  The relationship between point vortex dynamics and the properties of
polynomials with roots at the vortex positions is discussed. Classical
polynomials, such as the Hermite polynomials, have roots that describe the
equilibria of identical vortices on the line. Stationary and uniformly
translating vortex configurations with vortices of the same strength but
positive or negative orientation are given by the zeros of the Adler-Moser
polynomials, which arise in the description of rational solutions of the
Korteweg-de Vries equation. For quadupole background flow, vortex
configurations are given by the zeros of polynomials expressed as wronskians of
Hermite polynomials. Further new solutions are found in this case using the
special polynomials arising the in the description of rational solutions of the
fourth Painleve equation.
