Smale‘s 7th problem asks for a method to compute sequences of spherical points with very small logaritmic energy (a 2D analogous of the electrostatic potential).

In this paper we show that the configuration of the particles in the Coulomb gas on the sphere -a physical model for a gas consisting of charged particles- satisfies the demands of Smale’s problem with very high probability as long as the temperature is low enough, with explicit and concrete estimates.

This opens new possibilities in the study of Smale’s problem!