I have something with length $L = 1 \:\mathrm{km}$. $\log L = \log \mathrm{km}$ It seems that the unit of $\log…
Statec
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52
votes
8 answers

Does Gödel preclude a workable ToE?

Gödel's incompleteness theorem prevents a universal axiomatic system for math. Is there any reason to believe that it also prevents a theory of everything for physics? Edit: I haven't before seen a formulation of Gödel that included time. The…
BCS
  • 1,314
51
votes
5 answers

Book covering differential geometry and topology for physics

I'm interested in learning how to use geometry and topology in physics. Could anyone recommend a book that covers these topics, preferably with some proofs, physical applications, and emphasis on geometrical intuition? I've taken an introductory…
user7757
47
votes
8 answers

How should a physics student study mathematics?

Note: I will expand this question with more specific points when I have my own internet connection and more time (we're moving in, so I'm at a friend's house). This question is broad, involved, and to some degree subjective. (I started out as a…
Mark C
  • 1,665
47
votes
9 answers

Applications of Algebraic Topology to physics

I have always wondered about applications of Algebraic Topology to Physics, seeing as am I studying algebraic topology and physics is cool and pretty. My initial thoughts would be that since most invariants and constructions in algebraic topology…
Sean Tilson
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46
votes
8 answers

Is there something similar to Gödel's incompleteness theorems in physics?

Gödel's incompleteness theorems basically sets the fact that there are limitations to certain areas of mathematics on how complete they can be. Are there similar theorems in physics that draw the line as to how far one can get in physics as far as…
Simply Beautiful Art
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39
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9 answers

Why don't we prove that functions used in physics are continuous and differentiable?

I have studied physics up to 12th grade and I noticed that whenever new equations are introduced for certain entities, such as a simple harmonic wave, we never prove that it's continuous everywhere or differentiable everywhere before using these…
FoundABetterName
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39
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6 answers

Formalizing Quantum Field Theory

I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or conformal field theories, and of older approaches…
user566
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