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.
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.)