Kepler Conjecture

In 1611, Kepler Eric Weisstein's World of Biography proposed that close
packing (either cubic or hexagonal close packing, both of which have maximum
densities of pi/(3sqrt(2)) approx 74.048%) is the densest possible sphere
packing, and this assertion is known as the Kepler conjecture. Finding the
densest (not necessarily periodic) packing of spheres is known as the Kepler
problem.

Reference:
Introduction
http://mathworld.wolfram.com/KeplerConjecture.html

Proof
http://www.math.pitt.edu/~thales/kepler98/