Recent Progress in Sphere Packing

Abstract

The problem of nding the greatest density of any packing of equal spheres in n-dimensional Euclidean space is an old and important one, which has applications in geometry, number theory, and information theory. It is also di cult, as is shown by the fact that although the 3-dimensional case was raised by Kepler in 1613, it has only recently been solved, by Thomas Hales in 1998, with an important contribution from S. Ferguson. I shall say only a few words about the argument, which is long and complicated in detail.