Any ideas for topics in Mathematical Physics?

[skate_nerd]

Not really sure where this question belongs, but it is based on a school assignment so I'll put it here.
I'm a Physics major and math minor, and I am about halfway through my first group of advanced physics courses (namely intro classes for analytical mechanics, modern physics, and theoretical physics). However I am also taking a mathematical proofs class, and we have a term paper that was just assigned.
The goal of the paper is to tell a compelling story about a mathematical topic that is interesting to us. It should be told at the level so that another mathematics major would be able to read and comprehend it. Acceptable topics include famous solved problems, unsolved problems, history of a mathematical idea, a surprising result, or a mathematical controversy.
Being a physics major I would like to do a paper on mathematical physics, more specifically a famous solved or unsolved problem. I feel like I would be most interested in talking about something like that. However I'm not sure how many of those there are that would be easy to explain in a 3-5 page (single spaced) paper.
Basically I'm just hoping for some ideas. I've got a few myself, but I'd like to see some from people much more experienced in the field. Thanks!

 

[Fantini]

Some topics came to mind: you could speak about the three-body problem (or n-body problem), how Fourier theory (now known more broadly as harmonic analysis) motivated and shaped the way we think and work with functions today (specifically how it exposed the weaknesses in classical theory and showed us that we needed more care in our definitions) or the relations between quantum mechanics and linear algebra.

Hope these are interesting topics you can write about. :D

Cheers.

 

[alyafey22]

Gaussian Surface

 

[Fantini]

Silly me! How could I have forgotten Electromagnetism? You can always discuss the formulation of Maxwell's laws in differential forms terms. You could also exploit the link of analytical mechanics and differential geometry, also related you have symmetry in physics's laws and group theory. Noether's theorem should be something very interesting to delve deep in. :D

Cheers.

 

[Ackbach]

Several big unsolved problems in mathematical physics:

1. Rigorous mathematical framework for the Standard Model (especially Feynman path integrals).

2. Solving the Navier-Stokes equation.

The 3-body problem has already been mentioned.

 

[skate_nerd]

Thanks everyone. Those all seem like they would be great topics to discuss. Although now I have the opposite of the problem I began with...I'm going to have a hard time deciding between this plethora of topics! ;)