Overview

For nearly four centuries, the Kepler conjecture regarding the most efficient geometrical arrangement for stacked spheres remained one of the most complex and vexing problems in mathematics. Kepler's conjecture—a mathematical expression of commonplace packing techniques—states that the most efficient (i.e., the densest arrangement with the least unused or empty space) packing of spheres results from placing a layer of spheres as tightly as possible on top of an underlying layer. Although Kepler's conjecture seemed proved by everyday experience, a mathematical proof that no better packing arrangement existed seemingly eluded mathematicians until the last decade of the twentieth century.

Background

Although stacking problems are an intuitively ancient exercise for mankind, the formal incorporation of stacking theory dates to the sixteenth century when Sir Walter Raleigh (1554?-1618) challenged his assistant, English mathematician...