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October 4, 2011

Are Mathematical Communities Unique?

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Posted by Alan Wexelblat

Contrary to my off-hand assertion about the replicability of community models from mathematical sharing groups a couple of items came to my attention today that argue the opposite case: that these communities are not like others.

The blog entry on m-phi is initially concerned with discussing how a possibly revolutionary proof in fundamental mathematical theory was published, subject to scrutiny, and rapid consensus formed that an error had been made. The consensus and supporting arguments were sufficient to convince the original author of the theory to retract his assertion. This is no small thing, particularly since he had a book in the works to explain his discovery. The blog then goes on to reference Jody Azzouni's book chapter "How and Why Mathematics is Unique as a Social Practice".

As related in m-phi, the book's central contention is that mathematics as a discipline - and therefore the mathematicians who practice it - are "very peculiar" in that they tend toward consensus not as a result of social pressures or academic rigidity, but rather as a result of how mathematics works as a discipline. Some have even argued that this is evidence for the notion of Platonism in mathematics.

From a Copyfight perspective, this poses a strong challenge: how do we generalize this kind of behavior? I think it's reasonable to expect that people who read and contribute to this blog believe in the open sharing of ideas and information. We believe that such openness accelerates progress, solves problems more rapidly, and leads to the development of generally better solutions than structures where solutions are developed in isolation. So where else can we look for examples to support this hypothesis?

(once again hat-tip to Steve Landsburg and his "The Big Questions" blog.)

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