contributed by rebecca nguyen

Tim Gowers, a renowned British mathematician from the University of Cambridge, extended an invitation in 2009 for anyone-- mathematicians and nonmathematicians alike-- to join him in a “massively collaborative mathematical project”. Since the inception of that first “Polymath Project”, volunteer collaborators have flocked to integrate their own blogs and content into the Polymath open-source community. Gowers’ first project of networked science connected the expert knowledge of mathematicians, or, as we might think of them, “main characters in a play,” with ideas of active participants from the rest of the world. Each contributor built on another’s performance and all the comments added up to the creative process of doing mathematical research together.

Six weeks after the first Polymath Project was launched, its contributors solved a complex unresolved mathematical problem. This ad-hoc group of enthusiasts accepted Gowers’ challenge to use a combinatorial approach to solve the density Hales-Jewett theorem with three lines (k=3), but came up with a convincing proof using another method entirely. (http://gowers.wordpress.com/2009/03/10/polymath1-and-open-collaborative-...) The success of the Polymath project made visible the improvisational nature of collaboration. We can see this in the description Gowers provides in his March 10th, 2009 blog. Here he mentions how the group accepted his initial offer to use one approach to solve the DHJ(3) problem. Then through the process of responding to each others’ offers, new ideas emerged, were pursued, or “quietly abandoned”. This form of open improvisational collaboration may expand the range of scientific problems that we can hope to solve. The continued development of open networked science may lead to new ideas and will catalyze rapid discoveries. Although the project described here is one of mathematicians, we believe the call to open science is one for all scientists. We hope that people will respond to our invitation to do “open science” through enhanced improvisational performances in science and math.

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