Why is mass online collaboration useful in solving mathematical problems? Part of the answer is that even the best mathematicians can learn a great deal from people with complementary knowledge, and be stimulated to consider ideas in directions they wouldn’t have considered on their own. Online tools create a shared space where this can happen, a short-term collective working memory where ideas can be rapidly improved by many minds. These tools enable us to scale up creative conversation, so connections that would ordinarily require fortuitous serendipity instead happen as a matter of course. This speeds up the problem-solving process, and expands the range of problems that can be solved by the human mind.
from the first chapter of Reinventing Discovery: The New Era of Networked Science,
by Michael Nielsen. PDF excerpt here.