Any ideas for unsolved topics in Mathematical Physics?

[skate_nerd]

Homework Statement

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!

 

[UltrafastPED]

I like solved problems - for example how can the sizes of stars be measured?

This site introduces the topic: http://mysite.du.edu/~jcalvert/astro/starsiz.htm

 

[SteamKing]

There are quite a few unsolved topics in physics.

One of the oldest and most intractable is the general n-body problem arising out of Newton's theory of gravitation. Coupled with this is determining if a complex orbital system, like our solar system, is stable over a long period of time. This latter problem involves chaos theory.