This year, the hive mind proved a theorem, and is going to submit a paper under the pseudonym D.H.J. Polymath. The NYT reports:
In January, Timothy Gowers, a professor of mathematics at Cambridge and a holder of the Fields Medal, math's highest honor, decided to see if the comment section of his blog could prove a theorem he could not.
In two blog posts — one titled "Is Massively Collaborative Mathematics Possible?" — he proposed an attack on a stubborn math problem called the Density Hales-Jewett Theorem. He encouraged the thousands of readers of his blog to jump in and start proving. Mathematics is a process of generating vast quantities of ideas and rejecting the majority that don't work; maybe, Gowers reasoned, the participation of so many people would speed the sifting.
It's unfortunate that the NYT doesn't link to the blog, because the procedural discussion is very interesting. Part of the kickoff is setting the norms for participation, which are of course aimed at helping to move the massively distributed discussion forward. From an educational point of view, it's interesting to see the public record of how the discussion actually evolves -- that is, how people actually do high level mathematics. There remain thorny questions about credit, as publications are currency, and it's not clear how credit would work in this sort of collaboration. Gowers writes:
It seems to me that, at least in theory, a different model could work: different, that is, from the usual model of people working in isolation or collaborating with one or two others. Suppose one had a forum (in the non-technical sense, but quite possibly in the technical sense as well) for the online discussion of a particular problem. The idea would be that anybody who had anything whatsoever to say about the problem could chip in. And the ethos of the forum — in whatever form it took — would be that comments would mostly be kept short. In other words, what you would nottend to do, at least if you wanted to keep within the spirit of things, is spend a month thinking hard about the problem and then come back and write ten pages about it. Rather, you would contribute ideas even if they were undeveloped and/or likely to be wrong.