Mathematics
The Sphere Packing Problem and the Kepler Conjecture
Quick fact
The Kepler conjecture, proposed by Johannes Kepler in 1611, states that the densest way to pack identical spheres fills about 74.05% of space—a packing known as the face-centered cubic arrangement. This was finally proven by Thomas Hales in 1998.
Why this is interesting
Imagine stacking oranges in a crate. How can you pack them so that the most oranges fit in the same space? That simple question has puzzled mathematicians for centuries.