The Kepler Conjecture posits that no arrangement of equally sized spheres filling space has a greater average density than that of the face-centered cubic packing or hexagonal close packing, both of which have a density of approximately 74.048%. This conjecture, first proposed by Johannes Kepler in 1611, was proven by Thomas Hales in 1998 using a combination of traditional mathematical proof and computer verification, marking a significant milestone in the field of discrete geometry.