Packing Challenge Mastered At Last

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Abstract
Four centuries ago, Johannes Kepler proposed--but did not prove--that the densest possible packing of same-sized spheres is the "face-centered cubic" arrangement familiar today to anyone who9s ever admired a pyramid of oranges in a grocery store. There9s never been much doubt that the conjecture is true; the question has always been whether anyone can prove it. Now two mathematicians may finally have met the challenge, with a proof consisting of 250 pages of mathematical reasoning and computer programs that enumerate and check thousands of crucial details.

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