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A computer verification of the Kepler conjecture

Thomas C. Hales
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Abstract

The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than $π/\sqrt{18}$. 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.

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Thomas C. Hales. 2003-05-01. A computer verification of the Kepler conjecture. https://arxiv.org/abs/math/0305012

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