Beyond Facebook: How the World's Mathematicians Organize Online

Most Americans belong to an online community of some sort. Some share baby photos or funny videos with their friends. Others jabber about the news cycle or bacon.

And then there are those who want to know the natural process that produces Zipf's law or the formal consequences of the Riemann-Roch theorem. For mathematicians, the forum of choice is Math Overflow (which turned one year old on Tuesday), an online community powered by a particular type of software that's profoundly affecting the way researchers communicate and collaborate using the Web.

At a time when Malcolm Gladwell (among others) is questioning the value of the Internet as an organizational platform, Math Overflow is an excellent example of a complex and organized online project. Developed in 2009 by a group of Berkeley grad students and post-docs, Math Overflow was conceived as a question and answer forum for research-level mathematicians. Boasting 2,700 active users ranging from especially bright undergrads to Fields medalists, the basic function of the site is to answer the highly technical questions that crop up in math research.

"Sometimes you come across a problem that you can't solve yourself, but someone else has probably already solved -- if you only knew who to ask," said Anton Geraschenko, a UC Berkeley grad student and one of the minds behind Math Overflow. "Intermediary steps are incredibly important in math, and some intermediary proofs are usually regarded as so self-evident that they're difficult to track down in publication form. But instead of painstakingly having to prove something already taken for granted, you can find the solution or documentation elsewhere. Math Overflow seems like magic because you post a question and 'poof,' you get this answer that's extremely intricate in a short amount of time."

In the past, researchers would have gone to department tea to seek out solutions to intermediary problems, but these discussions were often limited to the faculty and resources of a given institution. Online mathematics forums are a more recent development, existing on sites like sci.math, group wikis like the Polymath Project, or in the comments on well-read math blogs.

But organizationally, Math Overflow stands apart from its predecessors. Math Overflow is a community-moderated forum; users vote on the most accurate answers to the questions posed and gain reputation points based on participation, the most active of whom are granted various moderation privileges. The best answers are voted to the top of the page, while the worst ones are voted to the bottom.

At first glance, MathOverflow looks like a scaled-down version of popular social news sites like Reddit or Digg. But users aren't voting on the most entertaining content or debating each other in sprawling threads. Math Oveflow is almost an anti-social network, focused solely on productively addressing the problems posed by its users. Heavily moderated, the guidelines for asking questions are designed to discourage unnecessary chatter and keep the community's focus on a question at hand. "Math Overflow is not for homework help," blares the FAQ page. "Math Overflow is not for discussion. Math Overflow is not your encyclopedia." Open-ended conversations are relegated to a separate meta thread.

"We've tried to make the forum as 'professional' as possible," said Scott Morrison, a Miller Fellow at UC Berkeley's math department and moderator at MathOverflow, when asked about the interactive nature of Math Overflow "We've been pretty strict about good behavior, too, absurdly beyond what is common on the Internet. If it wouldn't be appropriate at department tea or particularly during a seminar, it's not at Math Overflow, either."

The Math Overflow team has made a conscious effort to differentiate the site from social media in the minds of research mathematicians. "Mathematicians as a whole are surprisingly skeptical of many aspects of the modern Internet, despite having been early adopters of email, etc," said Morrison. "In particular, things like Facebook, Twitter, etc. are viewed as enormous wastes of time." Math Overflow does give rise to some social collaboration outside of the forum; Geraschenko notes that participants have on occasion authored papers with the "answerer" to their questions.

Geraschenko and Morrison both assert that the success of the community-moderated forum is inherently tied to its software, StackExchange. The software powers Stack Overflow, a  programming Q&A site founded in 2008 and original Stack Exchange site now utilized by nearly 18 million people worldwide each month.

"One of the things awesome about the Internet is the ability to chat, making communities, and forming friendships. On the other hand, we see that as not the same as getting answers to difficult questions," said Joel Spolsky, CEO of Stack Overflow Internet Services, during a phone conversation. "This is a different kind of activity."

Spolsky highlighted the meticulous process that went into formulating Stack Overflow's structure. "Software creators have to be anthropologists," said Spolsky. "How is this software going to work out in the wild when humans use it? How will it affect their behavior or our own? We started from this spot; we studied ethnology and cultural anthropology, and then created computer sytems like Stack Overflow where every aspect of the design is trying to shape objective design with productive solutions. Features like the voting system and reputation points are the result."

StackExchange's structure may look like an appealing social forum where digital friendships are born, but the goal is to conscientiously facilitate efficient problem solving online. "We've watched how people use things and seen what works and what doesn't work. There are millions of decisions on how the software should work that are totally optimized to creating the outcome we want," emphasized Spolsky. "In the discussion forums that existed before Stack Overflow, programmers asked questions and got answers primarily through discussion software. 'Did you do this?' 'Did you do this?' You'd have to sort through a seven page thread of people getting sidetracked."

Math Overflow has been a something of a revolution for how collaborative math is carried out on the Web, while Stack Exchange has proven itself as the premier software for tightly focused community collaboration. But could the highly-routinized Stack Exchange model be applied to other disciplines?

"The software is really adaptable to math because of the way mathematicians work. The mindset of breaking a problem down, debugging, is really important," said Geraschenko, noting that he and his colleagues were initially attracted to Stack Overflow in 2009 because of the shared debugging mentalities between programming and math communities "The same process could be applied to other lab sciences that operate this way. But you have to take into account the particular kind of community to harness. The area you are applying it to has to have a prerequisite culture, and any community that lends itself to question and answer format has a lot of advantages over a plain old discussion forum."

While Stack Exchange may not be the best software to debate Proust or discuss the revolutions of 1848, Math Overflow's success may highlight its applicability as a vehicle for efficient online collaboration in the natural sciences.