<p>In response to siserune’s post #77, I would like to point out that the Mathematical Association of America has offered a workshop for teachers, to assist their students in preparing for the AIME. The people organizing the workshop have concluded that a reasonably talented student can do well enough on the AMC to qualify for the AIME without assistance. However, they apparently find a higher-than-expected concentration of USAMO qualifiers in certain schools. One would expect some geographical concentration, just based on the high concentration of “techie” and math-oriented parents in some locales, of course. On the other hand, just having a teacher who is capable of posing challenging(ish) questions of the type that appear on the AIME and USAMO is incredibly beneficial.</p>
<p>A couple of additional comments: For the past few years, the people who are serious about the performance of the US IMO team have organized MathPath, a math camp for middle schoolers. This naturally feeds into Math Camp and the MOPs. I would be absolutely startled if the MOPs had no impact on the problem-solving capability of the students who attend them! The exposure to challenging problems–at the right level, so that they are a stretch, but not out of reach–is the key to mathematical growth, I think–at least of competition type. </p>
<p>The Art of Problem Solving web site is doing a lot to make interesting problems to solve available much more broadly.</p>
<p>Also, it would probably be illuminating to track the progress of students from MathCounts through to the olympiads.</p>
<p>Finally, to one other point raised by marite: There are some students who are not really interested in mathematical competitions. And some of them become quite successful as mathematicians. Melanie Wood has written about beginning graduate work in mathematics at Princeton and being informed that some students who did extremely well in competitions did not do very well in research! (This just seems like an unnecessary display of hostility by the faculty involved–although it is no doubt true that it’s a very different experience to frame your own questions of significance and try to solve them, when it’s unknown whether there is a solution, let alone one that can be written up in an hour or two.)</p>
<p>So, I agree with marite that some students who have significant mathematical talent will not make MOP, even, let alone the IMO team. I agree that “grooming,” as siserune seems to be thinking of it, will not produce a mathematician, nor even a successful contestant. But I think it would be wrong to assume that the whole MathPath/MathCamp/MOP route does not provide some pretty powerful preparation for the contests. For success, the interest has to be there, along with the willingness to think deeply and originally.</p>
<p>All of that said, I do not understand why Harvard would turn down a US IMO team member.</p>
<p>Thanks, QuantMech.</p>
<p>Regarding your last sentence, I don’t either. I am a firm believer in the fallibility of adcoms.</p>
<p>Re; Post: 79. Yes, he did, and he beat the IMO medalists for the prize for best performance.</p>
<p><a href=“JHS:”>quote</a></p>
<p>As far as I can tell, the statement “Nearly all of the capable math students can and do participate in competitions” is flat-out wrong.
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<p>It is a correct statement for the students under discussion, “who take rigorous college math as high schoolers [hence] are obviously standouts (and [according to some here] would probably do quite well on the IMO)”. We weren’t talking about whether a farm boy, pauper or ghetto genius might have a world-class mind hidden in dim surroundings. We were talking about students in settings where advanced mathematical material can be accessed while in high school. </p>
<p>In that population, pretty much anyone with the ability to “do quite well on the IMO” will have had enough opportunity, incentive, interest and confidence to (by the end of high school or much earlier) engage in sharper and riskier demonstrations of ability than just taking classes. To do nothing but take advanced math classes, in an environment full of opportunities for math competitions and math research, is a signal that the student recognizes the dangers of a visible calibration of abilities (and weaknesses), and is pursuing alternative strategies for entry into academia. It is typical of strong but not IMO-caliber (and not top research caliber, later on) students who are well connected, well counseled and well groomed for an academic career. </p>
<p>This is all quite similar to elite private high schools’ practice of cultivating and packaging students’ strengths while carefully minimizing their visible weaknesses. In mathematics, that strategy can be practiced all the way into grad school for those who enter the field through study rather than problem-solving (competitions, research) or raw IQ (prodigies, geniuses from other disciplines). After grad school, the course-taking academic workhorse strategy fizzles out, because research productivity becomes necessary and this does require problem solving skills not unlike the ones tested at the IMO.</p>
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<p>Avenues for revealing mathematical talent are very limited, just as in music (playing or composing) or chess (playing, composing, or analysis). The only known ways are excelling at hard competitions or in undirected research, which are very similar skills practiced in different conditions. This is why mathematical prizes are dominated by olympiad winners, upwards of 80-90 percent in some fields.</p>
<p>Might the explanation for Harvard’s rejection of such an applicant be attributable to a finite need or demand for math talent, however exceptional, in their class composition?</p>
<p>sewhappy:</p>
<p>I don’t believe so. There are far more math majors at Harvard than there are IMO gold and silver medalists. I believe a typical cohort of math majors is about 25-30.
We cannot know what that applicant’s file contained besides his obvious math ability (and even though the IMO medals are awarded after decisions are made, it is not that difficult to identify potential medalists).
Absent a true weakness in his application, I would put it down to sheer capriciousness on the part of the adcom.</p>
<p>siserune, I based my statement that all capable math students do not participate in competitions on five kids I know, all of whom were through calculus by the end of 9th grade and spent most of high school taking college math courses, all of whom were involved in directed research, four of whom were accepted by, and attended, Harvard (the fifth was accepted early at Yale and didn’t apply elsewhere; all the others were also accepted by Stanford, and by MIT and Yale if they applied), and none of whom (as far as I am aware) participated in math competitions other than taking the AIME. They did other stuff.</p>
<p>That’s not to say that I am certain they would have excelled at competitions. Maybe they wouldn’t have. And I don’t know exactly how their stories play out, either. One I don’t have any recent information about, one is in a math-related PhD program, one just finished a stint with Teach For America and is applying to math PhD programs, one went over to the dark side of finance, and one is just a junior.</p>
<p>JHS,</p>
<p>AIME is part of the series of USAMO and IMO team selection. If the five students you mentioned participated in AIME but did not do USAMO and further, the only explanation was because they did not survive AIME selection. Capable of doing calculus at 9th grade is no big deal.</p>
<p>The IMO at US started with students who are good (or think that they are good) with math, voluntarily take AMC10/AMC12. About 200, 000 students each year take AMC10/AMC12. From there, about 12000-15000 are selected to take AIME based on their AMC score. When the AIME result was out, 500 (used to be 250) students are selected to take USAMO. Out of those 500 students, 60 students are selected to go to MOP. Top 12 students from USAMO test then take the TST (team selection test) to select 6 US team members.</p>
<p>The reason that I look at those rejections (the in the post#1 was not alone) is really that US culture is hostile to intellects. I saw quite a few female students (math should be their hooks) from the first USGMO team got rejected or waitlisted by Harvard. Believe or not, some of these students are way well rounded and prevail in many areas. I want to ask one question here: how many of those Adcoms from Harvard have majored in hard sciences themselves to actually appreciate that type of talent?</p>
<p>I talked with someone who was at IMO levels, who also worked for hedge funds companies for a while. According to him, about 40% people at that level are actually working in financial industry, rather than doing research. Not because they cannot be successful research mathematicians, but our society does not recognize their talents in any real tangible or intangible way.</p>
<p>I dont want to fight with anyone here.</p>
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Please note that my definition of “rigorous college math” is not a differential equations course at a random local community college. I was referring to those who go above and beyond the standard curriculum in ways that may not have anything to do with what is covered on contests. Look at some of the topics RSI math students choose to pursue and you will see things not covered on any contest that I am quite sure were not just learned loosely and without depth.</p>
<p>Really, I think we agree overall.</p>
<p>I have no idea who the adcoms are besides the regional rep, but I understand that some members of the Harvard faculty are involved in the selection process on a volunteer basis and that, as necessary, other members of the faculty are asked to review specific applications. As well, the adcoms will look at everything an applicant sends. My S included a paper that he wrote for a math course. Had he written it while at Harvard, that paper would have qualified for the “junior essay” that is part of the requirements. </p>
<p>You are right that finishing calculus by the end of 9th grade is not that uncommon. It means that the pool of capable students is far larger than the pool of USAMO/IMO medalists. We cannot know why Harvard chose to reject some of these medalists and accept other students. We are not privy to the whole applications or the deliberations of the adcoms. Without knowing further details, I would think that it was a mistake not to admit the medalist referenced in this thread. </p>
<p>A lot of personal preferences are involved in college selection. In some years, Harvard admitted quite a few medalists, and all of them or nearly all of them matriculated. In some other years, the top students applied to MIT. Some of my S’s friends preferred MIT to Harvard for exactly the reasons that my S decided to attend Harvard over MIT. </p>
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D.E. Shaw recruits at top math programs and pays very well. If we look at some of the founders of top hedge funds, we see that several of them had long careers as math profs.</p>
<p>I once read that the only way that someone can be appointed to a tenure-track position in math is if someone else dies. I’m sure this is an exaggeration, but in academia, the jobs in math and physics are extremely limited. Furthermore, at some top universities, there are programs of hiring new Ph.D.s for only three years, further increasing job anxieties. We know Ph.D.s from the top programs who are teaching high school or have gone into finance.</p>
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<p>For some highly able students:
Incentive? zilch.
interest? close to zero.
Just taking classes? Some students live and breathe math without taking part in competitions.</p>
<p>I doubt that Harvard has anyone working in the admissions office who qualified for the USAMO–I would like to be proven wrong about this. Actually, I doubt that MIT has anyone working in the admissions office who qualified for the USAMO. It would be easy for a person who is not familiar with the tests to underestimate the significance of being a member of the US IMO team. Even when applicants’ files are circulated out to the faculty for comments, ultimately the decisions are being made in Admissions.</p>
<p>I am as skeptical as anyone of claims that a student “could have done well” on the USAMO or IMO–but did not, for whatever reason. However, I don’t really believe that anyone does well on these tests without having an environment that at least permits it. Some American high-school environments actively discourage it, as unthinkable as that would seem to someone coming from outside the American system. </p>
<p>siserune, are you a completely self-made mathematician? Possibly . . . but even Gauss had an uncle who introduced him to mathematical thinking!</p>
<p>I think it’s worth pondering <em>why</em> the Boston Math Circle does not encourage participation in mathematics competitions. I don’t know–but I am certain that it’s not to hide the lack of competitive ability of the students!</p>
<p>I will admit that I was as competitive as anyone (in the sense of “eager to compete”), when I was in high school. As a graduate student, I had to turn my thinking around somewhat, to realize that the subject was about <em>the subject,</em> and not about <em>me.</em> I had to stop directing my work toward proving that I was smart and go deep into the problems themselves, in the pursuit of truth. Perhaps the Boston mathematicians had similar experiences? </p>
<p>I have mixed feelings about incredibly talented mathematicians working for hedge funds. The tangible rewards can be extremely high there. I doubt that there’s any university mathematician in the country who makes more than $1 million a year. Not by a long shot! And someone could retire young-ish from the hedge fund work, and then support him/herself to do mathematics independently. So it makes sense as a career choice. But, despite marite’s comments, if a really talented young mathematician wants a faculty position (and is willing and able to work in a not-at-all-prestigious institution), it would probably be possible–with some odds of landing a really desirable spot. </p>
<p>From what I’ve heard, the hedge-fund environment provides the same heady rush of competition as the mathematics competitions, along with excellent compensation arrangements. Hedge-fund work provides frequent signals of success (or not), while eliminating many of the frustrations of the pursuit of pure mathematics: e.g., Julia Robinson’s “diary:”
“Monday. Tried to prove theorem.
Tuesday. Tried to prove theorem.
Wednesday. Tried to prove theorem.
Thursday. Tried to prove theorem.
Friday. Theorem false.” </p>
<p>Finally, I think that siserune’s comments about students who are accelerated in course work, but do not participate in competitions are probably true of a subset of that group. I, for one, think Math 25 or Math 55 at Harvard is challenging enough that the comments do not apply to any high school student who takes those courses. There are many different reasons for accelerating in mathematics. I would surmise that some of them are outside your realm of experience, siserune.</p>
<p>QuantMech:</p>
<p>I’ve sent you a PM.</p>
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<p>Marite is right. DE Shaw has hired one undergrad as summer intern since he was sophomore at Harvard. </p>
<p>Howvere DE Shaw and other major Hedge fund also hires top non math kids too. Many of these kids drift from math to other fields.</p>
<p>RSI/USAMO/IMO has many people working in the quant side of the finance industry.</p>
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<p>Sometimes kids pursue these courses in higher math but drift to other field as they find real life problem solving in what is happening around them more fascinating.</p>
<p>My kid (still in HS) participates in the math circle that does not encourage competition.
Still, most of the kids there(if not all) take top accolades in the state for math, be it AMC/AIME/USAMO , State Math Contest, ARML and so on.</p>
<p>I have a cousin with a math PhD from a very competitive program. He works for an options trading firm, one that was founded and is still run by former math professors. One of the things he learned about himself in graduate school was that he really, really disliked teaching. (“There’s only one thing I enjoy about it. Watching as the students slowly progress from happiness about having a native English speaker for an instructor to the realization that they would have been better off with someone who only spoke Chinese but who gave a crap about them.”) About his initial work at the trading firm, he said, “It’s interesting enough that I would probably do it for free, but it’s really nice to get paid a lot for it, too.” This guy was very much the pure nerd, and a little otherworldly. It has been a revelation to him that he could have a nice apartment and a car that starts reliably, and that cute women are interested in him.</p>
<p>(Nothing like an IMO team member, though. He was interested in physics, and didn’t really get turned on by the math until college. Not accepted at Harvard, either, despite being a fourth-generation legacy, and applying well before the recent bulge years. I’m sure it didn’t help that when he was 18 he sort of embodied the joke about the extroverted engineer, who looks at YOUR shoes when he’s talking.)</p>
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<p>There is no way to prove it, though. I was fairly advanced (calculus by the end of 10th grade) and was able to do as well or better as some of the USAMO/IMO people in advanced math classes like number theory or group theory . I didn’t qualify for USAMO though. So I sympathize with your point that there are people who can excel at math that cannot compete at the highest levels of math competitions. Still, if you are selecting for math at age 18, you just can’t disregard the fact that these IMO guys are proven quantities. I, for one, was never bothered that they typically get in everywhere.</p>
<p>Anyway, I really doubt they have turned down these IMO people for others because they think these other people may have greater latent math talent. It’s more likely that it was community service, extracurriculars, or some other part of the equation. </p>
<p>Frankly, I think it would be better if potential math and science students were selected by a totally different process–one closer to Caltech, where intellectual merit, creativity, and drive are the only criteria.</p>
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<p>Prove what? That some highly able students are not interested in competitions? have no incentive to compete? I know some. It does not mean that if they had competed they would have done well. Just that we’ll never know whether they would.</p>
<p>My point and the only point is that the pool of highly able math students is larger than the pool of USAMO/IMO medalists (look at the composition of Math 55 for instance, not all of them were medalists). </p>
<p>As I said, we’ll never know why Harvard turned down this particular IMO medalist. I doubt it is because he did not have interesting ECs.</p>