An overview of the Kepler conjecture

Thomas C. Hales

Published 1998-11-11, updated 2002-05-20Version 2

This is the first in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is the oldest problem in discrete geometry and is an important part of Hilbert's 18th problem. An example of a packing achieving this density is the face-centered cubic packing. This paper has a historical overview and a synopsis of the rest of the series. The other papers in the series are math.MG/9811072, math.MG/9811073, math.MG/9811074, math.MG/9811075, math.MG/9811076, math.MG/9811077, and math.MG/9811078.