A proof of the dodecahedral conjecture
  The dodecahedral conjecture states that the volume of the Voronoi polyhedron of a sphere in a packing of equal spheres is at least the volume of a regular dodecahedron with inradius 1. The authors prove the conjecture following the methodology of the proof the Kepler conjecture. (See math.MG/9811071.) 
Thomas C. Hales, Sean McLaughlin