Fields Medalist Stephen Smale was asked on the eve of the new
millenium to make a list of mathematics problems worthy of the 21st
century, according to his judgement and taste. I will talk about his 7th
problem, which concerns optimal point configurations on the sphere. The
talk will be at an introductory level and in physicists' language, yet I
will also speak about exciting new conjectures obtained jointly with
Johann Brauchart (Sidney) and Rachele Nerattini (Firenze).
