

It seems to appear that I have somehow managed to pass the 100,000 score milestone for reputation on MathOverflow. A hundred kiloreps! Does this qualify me for micro-celebrity status? I have clearly been spending an inordinate amount of time on MO… Truly, it has been a great time.

MathOverflow, an eternal fountain of mathematics, overflows with fascinating questions and answers on every imaginable mathematical topic, drawing unforeseen connections, seeking generalizations, clarification, or illustrative examples, questioning assumptions, or simply asking for an explanation of a subtle mathematical point. The mathematics is sophisticated and compelling. How could a mathematician not immediately plunge in?

I first joined MathOverflow in November 2009, when my colleague-down-the-hall Kevin O’Bryant dropped into my office and showed me the site. He said that it was for “people like us,” research mathematicians who wanted to discuss mathematical issues with other professionals, and he was completely right. Looking at the site, I found Greg Kuperberg’s answer to a question on the automorphism tower problem in group theory, which was one of the first extremely popular questions at that time, the top-rated question. I was hooked immediately, and I told Kevin on that very first day that it was clear that MathOverflow was going to take a lot of time.

I was pleased to find right from the beginning that, although there were not yet many logicians participating on MO, there were nevertheless many logic questions, revealing an unexpectedly broad interest in math logic issues amongst the general mathematical community. I found questions about definability, computability, undecidability, logical independence, about the continuum hypothesis and the axiom of choice and about large cardinals, asked by mathematicians in diverse research areas, who seemed earnestly to want to know the answer. How pleased I was to find such a level of interest in the same issues that fascinated me; and how pleased I was also to find that I was often able to answer.

In the early days, I may have felt a little that I should be a kind of ambassador for logic, introducing the subject or aspects of it to those who might not know all about it yet; for example, in a few answers I explained and introduced the topic of cardinal characteristics of the continuum and the subject of Borel equivalence relation theory, since I had felt that mathematicians outside logic might not necessarily know much about it, even when it offered connections to things they did know about. I probably wouldn’t necessarily answer the same way today, now that MO has many experts in those subjects and a robust logic community. What a pleasure it has become.

A while back I wrote a post The use and value of MathOverflow in response to an inquiry of François Dorais, and I find the remarks I made then are as true for me today as ever.

I feel that mathoverflow has enlarged me as a mathematician. I have learned a huge amount here in the past few years, particularly concerning how my subject relates to other parts of mathematics. I’ve read some really great answers that opened up new perspectives for me. But just as importantly, I’ve learned a lot when coming up with my own answers. It often happens that someone asks a question in another part of mathematics that I can see at bottom has to do with how something I know about relates to their area, and so in order to answer, I must learn enough about this other subject in order to see the connection through. How fulfilling it is when a question that is originally opaque to me, because I hadn’t known enough about this other topic, becomes clear enough for me to have an answer. Meanwhile, mathoverflow has also helped me to solidify my knowledge of my own research area, often through the exercise of writing up a clear summary account of a familiar mathematical issue or by thinking about issues arising in a question concerning confusing or difficult aspects of a familiar tool or method. Mathoverflow has also taught me a lot about good mathematical exposition, both by the example of other’s high quality writing and by the immediate feedback we all get on our posts. This feedback reveals what kind of mathematical explanation is valued by the general mathematical community, in a direct way that one does not usually get so well when writing a paper or giving a conference talk. This kind of knowledge has helped me to improve my mathematical writing in general.

Thanks very much again, MathOverflow! I am grateful.

A few posts come to mind:

There have been so many more great questions and posts. If you are inclined, feel free to post comments below linking to your favorite MO posts!

Concerning the MO reputation system, I suppose some might suspect me of harboring unnatural thoughts on reputation — after all, I once proposed (I can’t find the link now) that the sole basis of tenure and promotion decisions for mathematics faculty, as well as choice of premium office space, should be: MO reputation, ha! — but in truth, I look upon it all as a good silly game. One may take reputation as seriously as one takes any game seriously, and many mathematicians can indeed take a game seriously. My honest opinion is that the reputation and badge system is an ingenious piece of social engineering. The designers must have had a good grasp on human psychology, an understanding of the kinds of reasons that might motivate a person to participate in such a site; one thinks, for example, of the intermittent reward theory. I find it really amazing what the stackexchange designers have created, and who doesn’t love a good game?

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