Introduction to the Polymath Project and “Density Hales-Jewett and Moser Numbers”

by Michael Nielsen on May 1, 2010

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In January of 2009, Tim Gowers initiated an experiment in massively collaborative mathematics, the Polymath Project. The initial stage of this project was extremely successful, and led to two scientific papers: “A new proof of the density Hales-Jewett theorem” and “Density Hales-Jewett and Moser numbers”. The second of these papers will soon appear in a birthday volume in honour of Endre Szemeredi. The editor of the Szemeredi birthday volume, Jozsef Solymosi, invited me to submit an introduction to that paper, and to the Polymath Project more generally. The following is a draft of my introductory piece. I’d be very interested in hearing feedback. Note that the early parts of the article briefly discuss some mathematics, but if you’re not mathematically inclined the remainder of the article should be comprehensible. Many of the themes of the article will be discussed at much greater length in my book about open science, “Reinventing Discovery”, to be published early in 2011.

At first appearance, the paper which follows this essay appears to be a typical mathematical paper. It poses and partially answers several combinatorial questions, and follows the standard forms of mathematical discourse, with theorems, proofs, conjectures, and so on. Appearances are deceiving, however, for the paper has an………..

……. Linux is just one project in a much broader ecosystem of open source projects. Deshpande and Riehle have conservatively estimated that more than a billion lines of open source software have been written, and more than 300 million lines are being added each year. Many of these are single-person projects, often abandoned soon after being initiated. But there are hundreds and perhaps thousands of projects with many active developers.

……………… A similar process is beginning today. Will pseudonyms such as D. H. J. Polymath become a commonplace? How should young scientists report their role in such collaborations, for purposes of job and grant applications? How should new types of scientific contribution – contributions such as data or blog comments or lab notebook entries – be valued by other scientists? All these questions and many more will need answers, if we are to take full advantage of the potential of new ways of working together to generate knowledge.

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