Democratic, Free-market Mathematics

By Kareem Carr

Some of you may have already heard about MathOverflow, but for those of you who haven’t, let me tell you what you’ve be missing.

MathOverflow is a website where mathematicians, both actual and aspiring, ask each other questions. It is, by all appearances, a thriving hotbed of mathematical activity. There are more than 4.5 thousand users with more than six thousand questions asked. Everyday seems to bring new questions and new answers. Many of these are of extremely high quality. It can be quite addictive to spend hours constantly refreshing one’s browser, as there is always something novel and interesting to see.

More enticing than merely watching, though, is participating. The seemingly trivial baubles of points and badges have sparked in many participants something that is perhaps not unusual in the mathematics world, true obsession. Points are awarded for asking questions, and for answering questions, that are of interest to the MathOverflow community. Votes for questions give those questions prominence on the site, and gain the asker additional points. Answers to questions which receive votes gain prominence also, and so do the answerers.

Accordingly, users who habitually produce good questions and answers can accumulate large number of points. Those with the highest point totals are rewarded with greater ability to modify the MathOverflow site and thereby shape the direction of the MathOverflow community. Some users have accumulated an astounding number of points and badges; one user has accumulated almost 19 thousand points.

For a site that has only been active for a few months, the growth has been phenomenal. I spotted at least two fields medalists, Terence Tao and Timothy Gowers, among the many users.

However, there has been some criticism. For instance, there is some perception that some fields are more highly represented than others. Furthermore, On a companion site called meta.mathoverflow.net, some users have asked whether the competitive aspect is a net negative. Some have speculated that the level of competitiveness has led to a gender imbalance, where males are the predominant participants. However, it was also noted that there is a gender imbalance in mathematics as a whole and, of course, academic mathematics in general is no stranger to competitiveness.

Although, I do not consider it a criticism of the site, there is also some bias in which questions are allowed as appropriate and which are not. Both the tone of the question, and the community’s perception of the person asking the question, can be pivotal. For instance, this question, “Anything going on for a mathematician stuck at New York?” appeared during the period when volcanic ash from Iceland had stranded many people on the wrong side of the Atlantic. This context appeared to help increase acceptance of this non-techinical question, whereas had a similar question been asked by a undergraduate during a different time of the year, it would likely have garnered more negative attention, from what I’ve seen of the site.

Finally, there is also some risk that conflict on the website could lead to negative effects on offline career prospects. Perhaps for this reason, many users choose to be anonymous. However, for the many who are not anonymous, there is also the prospect of impressing one’s peers and senior mathematicians with positive effects on one’s offline career.

All in all, I think certain idiosyncrasies are to be expected and perhaps even welcomed. The site is young and will probably develop in character over time. My feeling is that it shows tremendous promise and every mathematics graduate student should at least give it a try. It holds out the promise of being an extremely fair and democratic place where the barriers to entry are lowered. This can only serve to increase the accessibility of research mathematics.

The founders of the site are to be applauded for doing something that is actually quite extraordinary, introducing an online model for group collaboration in mathematics that is both fun and productive — aspects which usually work in opposition to each other.

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