Thomas C. Hales
Published 2003-05-01Version 1
The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than $\pi/\sqrt{18}$. A computer assisted verification confirmed this conjecture in 1998. This article gives a historical introduction to the problem. It describes the procedure that converts this problem into an optimization problem in a finite number of variables and the strategies used to solve this optimization problem.
Journal: Proceedings of the ICM, Beijing 2002, vol. 3, 795--804
Orlicz addition for measures and an optimization problem for the $f$-divergence
On the volume of unions and intersections of congruent balls under uniform contractions
On the existence of completely saturated packings and completely reduced covering
![QR code for arXiv:math/0305012 [math.MG]](http://oss.arxitics.com/images/favicon.svg)