Introduction To The Polymath Project and “Density Hales-Jewett and Moser Numbers”

Abstract

At first appearance, the paper which follows this essay [7] appears to be a typical mathematical paper. It poses and partially answers several combinatorial questions, and follows the standard forms of mathematical discourse, with theorems, proofs, conjectures, and so on. Appearances are deceiving, however, for the paper has an unusual origin, a clue to which is in the name of the author, one D. H. J. Polymath. Behind this unusual name is a bold experiment in how mathematics is done. This experiment was initiated in January of 2009 by W. Timothy Gowers [5], and was an experiment in what Gowers termed “massively collaborative mathematics”. The idea, in brief, was to attempt to solve a mathematical research problem working entirely in the open, using Gowers’s blog as a medium for mathematical collaboration. The hope was that a large number of mathematicians would contribute, and that their collective intelligence would make easy work of what would ordinarily be a difficult problem. Gowers dubbed the project the “Polymath Project”. In this essay I describe how the Polymath Project proceeded, and reflect on similarities to online collaborations in the open source and open science communities. Although I followed the Polymath Project closely, my background is in theoretical physics, not combinatorics, and so I did not participate directly in the mathematical discussions. The perspective is that of an interested outsider, one whose main creative interests are in open science and collective intelligence.