Tuesday 10 July 2012

Solving problems through blogs and wikis - lessons from Polymath

I blogged a while ago about the Polymath project; an experiment in collaborative solving of major mathematical problems. Recently I read again the description of the project published here, and have some interesting conclusions to share with you about this sort of collective problem solving.

According to Wikipedia,

The Polymath Project is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution. The project began in January 2009 on Tim Gowers' blog when he posted a problem and asked his readers to post partial ideas and partial progress toward a solution. This experiment resulted in a new answer to a difficult problem, and since then the Polymath Project has grown to describe a particular process of using an online collaboration to solve any math problem.
So far, at least one major mathematical problem has been solved, using primarily  a combination of blogs and a wiki.

Polymath uses two types of blog
  • Blogs hosted by mathematicians, where particular aspects of the problem are addressed in the blog comments
  • An administrative blog, which summarises progress, and hosts administrative discussion.
  • The wiki provides write-ups of the work done on the blogs. Comments on the blogs are the working process, the wiki is the summary of the outcome.
There are a number of ground rules for participation in the project, for example
  • no working independantly on the problem without discussing progress on the blog
  • discussions should be polite and focused
  • any publications will be under a Polymath pseudonym representing the collective input
There are also some administrative conventions, such as the following
  • Any blog post is not allowed more than 100 comments. This convention forces the leaders to summarise, and then restart, progress
  • There are two leaders, both eminent mathematicians, whose main roles were to set the ground rules and conventions, and provide frequent summaries, highlightimg the relavenat comments and guiding the next steps.
  • Comments are divided into numbered comments (comments which make a direct contribution to the solution of the problem, and which are numbered for reference by other comments), and other comments, mostly about the process or administration of discussion ("metacomments").
One of the big challenges found on the project was the difficult of bringing newcomers up to speed. As one of the leaders says, "A number of people have commented that it is difficult to catch up with the discussion if you come to it late. We should try to start each thread in a way that makes it as self-contained as possible". Any problem-solving process using this approach needs to develop an effective way to bring newcomers into the process, as the majority of contributors to the Polymath outcome were those who joined in the first week.

Polymath has proved to be a great success.  In just over 6 weeks a collective group of distributed individuals accomplished some highly non-trivial mathematical feats. The scale of the collaborative approach was large compared to most collaborations in higher math. It is relatively uncommon for a mathematics publication to have more than 3 authors, let alone 40. Many of the crucial steps in the problem solving process were from relatively junior (based on publication count) mathematicians. These are the small red dots on the lower right of the diagram above, in the blue cloud marked "low volume, high importance." Polymath1 was a group solution to a problem, with recognised experts working shoulder to virtual shoulder with relatively junior mathematicians, to solve a big problem in a short time.

I think there is a lot we can learn from this experiment, when it comes to building collaborative groups within industry, specifically
  • the role of leadership
  • the need for ground rules and conventions
  • separation of substantive comment from metacomment
  • separation of discussion (on blog comments) from conclusion (on the wiki)
  • the need for regular summary and refocus, and
  • the need to cater for late joiners

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