Sunday, March 21, 2010

Collaborative tic-tac-toe

Problem Solved, LOL: A Complex Tic-Tac-Toe Puzzle Falls Thanks to Blog CommentsCommunity-based online efforts point to a new, faster approach in mathematics

...In some cases, citizen-scientists such as bird-watchers or amateur astronomers collectively can make significant contributions. “What about the solving of a problem that does not naturally split up into a vast number of subtasks?” he asked. Could such a problem be solved by the readers of his blog—simply by posting comments?

For a first experiment, Gowers chose the so-called density Hales-Jewett theorem. This problem, Gowers says, is akin to “playing a sort of solitaire tic-tac-toe and trying to lose.” The theorem states that if your tic-tac-toe board is multidimensional and has sufficiently many dimensions, after a short while it is impossible to avoid arranging X’s into a line—you cannot avoid winning no matter how hard you try. Mathematicians have known since 1991 that the theorem was true, but the existing proof used sophisticated tools from other branches of math. Gowers challenged his blog’s readers to help him find a more elementary proof, a problem generally considered quite hard.

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