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.

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Hi Jordan –

The analogy doesn’t really work unless you really see mathematics as some sort of hereditary tribe. Sure, many mathematicians have people in mathematics-related fields as parents. But would a maths-focused school necessarily strengthen the trend? Not if (a) it’s well-publicized in all schools in the state, (b) it’s tuition-free (or, as a second best, plenty of financial aid is available), and (c) what is typically needed to get in is clearly specified to all. In Peru, selection for mathematical olympiads (yes, I know, something that can be overemphasized) has actually resulted in a great broadening of the base for future mathematicians; now it isn’t just kids of maths teachers who can learn about proofs at age 12 or 13.

I agree that Juilliard (and similar places that train in ballet or athletics) are dealing with things that are genuinely different from math, and that it would be bad to have a school which tried to be the Juilliard or La Masia of mathematics. However, I think La Guardia (the Fame school) or other high school performing arts magnets are totally totally different from those. (My knowledge is mostly about PPAS, another NYC performing arts high school, which differs in several ways including allowing students to work professionally during high school. So it’s possible that I’m misunderstanding some things about La Guardia.) There are many many high school “music kids” and “theater kids” (I count high school me as the latter) who aren’t really training to become professionals but rather just want to spend time in high school in a performing arts environment surrounded by people like them. Furthermore, unlike Juilliard or La Masia, students at a school like La Guardia are given a broad education as well as a specialized one. They still take math and sciences, and have AP courses, and the school has sports teams. It’s not a training academy, it’s a school for music kids and theater kids, most of whom won’t work professionally as performers as adults.

(To be clear, I didn’t go to a performing arts magnet. All my knowledge about them is second hand. I did spend most of my free time in high school doing community theater.)

As a hopeful mathematician who went to the Fame school, or at least its reincarnation, I feel I have to say that it was wonderful to be at a high school where everyone had a passion for something. While the academic environment was not Stuyvesant level, say, it was quite preferable to most other schools because most students at least wanted to be there. That being said, I really like the concept of the proofs school as being maybe a quarter of the school. I like the idea of having a school where kids can say “I would like to specialize in math/science/writing/music/etc.” and really concentrate on that most of the time. This has the advantage that the courses you take that are not in your specialty would still be taught by amazing teachers. I would have loved to go to a school like that, provided that I did not have to give up on my interests in writing/science/music etc. altogether.

I don’t think music is so different from math. There’s Julliard, sure, but in the words of David Berman, “all my favorite singers couldn’t sing”….

Isn’t the right analogue something like Boston Latin, anyhow?

Hi Jordan,

I think that the strongest argument in favor of early immersion in math is that it takes so long to get to the forefront of research in the deepest parts.

Graduate students typically take introductory courses, learn knowledge specific to their fields, and then work on their theses, within a mere 5-6 years. There’s generally not enough time to learn, e.g. arithmetic algebraic geometry really deeply (e.g. at the level of working through all of SGA) in the course of graduate school. After graduate school, you’re “on the clock” and have to publish enough quality papers to get a tenure track position and then tenure, precluding the possibility of spending a great deal of time learning math that’s already been done. After tenure, you can spend years learning math that’s already been done, but by the time you finish, a significant chunk of your career is over.

Alain Connes said http://www.freewebs.com/cvdegosson/connes-interview.pdf

>The constant pressure for producing reduces the “time unit” of most young people there. Beginners have little choice but to find an adviser that is sociologically well implanted (so that at a later stage he or she will be able to write the relevant recommendation letters and get a position for the student) and then write a technical thesis showing that they have good muscles, and all this in a limited amount of time which prevents them from learning stuff that requires several years of hard work.

My main area of interest is special values of L-functions (e.g. the work of Darmon, Kato, etc.), but felt that if I stayed in academia I would have too much pressure to crank out papers for me to learn about these things deeply, which is one reason why I left.

A student is in a much stronger position to have time to learn advanced material deeply if he or she already has all of the undergraduate curriculum down pat by the end of high school.

One major difference between math and music is that everyone takes at least 10 years of math classes, and most kids don’t have 10 years of music classes. Starting from something like a more equal baseline, I don’t think it really is any more unrealistic for someone who took a half dozen years of lessons on some instrument without taking it more seriously than other subjects to be able to contribute to music as an adult as it would be for someone who did not take special interest in math before college to contribute to math as an adult.

However, one major difference is the odds. Any 18-year-old even remotely contemplating trying to be a musician knows their odds are abysmal. Indeed they are far worse than the odds of trying to be a mathematician. The alternatives if you fail as a musician also tend to be worse. So an 18-year-old who knows they are already somewhat behind because they haven’t focused on it early is much less likely to attempt a music career.

I think if it was as hard to make a living as a mathematician as it is to make a living as a musician, and alternative career paths for failed mathematicians were as bad as those (on average) for failed musicians, then math would become like music.

I think this is not a good situation for music and would not be a good situation for math.

(I am speaking as someone who probably would have been a musician if it was as plausible for a mediocre musician to make a living as it is for a mediocre mathematician to make a living.)