Point vortex dynamics: A classical mathematics playground

The idealization of a two-dimensional, ideal flow as a collection of point vortices embedded in otherwise irrotational flow yields a surprisingly large number of mathematical insights and connects to a large number of areas of classical mathematics. Several examples are given including the integrability of the three-vortex problem, the interplay of relative equilibria of identical vortices and the roots of certain polynomials, addition formulas for the cotangent and the Weierstraß ζ function, projective geometry, and other topics. The hope and intent of the article is to garner further participation in the exploration of this intriguing dynamical system from the mathematical physics community.