The print version of his address includes 23 problems.

In 1900, David Hilbert’s address at the International Congress of Mathematics in Paris described 10 problems that he felt would strongly influence the direction of mathematical research in the 20 th century. This problem attracted the attention of mathematical giants such as Carl Gauss, who proved a special case. Efficient packing is the name of the game. The hexagonal close-packing arrangement yields an average density of π/(3√2) ≈ 74 percent. If equal-sized balls are dropped into a large container at random, experiments suggest that the density-the proportion of the container’s volume filled by balls-is roughly 65 percent. Specifically, the arrangement of equal-sized spheres to fill a space with the minimum amount of wasted volume is the so-called close packing, which consists of layers of spheres whose centers form a hexagonal lattice.

Sometimes called the Cannonball Problem, it asks whether the traditional pattern used to stack oranges (or cannonballs) is optimal. Conveniently, the mathematical tools Hales used to prove the Honeycomb Conjecture were recycled after having settled another long-standing open problem, Kepler’s Conjecture.

Hexagon nature's perfect shape