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Thursday, August 14, 2014

Proof confirmed of 400-year-old fruit-stacking problem

"A computer-verified proof of a 400-year-old problem could pave the way for a new era of mathematics, in which machines do the grunt work and leave humans free for deeper thinking." continues New Scientist.

The problem is a puzzle familiar to greengrocers everywhere: what is the best way to stack a collection of spherical objects, such as a display of oranges for sale? In 1611 Johannes Kepler suggested that a pyramid arrangement was the most efficient, but couldn't prove it.
Now, a mathematician has announced the completion of an epic quest to formally prove the so-called Kepler conjecture. "An enormous burden has been lifted from my shoulders," says Thomas Hales of the University of Pittsburgh, Pennsylvania, who led the work. "I suddenly feel ten years younger!"
Hales first presented a proof that Kepler's intuition was correct in 1998. Although there are infinite ways to stack infinitely many spheres, most are variations on only a few thousand themes. Hales broke the problem down into the thousands of possible sphere arrangements that mathematically represent the infinite possibilities, and used software to check them all.

Photo: New Scientist
But the proof was a 300-page monster that took 12 reviewers four years to check for errors. Even when it was published in the journal Annals of Mathematics in 2005, the reviewers could say only that they were "99 per cent certain" the proof was correct.
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Source: New Scientist