I just posted this over on a discussion thread at meta.MO, and I thought it might deserve more visibility.
We’ve had some questions on meta.MO about how undergraduates applying to graduate school should view a presence on Mathoverflow, math.SE or in the math blogosphere. I was on the graduate admissions committee for the University of Michigan last year so, for what it is worth, here is my take:
I did not make a routine practice of googling applicants, because I didn’t have time. I read every file I was given but, if that gave me enough data, I didn’t go looking for more.
However, when I felt I needed more data, I would often google the applicant’s name, and I often found Mathoverflow or blog activity. This might be because the candidate’s file was borderline, but it more often meant that I felt there was a part of the picture missing. Perhaps the applicant was in 2 REU’s and claimed to have produced research papers, but the file didn’t give me a place to read about the research. Or recommendations talked about the applicant’s strong involvement with his undergraduate math club, but the applicant’s own statement said nothing about it. Or, of course, if recommendations said “the candidate has given several interesting answers on MO”, as happened more than once.
There was much more opportunity to impress me than to disappoint me. My default assumption, and one which was borne out by the majority of the files, was that the applicant was a standard undergraduate with little knowledge of advanced math. If what I found confirmed that, I moved on and didn’t note it. In order to get into a top grad school like UMich, you need to stand out from that assumption, so anything which showed more mathematical knowledge or interest than that struck me as positive. Even MO questions which were below the level of the site struck me as a sign that the applicant was seeking out professional fora, and had mathematical interests outside his or her classes.
By the way, evidence of a social life was neither a positive nor a negative. I went to parties in college; if my applicants did likewise, I didn’t hold that against them.
However, there is one thing that could be a negative. Our committee chair, Sergey Fomin, clearly told us to flag any file that indicated a student who would be socially difficult. I don’t mean loners or odd people — our department has plenty. But if there were signs of an applicant who was regularly in fights with others, if there was someone whom we wouldn’t be able to trust with the responsibility of teaching an undergraduate class, if we had someone with a record of blowing off assignments and deadlines, that was a problem, and we would have to look at the issue seriously no matter how skilled their mathematical level.
Now, this issue didn’t particularly come up in my google searches. But I could easily imagine it; there have been people who have made a bad impression through rudeness on MO, and it could be relevant when they apply to schools or for jobs. (Please don’t mention specific examples in the comments. I will delete any comments that do so.)
In short, being mathematically active online is a good thing, and you don’t have to look smarter than an interested undergraduate. But being rude online is a bad thing, and it can turn up in google. I would imagine this might be good advice for people other than grad school applicants.