From the abstract: "ew innovations by math
ematicians 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 ques
tion 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 er
ror. Responses typically present information known to the
respondent, and readily checked by other users: thus the
effectiveness of
mathoverflow
comes from information shar
ing. 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 compu
ta
tional mathematics, in particular how to handle error, anal

ogy and informal reasoning."