2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67330The 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.Metric Geometry52C17text