Kepler Conjecture

The Kepler Conjecture posits that the most efficient way to pack equal-sized spheres in space—like oranges in a storage—maximizes density by arranging them in a close, honeycomb-like pattern called face-centered cubic or hexagonal close packing. This arrangement achieves about 74.04% space utilization, meaning roughly three-quarters of the space is filled with spheres. Proposed by Johannes Kepler in 1611 and proven in 1998 by Thomas Hales, this conjecture explains how natural and manufactured densely packed arrangements are optimized for space efficiency, with applications in materials science, communication networks, and more.