Everything is relative. There’s no question that Princeton has a much stronger math department than your other choices. Whether Princeton is right for your son as a math major depends on his preparedness, his ability to rise to the challenge, and his ability to comprehend difficult concepts quickly and thoroughly. Abilities of students in challenging subjects (math is certainly one of them) vary a great deal and this will become obvious as soon as he takes a challenging class. The big question is whether he would rise to the challenge or become frustrated. None of us here knows for certain unless you tell us a lot more about him (beyond just a few courses he’s taken).
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I would emphasize some ability/comfort with proofs, and patience and work ethic. I wouldn’t scare someone off by suggesting that stuff has to be learned “quickly” in a frenzy. A lot of time is spent mulling over things rather than rushing through things. Incidentally the department discourages kids from using intuition over rigor.
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As an example, in my math undergrad program, which was similarly strong, we knew by the end of the first term pretty much where everyone ranked, and that barely changed over the following three years. I imagine it was dispiriting for many of those who found themselves in the bottom quartile (especially after being easily the best math kid in their high school), though those in the middle of the pack generally seemed OK with it, after all they were competing with some of the best mathematicians in the world.
I think this is not at all the same as working hard. And in fact “working hard” in math is not like a science subject where you run lots of experiments or a humanities subject where you read lots of books and write lots of essays. It’s about getting yourself in the frame of mind where you “see” the answer to difficult problems, often when you are doing something else. Being distracted by that background thinking (and therefore not attentive to a spouse) doesn’t help personal relationships.
A friend who is now an Oxford math professor said that you need 2 hours of inspiration in 3 years to get a great (pure) math PhD. Mine wasn’t great, but i found that exactly right, all my decent work was done in the bath, lying in bed and even rowing crew. Dreaming the solution to math problems is definitely a thing.
Rigor is absolutely needed in your work, but without intuition you may struggle even to get started with a difficult problem set.
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I think maybe this is the correct perspective. I stand corrected.
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I love this! I think you captured it very well.
I’m not a math major but I can totally relate to this. Have had the same experience with cracking hard CS problems.
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Like Kekule 
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Kekule: “It is also said that genius thinks by leaps and bounds. Gentlemen, the waking mind does not so think.”
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If I were doing my undergrad all over again, Williams might be the only school for which I would turn down an offer of admission from Princeton. But that’s given my academic interests, not his. I think P vs. W is literally the top university (for undergrads) vs. the tippy-top LAC all-around.
That being said, given his known interests, I think that – unless one of the other schools really, really vibes with him – Princeton is the best choice.
Ultimately, there is no wrong choice here if he follows his preferences and all are affordable. But all else being equal, I think Princeton is the best option.
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Lots to think about. He will graduate salutatorian of a public school of 600+ kids. He definitely has the grit and dedication part down. He will have I imagine a big adjustment period of not being at the top of the class.
He doesn’t really know what he wants to do with the math because I think he needs much more exposure but he has aspirations of being the first PHd of the family. (I immigrated from Colombia). I guess I just want to make sure that Princeton will provide not only top notch academics but also an environment where is a bit more than swim or sink while he gets the chance to get his math skills to a higher level.
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Princeton’s grad rate is like 98%, and you can bet that some of those 2% leave for reasons other than academic hardship. If he works hard, he should be fine. Math is (probably) hard everywhere.
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In that case, go to Princeton. He might as well get used to the challenge, because that’s what he would need pursuing a PhD in math. Princeton would prepare him better (not that the other schools can’t) and potential PhD advisors, who make the decisions to admit him to their PhD programs, would universally have better regard for the Princeton program.
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If you would like to say, which school did your son choose?
He is going to be a Tiger. He will attend Princeton. It was financially his best offer in addition to all the other obvious reasons to attend. (other than the NJIT almost full ride). He would had been happy to attend any of the other places. His biggest reservations where with TX as a state but Rice itself was very appealing to him. We are very thankful for the insight in CC.
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