  We consider $N$ point vortices $s_j$ of strengths $\kappa_j$ moving on a
closed (compact, boundaryless, orientable) surface $S$ with riemannian metric
$g$. As far as we know, only the sphere or surfaces of revolution, the latter
qualitatively, have been treated in the available literature. The aim of this
note is to present an intrinsic geometric formulation for the general case. We
give a simple proof of Kimura's conjecture that a dipole describes geodesic
motion. Searching for integrable vortex pairs systems on Liouville surfaces is
in order. The vortex pair system on a triaxial ellipsoid extends Jacobi's
geodesics. Is it Arnold-Liouville integrable? Not in our wildest dreams is
another possibility: that quantizing a vortex system could relate with a
million dollars worth question, but we took courage - nerve is more like it -
to also present it.
