Perception becomes reality. Many students are making the same calculation as you, and concluding that Princeton has a stronger UG math program. Therefore, many of the top students are choosing to go to Princeton (making it a stronger math program).
Can anyone comment on the elitism or lack thereof of Princeton’s earing clubs? To what extent does Princeton deflate grades?
As for Yale vs. Princeton: I doubt there are more than three or four prospective undergraduates per year who would ever expect, while they are still in college, to be able to tell the difference between the #1 math department (which Princeton arguably is, or at least is one of four or five universities that could make the claim) and the #10 math department. If you are one of them, you already know it, and you probably also already know where you are going to college. If you are not one of them, comparing top math departments is just about as useful as debating how many angels can fit on the head of a pin.
The numbers cited above are pretty misleading. According to the NCES website, last year Princeton graduated 35 math majors, and Yale graduated 25 math majors, 8 applied math majors, and 2 statistics majors. Both figures, however, meaningfully understate the size of the undergraduate math communities at both universities. Princeton does not permit double majors, so its major number is reliable, but it had 52 operations research majors and 83 computer engineering majors, most of whom will have taken lots of upper-level math, as well as 183 economics majors, many of whom could easily have had math as a second major. Yale does permit double majors, so it probably had many more than 35 people who completed math majors, among them some of its 166 economics majors, 35 computer science majors, and 2 computer science and mathematics majors. Both colleges will also have any number of lab science majors with a strong interest in math, too.
In other words, there may be a slight numerical advantage at Princeton, but it’s nothing like 3-1. Probably more like 10-9.
Interestingly, the number of math majors at Princeton and Yale both significantly trail the numbers at other liberal arts universities with strong math departments. The NCES figures have Harvard with a total of 120 graduating majors in math/applied math and Chicago with 116, including 10 statistics majors. Harvard and Chicago, essentially peers of Princeton, are both a little bigger than Yale or Princeton, but not that much bigger. Like Princeton, Harvard does not permit double majors per se, although it does allow joint concentrations, and I believe there are several joint concentrations involving applied math every year. Chicago does permit multiple majors, and it publishes numbers. As of June 2015, there were over 500 second, third, and fourth year students with declared majors in math, applied math, or statistics. That’s well over 10% of the student body, and it doesn’t even count math-oriented economics and lab science majors who haven’t bothered to declare a second major. Stanford, another peer in terms of math prestige, had 55 math majors in NCES numbers (and scads of operations research and computer science majors, and economics majors). Berkeley, which is much larger of course, had 323 primary math/applied math/statistics majors, plus the OR and computer science people and the economics people.
“If you are one of them, you already know it, and you probably also already know where you are going to college.”
You already know what? That you are one of the three to four, or the differences between schools’ math departments? If the former, why does it follow that you know where you’re going to college?
The school selection criteria of those exceptional few would be very closer, if not the same, to the one by the top PhD applicants. Then, being in a top ten program in general is a good thing but the number one or ten in general by a magazine is not make a difference for his Math training.
I don’t think you can do better than Princeton if your intention is to major in mathematics.