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Friday, October 16, 2009

More on the Polymath project: collaborative open mathematics

Timothy Gowers and Michael Nielsen, Massively collaborative mathematics, Nature, October 14, 2009.

On 27 January 2009, one of us — Gowers — used his blog to announce an unusual experiment. The Polymath Project had a conventional scientific goal: to attack an unsolved problem in mathematics. But it also had the more ambitious goal of doing mathematical research in a new way. Inspired by open-source enterprises such as Linux and Wikipedia, it used blogs and a wiki to mediate a fully open collaboration. Anyone in the world could follow along and, if they wished, make a contribution. The blogs and wiki functioned as a collective short-term working memory, a conversational commons for the rapid-fire exchange and improvement of ideas.

The collaboration achieved far more than Gowers expected, and showcases what we think will be a powerful force in scientific discovery — the collaboration of many minds through the Internet. ...

Over the next 37 days, 27 people contributed approximately 800 substantive comments, containing 170,000 words. ...

Progress came far faster than anyone expected. On 10 March, Gowers announced that he was confident that the Polymath participants had found an elementary proof of the special case of [the density Hales–Jewett theorem, the problem studied], but also that, very surprisingly (in the light of experience with similar problems), the argument could be straightforwardly generalized to prove the full theorem. A paper describing this proof is being written up, along with a second paper describing related results. ...

The working record of the Polymath Project is a remarkable resource for students of mathematics and for historians and philosophers of science. For the first time one can see on full display a complete account of how a serious mathematical result was discovered. ...

The process raises questions about authorship: it is difficult to set a hard-and-fast bar for authorship without causing contention or discouraging participation. ... As a provisional solution, the project is signing papers with a group pseudonym, 'DHJ Polymath', and a link to the full working record. One advantage of Polymath-style collaborations is that because all contributions are out in the open, it is transparent what any given person contributed. ...

The project also raises questions about preservation. The main working record of the Polymath Project is spread across two blogs and a wiki, leaving it vulnerable should any of those sites disappear. In 2007, the US Library of Congress implemented a programme to preserve blogs by people in the legal profession; a similar but broader programme is needed to preserve research blogs and wikis. ...

Similar open-source techniques could be applied in fields such as theoretical physics and computer science, where the raw materials are informational and can be freely shared online. The application of open-source techniques to experimental work is more constrained, because control of experimental equipment is often difficult to share. But open sharing of experimental data does at least allow open data analysis. The widespread adoption of such open-source techniques will require significant cultural changes in science, as well as the development of new online tools. We believe that this will lead to the widespread use of mass collaboration in many fields of science, and that mass collaboration will extend the limits of human problem-solving ability.

See also our past post on the Polymath project.