'[B]ut this is blog maths and we're free to make up conventions as we go along': Polymath1 and the modalities of 'massively collaborative mathematics'

In February, 2009, an international group comprising mathematicians ranging from amateurs to elite professionals converged on the WordPress blog of Cambridge mathematician Timothy Gowers in order to attempt to prove a mathematical theorem---a project Gowers called Polymath1. Their results surprised even the project's most optimistic participants. In six weeks, the group had managed to combinatorially prove the density Hales-Jewett theorem, yielding in the process a host of new mathematical insights. This paper explores how the mathematicians of Polymath1 worked within and adapted the WordPress blog environment to their uses. I examine from a qualitative sociological perspective how procedural and technical questions interacted in a mathematics research setting as the project moved from its nebulous beginnings toward completion. The paper thus indirectly considers the ways in which such meta-mathematical questions are inscribed in research environments, and opens up several methodological questions for the sociology of mathematics and the Internet. Between the mathematical and meta-mathematical negotiations of the Polymath1 project, there emerges a rich virtual site for the study of collaboration in mathematics and related disciplines.