Last week I was listening in on a fascinating conversation between a group of research mathematicians about Polymath. Polymath is a community of massively collaborative online mathematical projects which is achieving impressive results and is widely cited as an exemplar of the benefits of crowd sourcing.
Yet despite its apparent openness, my group felt excluded from Polymath – excluded by the pace of results production. There are, apparently, only a handful of mathematicians in the world clever enough to contribute effectively and the rest are left gasping behind. My group argued explicitly that what is important about mathematics is not getting results, but being engaged in the process, and Polymath does not allow this in practice even though it might in theory.
Their comments reminded me of James Clerk Maxwell’s remark to Arthur Schuster that, ‘The question whether a piece of work is worth publishing or not depends on the ratio of the ingenuity displayed in the work to the total ingenuity of the author.‘. Like the mathematicians, he was arguing that engagement was the important thing, not results. For Maxwell there was an intensely moral imperative behind this view. Engagement in an abstract cause such as maths or physics helped one control baser desires. I’m not sure my mathematicians would have gone this far, but the value to society of participation is well worth thinking about.
Maxwell, of course, was one of the lucky ones. He was one of the handful that would have been able to keep up. And in fact he indulged in collaborative exchanges with William Thomson and Peter Guthrie Tait that bear many of the hallmarks of Polymath – all conducted on postcards through the Royal Mail . These collaborations were thus less visible than Polymath. Were they less discouraging to contemporaries who might be engaging in their own collaborations at their own levels?
It seems that there is not much new in collaborative mathematics, but that being online and very visible may have downsides as well as benefits.
 Schuster, A. (1910) in A history of the Cavendish laboratory, 1871-1910, (Longmans, Green, London, 1910) p.32
 P. M. Harman ed. (1995-2002) The Scientific Letters and Papers of James Clerk Maxwell, vols I, II, III Cambridge University Press.