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WHAT is the best way to stack a collection of spheres? This age-old problem, known by fruit sellers everywhere, now has a computer-verified proof. It could herald a new era of mathematics in which machines check proofs, leaving humans free for deeper thinking.
聯This could herald an era in which machines check proofs, leaving humans free for deeper thinking聰
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Johannes Kepler suggested in 1611 that a pyramid was the most space-saving arrangement for stacking spheres, but couldn鈥檛 prove it. In 1998, at the University of Pittsburgh in Pennsylvania used software to try to show Kepler was right, but his proof was so long that human reviewers couldn鈥檛 fully verify it.
Now he has used computerised formal-proof assistants that build on a small kernel of logic to check logical statements to verify that his proof was correct. 鈥淭his technology cuts the mathematical referees out of the verification process,鈥� says Hales. 鈥淭heir opinions about the correctness of the proof no longer matter.鈥�
This article appeared in print under the headline 鈥淔ruity proof鈥�