The Curved N-Body Problem: Risks and Rewards

Exploring new mathematical territory can be a riskyadventure. With no landmarks in sight, it’s easy toerr, as all the giants, from Fermat and Newton to Gauss and Poincaré, well knew. Still, an expedition into the unknown is highly rewarding if planned with care and advanced with restraint, a thing the masters knew too. I learned this lesson not only by reading them and about them, but also from experience. A Brief History of the Problem The curved N-body problem is a short name for the equations that describe the motion of gravitating particle systems in spaces of constant Gaussian curvature. I dis-covered this universe a few years ago, and found it fascinating. Later I also looked into its history, which proved to be as gripping as the universe itself. The classical N-body problem has its roots in the work of Isaac Newton, who introduced it in his masterpiece Prin