One of the inspirations for Collaborating Minds is a project called Polymath. Some people have been asking about it lately so I’m updating an old blog post I wrote a few years ago for Positive Structures, a blog where I think about personal and organizational structures that can make a positive difference (like Collaborating Minds, for example).
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.
Who and how to give credit was an important issue. As #11 above indicates, the decision was made to publish as a group, and in fact a paper was published under the name DHJ Polymath. For people who needed to show tenure committees their contribution, the suggestion was that committee members be directed to the site, which held the entire discussion, and they could take a look. Because of the written/typed record, each person’s contribution could be judged by an observer.
There have been several Polymath efforts in the past few years, with apparently varying degrees of success. Michael Nielsen, a participant, has written a book about the whole idea of collaboration in science, which I commented on in Reinventing Discovery and Collaborating Minds.
What do you think about this?