The Kepler conjecture
Prove that no packing of equal balls in three-dimensional space has average density greater than , the density of the familiar cannonball stacking (face-centered cubic packing).
History and references
Solved in 1998 by Thomas Hales (with Samuel Ferguson).
Kepler stated the conjecture in 1611 in a short work on snowflakes, after corresponding with Thomas Harriot about stacking cannonballs. Gauss proved in 1831 that it holds for packings arranged in a lattice, so any counterexample would have to be irregular. Following a strategy suggested by László Fejes Tóth, Thomas Hales, helped by his student Samuel Ferguson, reduced the problem to a huge but finite optimization over thousands of configurations, checked by computer, and announced a proof in 1998. The referees said they were 99% certain it was correct. Hales then led the Flyspeck project, which completed a fully formal computer-verified proof in 2014, published in 2017.
References
Solutions 0
Sign in or create an account to publish a solution