  The highest level of mathematics research is traditionally seen as a solitary
activity. Yet new innovations by mathematicians themselves are starting to
harness the power of social computation to create new modes of mathematical
production. We study the effectiveness of one such system, and make proposals
for enhancement, drawing on AI and computer based mathematics. We analyse the
content of a sample of questions and responses in the community question
answering system for research mathematicians, math-overflow. We find that
mathoverflow is very effective, with 90% of our sample of questions answered
completely or in part. A typical response is an informal dialogue, allowing
error and speculation, rather than rigorous mathematical argument: 37% of our
sample discussions acknowledged error. Responses typically present information
known to the respondent, and readily checked by other users: thus the
effectiveness of mathoverflow comes from information sharing. We conclude that
extending and the power and reach of mathoverflow through a combination of
people and machines raises new challenges for artificial intelligence and
computational mathematics, in particular how to handle error, analogy and
informal reasoning.
