8
votes
6answers
1k views

Intuitionistic logic as quantization of classical logic?

A classically trained mathematician is more likely to be familiar (at least anecdotally) with an area of mathematical physics such as deformation quantization than with Intuitionistic logic. It is ...
4
votes
3answers
582 views

Meaning of a phrase from “The algebra of grand unified theories”.

Motivated by an answer to this mathoverflow question I've been making an effort to understand Baez and Huerta's article "The algebra of grand unified theories". As far as I can tell, mathematically, ...
31
votes
7answers
3k views

The Unreasonable Effectiveness of Physics in Mathematics. Why ? What/how to catch?

Starting from 80-ies the ideas either coming from physics, or by physicists themselves (e.g. Witten) are shaping many directions in mathematics. It is tempting to paraphrase E. Wigner, saying about ...
69
votes
16answers
4k views

Does Physics need non-analytic smooth functions?

Observing the behaviour of a few physicists "in nature", I had the impression that among the mathematical tools they use a lot (along with possibly much more sofisticated maths, of course), there is ...
6
votes
2answers
1k views

Advice on doing physics under the umbrella of mathematics and the converse

Note: This is a question directly copied from Theoretical Physics SE primarily to get the advice of people indulged in mathematics. In the current scenario of research in QFT and string theory (and ...
3
votes
2answers
865 views

What is soliton

I am new to this word.. This is not research level problem and it is soft question in nature. Just for curiosity, i am asking.. In literature, i am finding following words:(Wikipedia+ others). ...
21
votes
1answer
2k views

Math and Wormholes

Hopefully Math Overflow is the correct place for this. I had a student approach me ask me what kinds of mathematics goes into the study of wormholes. She specifically asked whether there is any ...
27
votes
10answers
3k views

Is there a mathematical axiomatization of time (other than, perhaps, entropy)?

Since Euclid's axiomatization of space, we have developed a sophisticated mathematical model of space. Given a category of structures (measures), local space is modeled the spectrum of measurements ...
7
votes
0answers
644 views

triangulated/derived categories in Physics and algebraic geometry

Why do physicists care about the triangulated/derived categories? I mean what are the problems we want to approach using the machinery of triangulated/derived categories. e.g. in homological mirror ...
1
vote
1answer
847 views

Best examples of physics providing insight into math [duplicate]

Possible Duplicates: Examples where physical heuristics led to incorrect answers? Examples of using physical intuition to solve math problems V. I. Arnold argues ...
20
votes
5answers
2k views

Is symplectic reduction interesting from a physical point of view?

Do you think that symplectic reduction (Marsden Weinstein reduction) is interesting from a physical point of view? If so, why? Does it give you some new physical insights? There are some possible ...
4
votes
2answers
2k views

Mathematicians and string theory?

Hello, I'm curious on whether say, a ph.d in mathematics with no experience in physics could pick up a book on String theory (say some intro for mathematicians) and learn it and then do research kinda ...
13
votes
4answers
3k views

What is a symplectic form intuitively?

Hi, to completely describe a classical mechanical system, you need to do three things: -Specify a manifold $X$, the phase space. Intuitively this is the space of all possible states of your system. ...
15
votes
9answers
2k views

How can I conclude that I live in a solar system?

Well, this is an awkward question and I don't know if it is mathematical enough for MO (I'm sorry if not) but I'll try it: What observations in the coordinate system centered in my fixed position on ...
2
votes
3answers
1k views

The problem of infinity [closed]

Background and motivation The following is copied from my blog since someone thought it was the clearest statement I had made regarding a problem I recently posed. On their advice, it is a community ...
9
votes
2answers
681 views

What are important examples of filtered/graded rings in physics?

Hi, what comes to the mind of a physicist, when he hears words like filtered ring and associated graded? What do these guys describe? What are basic/typical/illuminating examples in physics? Of ...
23
votes
7answers
2k views

Does every ODE comes from something in physics?

Not sure if this is appropriate to Math Overflow, but I think there's some way to make this precise, even if I'm not sure how to do it myself. Say I have a nasty ODE, nonlinear, maybe extremely ...
41
votes
11answers
4k views

What is Quantization ?

I would like to know what quantization is, I mean I would like to have some elementary examples, some soft nontechnical definition, some explanation about what do mathematicians quantize?, can we ...
4
votes
4answers
413 views

Does it help to learn statistical mechanics in order to learn thermodynamic formalism?

Does it help to learn statistical mechanics or thermodynamics (as in physics or mathematical physics) in order to learn thermodynamic formalism: the study of equilibrium states, Gibbs measure, maximal ...
13
votes
7answers
3k views

Mathematical Physics? (Particularly computational)

I just saw a post like this one, but particularly for statistical mechanics, I thought I'd ask the question in general. Where does a mathematically trained person go to learn mathematical physics? By ...