In the mid-20th century the encyclopedic works of French mathematician Nicolas Bourbaki traced every mathematical concept back to the subject’s foundations in the theory of sets—the stuff of Venn diagrams—and changed the face of his field. Like many of his notions, Bourbaki existed only in the abstract: he was the pseudonym for a tight-knit group of young Parisian researchers. The Internet-age version could be D.H.J. Polymath, another collective pseudonym who could define a new style of mathematics.
Polymath began life on the blog of Timothy Gowers, a University of Cambridge winner of the Fields Medal, mathematics’ most coveted prize. In a blog post in January 2009, Gowers asked whether spontaneous online collaborations could crack hard mathematical problems—and if they could do so in the open, laying the creative process out for the world to see. Web-based scientific collaborations and even “crowdsourcing” are now common, but this one would be different. In typical online collaborations, scientists each perform a small amount of research that contributes to a larger project, Gowers pointed out. 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?