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I'm trying to estimate how many math PhD offers are awarded each year in the United States, say at the top 50 schools, if that constraint helps. (I'm interested in departments called "math," not "applied math.") For the top 50 schools, is it on the order of 500? More than that? I know programs vary greatly in size, so I'm looking only for a rough estimate of the total.

I know that the AMS releases data on the number of PhD's awarded each year, as well as the average completion rate for PhD students. But is there data showing how many PhD offers are extended each year, or at least how many students matriculate?

One reason I'm interested in this question is that I know that between 4000 and 5000 people take the GRE math subject test each year. I'm curious to what extent the top 500 scorers on this exam fill the spots at the top 50 schools, but that is a harder question to answer, because so few schools release data on their admitted students.

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    Those between 4000 and 5000 people taking the GRE math subject test each year may not go to top 50 US math schools. They may go to top 200 math graduate schools. They may go to math graduate schools outside the US. They may never go to math graduate school at all. – scaaahu May 15 '16 at 6:09
  • @scaaahu: yes, obviously. But most top 50 U.S. schools require the subject test, as far as I can tell. If they offer around 500 spots, I doubt they're taking a lot of people below the 90th percentile. (Not necessarily because their scores are high, but because those are the people who are most likely to have strong applications on the whole.) – symplectomorphic May 15 '16 at 6:18
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    The total pool of PhD applicants accepted by the top 50 schools is more or less the set of people who end up going to the top 50 schools. Schools make a lot of offers that aren't accepted, but most of these people end up going to a different top 50 school. – Peter Shor May 15 '16 at 13:02
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    At MIT, in pure math, if we used the GRE as the sole basis of admission, we'd probably only take people who scored 98% or higher. But we always admit a reasonable number of people who score below 90%, and occasionally admit people who score as low as 60%. Extrapolating, I'd guess that there are a lot of people who aren't in the top 500 GRE scorers who get offered one of the top 500 spots in U.S. math graduate schools. – Peter Shor May 15 '16 at 13:22
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    @DavidKetcheson -- having been on our graduate committee for the past 3 years, I can say that if we only took the top scorers in the Quantitative GRE test, we'd have more Chinese, but not 99%. Maybe 50-60%. I can't speak to the Math GRE since we don't require that. – Wolfgang Bangerth May 16 '16 at 3:34
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If all you're interested is a ballpark number, then here is one way to estimate: At Texas A&M, the math department hires 20-25 graduate students every year. (We make about twice as many offers.) If this was representative, then the top 50 schools would hire 1000-1250 students each year.

Now, A&M is a big department (~85 tenure track faculty). Most departments will be smaller, but in the top 50, most will be at least half the size. So my best guess is that the top 50 programs together will hire ~750 students each year, plus or minus maybe 250.

(And, for comparison: Practically all of our hires have a Quantitative GRE score above 163. This coincides with about the 85th percentile.)

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    Thanks for these numbers. But I'm not talking about the general GRE, measured 120-170 on quant and verbal; I'd expect most top PhD math students to get a perfect score on the quant section of that. I'm referring to the GRE subject test in math. – symplectomorphic May 16 '16 at 4:11
  • I don't have any experience with that since we don't require our applicants to take it. – Wolfgang Bangerth May 16 '16 at 17:59

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