Wednesday, November 18, 2009

The Polymath Project

An unusual experiment began on January 27, 2009. That was the day Timothy Gowers of the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, announced The Polymath Project. The project had a conventional scientific goal, to attack an unsolved problem in mathematics, but it proposed to engage the mathematical research in a very new way – massively collaborative mathematics. In a manner modeled after the BOINC project with its massively parallel resources for computation, the Polymath Project takes advantage of the insights and efforts of a plurality of minds.

The specific aim of the Polymath Project was to find an elementary proof of a special case of the density Hales-Jewett theorem (DHJ), which is a central result in the field of combinatorics (discrete mathematics). A long and complicated proof already existed, but the mathematics community sought a simpler one so the collaborative approach was employed.

Gowers started the project by posting a description of the first problem, pointers to background materials and a list of rules for collaboration on a blog/wiki. Comments started to flow in at a steady pace. Participants from all over the globe began to take part. Even a Fields Medalist (the equivalent of a Nobel Prize for mathematics), Terrance Tao from UCLA joined in. No one was specifically invited to participate and anybody could provide input, although by the nature of the problem only graduate students and professional mathematicians would have the requisite knowledge.

Progress towards the desired proof came far faster than anyone could have anticipated. By March 10, Gowers announced a proof had been found. A formal paper is being prepared describing the proof.

I recommend that math enthusiasts visit the Polymath Project website. It is fun and fascinating to follow through the comment threads to see how the group arrived at a final solution. This is an excellent way to learn about contemporary mathematics performed by leading mathematicians. The Polymath Project delivers rare insight into the world of mathematics.

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