Kepler’s conjecture

Kepler's conjecture, in mathematics, is a problem in combinatorial geometry concerning the most efficient way to pack spheres within a given space. It was proposed by Johannes Kepler in 1611, who conjectured that the densest packing of spheres is achieved by arranging them in a face-centered cubic or hexagonal close-packed structure. This arrangement, often seen in stacking cannonballs, fills approximately 74% of the available volume.12

While Johannes Kepler is primarily known for his three laws of planetary motion, which describe how planets orbit the Sun in elliptical paths and at varying speeds, his conjecture on sphere packing is a significant contribution to geometry. The conjecture remained unproven for centuries until it was finally established in 1998 by Thomas Hales.324