[seqfan] Timothy Gowers, Combinatorial proof of Hales-Jewett theorem
quantum pkt
qntmpkt at yahoo.com
Fri Mar 19 18:23:01 CET 2010
http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/
...
Scientific American, April 2010:
"For a first experiment, [in "crowdsourcing" proofs - akin to some proofs provided by Seqfan] Gowers chose the so-called density Hales-Jewett theorem. This problem, Gowers sayis, is akin to "playong a sort of solitaire tic-tac-toe and trying to lose" The theorem states that if your tic-tac-toe board is multidimentional 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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