cannonball conjecture

for four centuries, mathematicians had been unable to prove famed astronomer and mathematician Johannes Kepler's 1611 conjecture that the pyramid is the best way to stack cannonballs. That is, until July 2006 when University of Pittsburgh mathematician Thomas C. Hales, and his former graduate student, Samuel P. Ferguson, published their proof of one of mathematics' most famous puzzles -- the Kepler conjecture.Dr. Ferguson is a mathematician with the National Security Agency. Dr. Hales, 48, is Pitt's Andrew Mellon Professor of Mathematics. The cannonball proof has blasted Dr. Hales and Dr. Ferguson's names into the stratosphere of mathematical accomplishment.The proof is about 300 pages long -- not counting 40,000 lines of computer code and three billion bytes of data necessary to solve the puzzle that left mathematicians scratching their scalps for centuries.
Kepler came up with conjecture after Sir Walter Raleigh asked mathematicians to determine the best way to stack cannonballs on ship decks. Intuition suggests the pyramid is the most efficient -- or densest -- way to stack cannonballs, but Kepler never proved the conjecture.Centuries of mathematicians solved portions of it but never proved that cannonballs in a pyramid occupy less space than in any other configuration.Twentieth century mathematicians figured out how many calculations were necessary to solve the conjecture, but the number was too enormous to undertake. Dr. Hales started considering the conjecture in 1988 and had two things going for him -- computers and enjoyment of exhaustive mathematical problems to solve.He and Dr. Ferguson studied 5,000 configurations of stacked spheres, which they reduced to 100 candidate configurations. Then after years of effort, the "eureka moment" occurred in November 1994, when Dr. Hales figured out the ideal geometric forms that best described the relationship between spheres and the space they occupied.Reducing the problem into creative geometry allowed a computer to do the calculations. But the computer had to run nonstop for three months to do many billions of calculations to complete the proof, he said.