Why do bees build their honeycombs out of hexagonal cells? As early as the first century BC, Marius Terentius Varro—Rome's answer to Isaac Asimov, the most prolific science writer of his day—speculated that it had to do with the economy, rather than the symmetry, of the design. From Varro to the present, scientists have assumed that a hexagonal lattice allows bees to store the most honey in a single layer of equal-sized cells, while using the least beeswax to separate them. Until this summer, however, no one could prove that a honeycomb was the sweetest solution. Now, a mathematician has removed all doubt: Bees do it best. The result also confirms the intuition of human engineers, who have relied on honeycomb composite materials made of paper, graphite, or aluminum to reduce the weight of components for cars, planes, and spacecraft with little sacrifice in strength.

Last month, at the Turán Workshop in Mathematics, Convex and Discrete Geometry in Budapest, Thomas Hales of the University of Michigan, Ann Arbor, presented his proof that a hexagonal honeycomb has walls with the shortest total length, per unit area, of any design that divides a plane into equal-sized cells.(The proof has also been available on the Web since June.) Hales says that he began working on the honeycomb conjecture just last year, after solving a similar conjecture on the packing of spheres (Science, 28 August 1998, p. 1267). That problem, called the Kepler conjecture, stated that the densest packing of spheres is a face-centered cubic lattice, the pattern a grocer makes when he stacks apples. The proof had taken years.“After the Kepler conjecture, I expected every problem to be very difficult,” Hales says.“In this case, I feel as if I won the lottery.”