Kepler Conjecture

In mathematics, the Kepler conjecture is a conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equal spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements is a little over 74%.

In 1998 Thomas Hales, presently Andrew Mellon Professor at the University of Pittsburgh, announced that he had a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving checking of many individual cases using complex computer calculations. Referees have said that they are "99% certain" of the correctness of Hales' proof. So the Kepler conjecture is now very close to becoming a theorem.