Re Proof School: I have no problem with Julliard or the Fame school, nor do I object to those schools carving out a category of “young performer” and saying “these kids, not anyone else, is who this school is really for.” Is there really a difference?
I guess that in my heart I don’t believe math is much like music. I don’t think you have to give yourself wholly to it as a child in order to make meaningful contributions as an adult. (Is music even actually like that? All I know about it is from watching Fame.) I like it about US math education as opposed to Europe that, even in college, our math majors take all kinds of courses, spending maybe a quarter or a third of their time on math. As far as I can see, this doesn’t hurt them in grad school.
Another thought: I have made a couple of visits Canada/USA MathCamp, the amazing summer program Mira Bernstein founded — the intensity of feeling and learning there is really quite remarkable, and I’d send my kids there in a heartbeat if they wanted to go (and if they could pass the qualifying quiz!) I love it — but I never once felt “I wish this could be all year round!” The short span is what makes the fire so hot.
But then again, I went to a high school I really loved, where I learned a ton (albeit nothing about mathematics.) If I’d gone to a mediocre school where I didn’t have anybody to talk to, I probably would have wanted to go to MathCamp year round.
Apparently this is “small tribal communities I’m clearly part of but whose separation from the rest of humanity I’m very ambivalent about” week on Quomodocumque.