Sir Michael Atiyah, A Problem in Elementary Euclidean Geometry

Abstract:

Over a decade ago I stumbled across a new and apparently very elementary problem in Euclidean Geometry involving n distinct points in 3-space. Except for n =2,3,4 it remains unsolved and a challenge to all, though computer simulations have given strong evidence in its favour up to around n = 30.

I will describe the problem and various generalizations as well as surprising links with physics.

I hope this talk stimulates students (and others) to think about this problem.