For every set of n point masses, and every dimension less than n, there exists at least one central configuration of that dimension. For almost all n -tuples of masses there are finitely many "Dziobek" configurations that span exactly n − 2 dimensions. It is an unsolved problem, posed by Chazy (1918) and Wintner (1941), whether there is always a bounded number of central configurations for five or more masses in two or more dimensions. In 1998, Stephen Smale included this problem as the sixth in his list of "mathematical problems for the next century". As partial progress, for almost all 5-tuples of masses, there are only a bounded number of two-dimensional central configurations of five points.