Kepler's conjecture

Kepler's conjecture states that the most efficient way to pack equal-sized spheres (like oranges in a box) in three-dimensional space is in a pattern called face-centered cubic or hexagonal close packing. This arrangement maximizes the density, meaning it uses the least space possible with minimal gaps, filling about 74% of the volume. Proposed by Johannes Kepler in 1611 and proven in 1998 by mathematicians Thomas Hales and collaborators, it confirms that no other arrangement of equal spheres can pack more densely than these two well-known patterns.