Hi everyone! I’m an aspiring math major who’s considering Harvard and Princeton (and bemoaning my obligation to make a final commitment in two weeks). I’ve researched their departments to death, but I’m wondering about some of the more intangible elements of the “math experience” at both schools. What is the mathematical culture like? Collaborative? Fiercely competitive? Tight-knit? Receptive to undergraduates as much as graduate students? Any fine points would be thoroughly appreciated.
One of the reasons I’m asking is that, although Harvard’s rigor and superlative faculty are enticing, I worry about a sense of academic filtration. I’ve heard that professorial attention concentrates on the very upper echelon of math students, and that talented but less decorated kids go by the wayside. I’m pretty experienced when it comes to proof-based math, but I don’t have an IMO victory or Intel first prize to show for it. I fear that I might not feel empowered by or have actual access to Harvard’s incredible math resources.
On the flip side, I’ve heard that it’s substantially more difficult for people at Princeton to delve into graduate coursework; there’s a sort of “undergrad ceiling.” There’s also the matter of grade deflation and a significantly smaller department. That said, Princeton math seems a bit more egalitarian in the sense that all majors are expected to write a thesis and think deeply about the unexplored. This is typically reserved for the top few at Harvard.
So those are some of my preliminary thoughts. I’d love to hear what anyone has to say, firsthand experience or otherwise!
@abstract1 You posted that you were taking Honors Math last year at Columbia. Only a very tiny number of High Schools in the NYC area have kids taking math classes there. You should try to get in touch with recent alums through the math department at your HS who have experience in the math departments at H & P. You’d get much more reliable info going that route instead of looking for answers here.
@abstract1, you’ve certainly done your homework! Yes, Harvard does have the amazing Math 55 course, and taking that course (like Bill Gates did) makes you a campus god, such being the culture of the place, but Harvard does tend to “teach to the top of the class”, and that could be a problem for mere mortals who are not mentally prepared to be on the receiving end of such instruction in some (not all) of the upper-level courses. (When I say “mere mortals”, I include some of the students who are able enough to take Math 25, where many of the students have already done some Analysis, and the course text book was Baby Rudin until recently – I don’t know now.)
And yes, though Princeton tends to be more nurturing to all its students, it also does “nanny” you with restrictions and requirements. Compare their major requirements and distribution requirements vs Harvard’s (and as you noticed, discouragement against taking graduate courses), and if you read carefully, you’ll find a very different philosophy on how much freedom and flexibility smart students should get.
With respect, you’re looking only at academic fit. While that’s really important, it’s not the sole variable to consider:
Which housing resources and tradition do you prefer? (eating clubs vs. final clubs)
Tied to that first question partially, which social vibe do you prefer? Which school is more friendly to your "party style" or lack thereof? Which school and area offers more cultural, culinary, sporting and other such entertaining and enriching opportunities? In Princeton's case, would you mind traveling to NYC or Philly for them, if you're into that?
Which campus is easier to get around and offers relative ease of access to the surrounding town or city and other cities?
And for academic fit, also consider:
Gen-Ed class sizes
Personal academic support
Ease of access to profs
Relative # of TAs leading discussions and labs.
Ease of entry into, and exit from, a major. (many students change their minds)
Curriculum/graduation requirements.
Obviously both are at the tip-top of undergraduate education. Congrats and good luck!