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I am the director of my university's mathematics honors program, and we just had an inquiry from the parent of a 15 year old who has already completed most of the math courses for a standard undergraduate degree (and who is already sitting in on grad classes).

The problem is that the kid isn't interested in taking anything but mathematics. Standardized tests indicate that he's no slouch at the sciences and reading/writing, but he wants to do math all the time. I haven't seen the details of his application, but everything points towards him being extraordinarily gifted in mathematical ability.

Our program can handle him, but my feeling is that he should go to the most prestigious place possible. Are there any top-notch programs out there that would let a student focus almost entirely on mathematics for their undergraduate degree?

Edit: Thanks everyone for the responses!

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I've heard good things about the Langlands program. –  Unreasonable Sin Nov 17 '11 at 0:30
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Not to sound pessimistic, but you should have an interview with the child before thinking about anything else, to determine the the breadth and depth of his knowledge. Parents (who aren't also mathematicians) of gifted childen often do not understand the state of their childs knowledge, and embellish or over estimate some achievements. I have tutored several children whose parents were unaware their child was lacking fundamentals quite seriously in certain areas. Before we rush him off to Harvard, check if maybe an extra year or two building a solid foundation would help. –  Ragib Zaman Nov 17 '11 at 0:32
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Question: @Todd Is he not interested in competition math? I saw that this is Ohio University, and on the state math team / numerous state competitions / USAMO records in Ohio, I (nor my friends) have never seen a 15 year old... If not, let him know about these (and especially the state math team for ARML!) –  MathMathCookie Nov 17 '11 at 0:37
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He needs to be someplace where he’s in no danger of running out of math courses, but I don’t think that he’d be particularly well served by being permitted to focus almost entirely on mathematics as an undergraduate. –  Brian M. Scott Nov 17 '11 at 0:45
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I disagree with Brian M. Scott. He should certainly be made aware of what's good about other fields of study, but the principal fault of nearly all systems of education is that they try to coerce people to become educated. There would be a lot more education if it were made available to those who want it rather than forced on everybody. –  Michael Hardy Nov 17 '11 at 1:03

2 Answers 2

In lieu of other answers: in the U.S., essentially no undergrad program allows focusing on a single subject. The UK schools are the opposite, essentially.

To ask whether we should "allow/encourage" a student to focus on only one thing...?

And, yes, there's the pragmatic issue of whether parental or other essentially not-professional-research-mathematician opinions are accurate. E.g., not every tall person has a future in the NBA.

In fact, Hahvahd, Princeton, and such [EDIT: I was unaware until I saw @Zev C's answer that Brown allows essentially unlimited flexibility in course selection. Pretty amazing! Unusual among research universities. The "self-designed major" is more typically possible only at small colleges in the U.S.] ... do require considerable exertion outside one's field of special interest. For a kid with a rather narrow capacity-of-interest, a big state school (e.g., Big-Ten, ...) might actually be better: the out-of-subject classes are not super-strenuous, and the "graduate" courses in math will probably be constructive, but not toooo critical. (We anticipate that, even if a kid has some gifts/talent, it doesn't always quickly mature to allow writing coherent, adult English (or whatever) narratives concerning serious issues.)

These days, faculty at at-worst-second-tier universities are mostly graduates of top-tier universities, so understand the sensibilities of those places, and, for that matter, know the people at the top places, and can communicate on behalf of a kid who deserves a place there...

My bonus comment is that there is considerable fragility in choice-to-exclusion-of-other... when a teen decides math-is-it. Much as a kid in an "arts high school" blows-off all other subjects. It is a gamble. We may be sympathetic to the gamble, but, as responsible adults/advisors, we should hedge the bets of our proteges, on their behalf, no matter their "enthusiasms".

In my own life, by accident, I went to a state school (Purdue), and was given great latitude... understood in hindsight... "to figure things out" mathematically. The environment was perhaps a little too "quiet", but for a young kid this may be extremely useful. That is, over-stimulation is not a positive thing for many (capable) people. Even when one eventually discovers that people had thought about one's current "pet" issues 150 years ago, it is xxxtremely helpful to have had a quiet, safe environment to have developed the enthusiasm for the (long dead, but, hey, interesting...) issue.

From another tack: some of my fellow grad students at Princeton long ago were from much fancier places than Purdue, ... and/but they didn't retain the affection for mathematics that the lower-stress environment had allowed me.

So... A personal interview is absolutely necessary, to figure out what a kid needs. Prestigious undergrad institutions are all very nice... if one can distinguish oneself... but one's career is initially determined by the grad school. Sooo...

(That's all I know... :)

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Top-notch program? Would let a student focus almost entirely on mathematics?

I think there is no better recommendation than Brown University*. Starting in 1969, Brown has let students take any courses they want, given of course that they take the necessary courses for whatever they end up majoring in.

This is precisely what I have done during my time at Brown, and for me, it has been an immensely valuable experience. I cannot imagine having grown mathematically as much as have anywhere else. However, I also think that my secondary education was reasonably high quality and well-rounded, and I would recommend that this student take at least a few courses outside of math - it's not the end of the world. For example, I came to Brown also mildly interested in physics and philosophy, and I took a few courses in both until my interest waned / I decided I'd really prefer to be doing math.

Notably, Brown lets you take any course you want to as a pass/fail, and if you do fail, it is erased from your transcripts! The entire system at Brown is designed to completely free the student, from school-imposed decisions about what they should learn, and from self-imposed fear of taking something they might do poorly at.

*I guess being in the Ivy League does not even qualify a school as "and such"? :)

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