I had the opportunity to put together some information on the Polymath collaboration from last year for a presentation in a series called "Collaboration on Collaboration". So it's very easy to share some of the details here. Polymath is a favorite collaboration story because it involves many people working on a single problem.

Tim Gowers (the gent shown here) wanted to answer the question -- Is massively collaborative mathematics possible. He decided to tackle something called the density Hales-Jewett Theorem (DHJ) (and no, I don't know what that is). He had an idea but wasn't sure it was useful -- and thought someone else could perhaps help. He was working on a specific case, when k=3 (in some description or equation). He didn't want to prove the theorem, just to figure out if his approach was useful or have someone tell him why it wasn't

So he launched the question on his blog. Most interesting to me was the set of rules he established, which are paraphrased below but which are listed in full in one his posts. The blog was the setting for the collaboration, although some of the discussion migrated over time to another blog and to a wiki that was set up to help keep track of ideas that seemed solid.

The results were outstanding, much exceeding Gowers' expectations. The group succeeded dramatically. It bypassed Gowers' question and went on to prove the case of the theorem that they had begun with, and did it in a way that led to a more general set of insights about the problem and about other problems. In 37 days twenty-seven people made contributions (and many more followed the action).

Gowers' take on this all, reported in his blog, was that while the collaboration was terrific it wasn't as "massive" as he had hoped. Other participants commented on the difficulty of following the developments at the speed they came -- especially since some of the discussion was sophisticated and required meaningful understanding of the problem domain (which many of the mathematicians apparently didn't have).

Despite the lack of "massiveness," this is an intriguing example of people working together in a different way. My view is that the "rules of the road" were important to making it work.

There has been at least one other Polymath effort that is still going on, and another under consideration, and Gowers has also launched another one. It will be interesting to see which make progress and why (and I for one, will be unable to tell you if the difficulty of the problem had anything to do with it!!).

What do you think about this?

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