Massively Collaborative Mathematics

I like this story from the 15 October  2009 issue of the journal Nature, about how a pair of blogs allowed dozens of contributors to collaboratively solve a theorem that no single mathematician had been able to solve: the Density Hales-Jewitt Theorem (DHJ for short). The mathematician who created the blog was Timothy Gowers, a Professor at the University of Cambridge and a holder of the Fields Medal, the highest honor a mathematician can receive. Even someone of Gowers’ high caliber was not able to solve the theorem. So he decided to try an experiment: He posted on his blog an invitation, to join a collaborative process of working on the theorem. He called it “The Polymath Project.”

Gowers’ blog regularly had thousands of readers, including many of the world’s top mathematicians, so the blog thread soon had thousands of words and dozens of top mathematical thinkers participating. Six weeks later, the theorem was proven and the proof will be submitted to a top math journal, under the collective name “D.H.J. Polymath”. The Nature article describes a creative process just like the one that creativity researchers have identified, of creativity as a series of small insights, as described in my book Group Genius:

For the first time one can see on full display a complete account of how a serious mathematical result was discovered. It shows vividly how ideas grow, change, improve and are discarded, and how advances in understanding may come not in a single giant leap, but through the aggregation and refinement of many smaller insights.

The article concludes:

We believe that this will lead to the widespread use of mass collaboration in many fields of science, and that mass collaboration will extend the limits of human problem-solving ability.

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