I’m a senior undergrad right at a small liberal arts college right now who is applying to math PhD programs in the U.S. I would like to eventually become a professor at a relatively good university that has a good environment for doing mathematics. But I’m concerned that since the schools I’m applying to are not at the very top, I am basically preventing myself from having that opportunity. For example, some professors at my college suggested that I apply to Univ. of Oregon and Univ. of Georgia, because they have strong faculty in algebra. But I looked at where past doctorate recipients from Oregon went, and they usually end up in small colleges that are pretty unknown. That is making me hesitant about applying to Oregon.
I consider myself a strong student (and so do my letter writers, and I guess that’s what really matters) but I have poor math GRE scores that my professors think will severely limit my chances of getting into a program at the top 40 schools (e.g. they said I had a shot at, say, Univ. of Washington, UCLA, Chicago, and Michigan, before I got my GRE scores).
Some of my professors don’t think the prestige of the grad school matters that much (i.e. as long as I write an interesting thesis and make my results known, I should be fine). But I have a feeling that my professors may be a bit out of touch, since I go to a liberal arts college, not a research university. And when I look at where past PhD students from good programs (e.g. in the Group I list in the AMS rankings but not top thirty) go to, I get a bit concerned. Maybe I should take a year off and try again next year. I was wondering if anyone had any advice.
I am a (tenured, associate) professor at UGA, which is a top 50 math department but is not part of the AMS Group I list. I got my PhD at Harvard, which is consistently ranked as one of the top three programs in the US (along with Princeton and Berkeley, with places like Chicago, MIT and Stanford close behind).
At every math department I have ever seen it is quite true that, on average, if you succeed in landing a tenure track academic job at all, it will be in a department which is at least a level below the program where you trained as a graduate student. Looking at the numbers involved explains why this has to be the case: a decent-sized department may grant 10 PhDs each year and hire tenure track faculty once every two or three years. So everyone can expect to hire a candidate of much higher quality than the average PhD they produce. (I should add that the candidate’s “quality” depends on many things other than where they themselves got their PhD. A Harvard PhD does not guarantee a tenure track job at a top 50 department: the percentage of Harvard PhDs who get such jobs is probably around 50%, maybe a little lower.)
Many — probably half or more — of the graduates of the PhD program at UGA are interested in primarily teaching positions in regional colleges and universities. But a non-negligible percentage go on to strong research careers. For instance, there is
James Haglund, a 1993 PhD, now a tenured associate professor at UPenn,
Kevin James, a 1997 PhD, now a tenured associate professor at Clemson,
Ernie Croot, a 2000 PhD, now a tenured associate professor at Georgia Tech,
Gerard Awanou, a 2003 PhD, now a tenured associate professor at Northern Illinois,
Valerie Hower, a 2007 PhD, now a tenure track assistant professor at U. of Miami,
and this is not an exhaustive list. So getting a PhD at a place like UGA certainly keeps alive the dream of a career in mathematical research.
Also, I don’t want to sound discouraging, but based on what little information you’ve provided it’s not clear that you’re a shoo-in for admission at a department like UGA. A lot of it depends whether your “small liberal arts college” is a place like Amherst or Colby or Smith — i.e., a place where we will probably know your letter writers, at least by reputation — or a small liberal arts college that we’ve never heard of. Excellent grades at a place we’ve never heard of and excellent recommendations from people we’ve never heard of combined with poor GRE scores has not in the past been a formula for success at UGA.
I do think that trying to get a PhD at a department significantly worse than UGA — say, not in the top 100 programs — is not laying much groundwork for a future academic research career. If you don’t get into a top 100 program this year, then spending a year improving your application and, especially, your GRE scores, is a better strategy than enrolling in a program none of whose graduates go on to research careers.