Innovation in Mathematics (It’s Not About the Lone Genius)

Dr. Jordan Ellenberg, a child prodigy and now a professor of mathematics at the University of Wisconsin, challenges “The cult of the child genius” in the Wall Street Journal:

There is a myth that progress in mathematics is driven by the cognitive one percent of one percenters, marked at birth, who blaze a path for the rest of humanity to trot along. But in the real world, math is a communal enterprise. Each advance is the product of a huge network of minds working toward a common purpose, even if we accord special honor to the person who sets the final stone in the arch. As Mark Twain said, “It takes a thousand men to invent a telegraph…and the last man gets the credit and we forget the others.”

Dr. Ellenberg might have been reading my book Group Genius; in that book I show that Samuel Morse did not invent the telegraph in a brilliant burst of inspiration, but how instead it emerged from collaboration. The real stories of innovation are always collaborative and distributed. Ellenberg continues:

Terry Tao, a UCLA professor and a winner of the Fields Medal, the highest honor a young mathematician can achieve, once wrote: “I find the reality of mathematical research today–in which progress is obtained naturally and cumulatively as a consequence of hard work, directed by intuition, literature, and a bit of luck–to be far more satisfying that the romantic image that I had as a student of mathematics being advanced primarily by the mystic inspirations of some rare breed of ‘geniuses.'”

This is the reality of creativity and innovation in all of the arts and sciences, and that’s why we the real story is always one of group genius, not lone genius.


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.