The compelling mathematical challenge of the three-body problem

The history of this problem is even more interesting than they let on. Because I'm a self-indulgent twat I put a chapter on this in my dissertation; it dates back to Eudoxus of Cnidae's work on the motions of the Moon; he developed a sort of "ancient Greek Fourier transform" to deal with it, with guys like Hipparchus of Rhodes, Ptolemy taking the idea farther. The figures in classical physics that were mentioned; Newton, Lagrange. It was also crucial in development of quantum mechanics -there was no way at the time of applying Bohr's semiclassical picture to the helium atom, so they had to develop matrix mechanics and the Schroedinger picture. Eventually (in the 90s) we got the semiclassical quantization by the great Dieter Wintgen, using the tools developed by Gutzwiller, and well, I guess this guy was probably the last important contributor to the problem (I, alas, didn't do anything good).

In physics, folks like to refer to simple models which inform other models: the harmonic oscillator, the hydrogen atom, two body scattering and so on. The three body problem is one of the simplest commonly encountered physical problems for which there is no general solution on the torus (Montgomery found a particular solution on the torus). As such, it has driven forward a lot of research and innovation in theoretical physics tools. You could write a pretty good and beefy physics book where you only talk about the three body problem with central potentials.

I found a 2015 post on HN listing some stable n-body choreographies[0].

[0] https://news.ycombinator.com/item?id=8867741

I often wish I had considered studying math back when I was considering getting a PhD in chemistry, but wound up as a programmer instead. But it's hard to make a living doing math research, you either wind up teaching or working in some practical field like programming or AI. I know two PhDs in math who each do one of those and neither can do any original math.

I wonder if the choreographies are stable or not.

I took linear algebra with him at UCSC! Super nice guy