Good relative to the grad students I’ve work with at the other institutions I’ve worked in, visited, or studied in. Admittedly that is not a large sample.
There probably is a small tail difference for UGs too. But overall I agree with you about the UG distribution.
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This I disagree with. I remember an old posting where someone counted the number of MIT students that won a national math award in their country, and it ended up being over 10% of the class. MIT is also less willing to take academically weaker students compared to say Harvard, so on a percentile basis there is less of a difference between the strongest and weakest students.
The result is a pretty significant skew to the right even compared to other strong engineering colleges.
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I don’t believe this at all. I believe the the qualities that that differentiate at the margins are innate, and not imbued by the institution. The differences between CP and Caltech at the undergraduate level are stylistic.
The most “elite” schools also have some outstanding students that are rarely found at other schools. For example, at Data Open championship sponsored by Citadel (both graduate and undergraduate students can participate), an all undergrads team from Caltech won. The second and third place teams both had graduate students, including PhDs:
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Terry Tao straight up said that math competitions are fun, but they can be trained and have no correlation to success in math research.
University of Nevada Reno won the 3 year DARPA CERBERUS Challenge. The prize was $2M. 
Terence Tao tried to be modest. He didn’t have that much training by modern standard when he won his first IMO medal at the age of 10. It’s also no coincidence that he has an IQ well over 200.
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His point was that the skills aren’t necessarily transferable. He’s certainly not the only one to say this. The competitions are largely dominated by families that throw money at them.
Pick any typical excellent student. You can throw all your money at her/him. The odds are s/he will never even qualified for IMO, let alone winning a medal.
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That’s not the point. There are MANY talented in math who don’t get the exposure. There’s a presumption that USAMO medal winners are the cream of the crop. They are…of the ones who knew to participate. The VAST majority don’t.
We’re veering into debate territory though, and away from the OPs (ill conceived) question. 
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No one is saying only medal winners are talented in math. We’re saying there’re different levels of talent. The difference is even more dramatic among the “talented”. Of course, competition is only one way to discover such talent. There’re other means.
NO DOUBT, and USAMO differentiates those who know to participate. They are not the arbiter of all talent.
Without getting into the details, through my son I have a lot of exposure into both math competitions and math research. We have also attended a talk by Terence Tao where he discussed this and other math related topics.
The no correlation bit is misleading. It’s a bit like asking if a nationally ranked 100m sprinter can win a national marathon or vice versa. Based upon wins at that level, they appear uncorrelated, but based upon raw running athleticism, they are highly correlated.
That is what the contests show, the equivalent of athleticism in the topic.
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His words, not mine. And remember, my point is that the number of kids that have exposure is quite small, not that USAMO kids aren’t good at math.
“Also, I should say that while mathematics competitions are certainly a lot of fun, they are very different activities from mathematical learning or mathematical research; don’t expect the problems you get in, say, graduate study, to have the same cut-and-dried, neat flavour that an Olympiad problem does. (While individual steps in the solution might be able to be finished off quickly by someone with Olympiad training, the majority of the solution is likely to require instead the much more patient and lengthy process of reading the literature, applying known techniques, trying model problems or special cases, looking for counterexamples, and so forth.) So enjoy these competitions, but don’t neglect the more “boring” aspects of your mathematical education, as those turn out to be ultimately more useful.”
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You are equating “Smart” = “Good at Math”.
MIT is primarily focused on fields that require a high level of math. Harvard provides a Liberal Arts education. Consequently, they have fewer of the top math students.
MIT is the top school for engineering, and Harvard only makes it into the top 20 when people are giving it a boost because of “prestige”. So of course MIT gets the best kids at math. They are not getting top student sin multiple other fields, because that is not what they are all about.
I do not think that those math awardees would do nearly as well in history, critical analysis of text, creative writing, psychology, biomedical research, etc. Harvard is accepting students who will study those as well, and for those you don’t accept a person whose primary achievements are winning math competitions.
No, he was correct, and you are incorrect. In fact, he missed a question on his third IMC competition (where he got the gold), because he had not learned the “trick” that was needed to solve it (his own words). Moreover, why would you think that self-training is not training? You go over the questions from past tests and see the answers and figure out what types of questions they ask, and what type of answers they expect. It is no different than having kids do a bunch of older SAT tests as practice. It works the same way.
However, the ability to figure out these methods quickly and to use them to answer canned questions with existing answers is far from demonstrating creativity and originality.
As for “IQ”? Again with the idea that you can describe something as multifaceted and as complex as intelligence with a single number. The idea that you can actually measure it using standardized multi-choice questions is ludicrous. The idea that you can use the same scale for text analysis and mathematics is similarly ludicrous.
All these tests do, at BEST, is test for technical abilities in these narrow set of topics. Not a single one tests for creativity, originality, or mental flexibility. It is simply impossible to test for creativity when the answer has been determined based on well established and know thought patterns and processes. In a multiple choice question, you are not formulation the question, since it was presented to you. You are not providing an innovative and creative solution, you are choosing the one which was provided to you. You are not using a creative answering process, since you are expected to use the same process as the person who wrote the question.
As for scientific abilities? The set of talents and skills needed for research is wide and deep, which requires the ability to figure out an important research question, to formulate a working theory, to establish a set of null hypotheses, to figure out the correct research methods and protocols, to figure out the right way to analyze them and the understand what this all means. You have to do all of this, as well as troubleshoot any accidents of issues that arise, to turn on a dime and change protocols, to be able to try new methods at any pint, and to communicate to three other people who are doing this with you.
I am sorry, but no so-called “IQ test” can actually test a person’s ability to do this.
No Science Olympiad can test the ability to do this either.
The only competitions that are actually worth anything in testing whether a person has abilities and skills in any field are those that require those skills.
So the Davidson Fellows Competition, the Sciences Symposia, or any competition which requires a person or team to run research from beginning to end.
Unfortunately, math has yet to develop an good one. All are dependent on being able to do the technical work of solving a problem is a limited amount of time. They are asking them to do the equivalent of the job of a highly skilled lab tech. These are great skills to have, but having those skills does not indicate that a person has the ability to become a chemistry researcher. Moreover, deep math doesn’t take three hours, and many of the top minds in math do not do their best work under a time constraint. In fact, no mathematical researcher is doing solving canned problems quickly as part of their job.
The only way to know whether a student has the type of math abilities that are required at the top is by having them discover an important open problem, or solve a known open problem.
Terence Tao is beyond brilliant in mathematics, but we know that from his actual mathematics work. He has both formulated and solved some of the most difficult questions. THAT is why we know that he is a mathematical genius, NOT because of some number derived from the ability to solve a standardized canned set of questions.
That number there means absolutely nothing.
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The whole post is spot on! My only quibble is the quote above. MIT gets the highest number of math contest kids. It could be argued tough that Princeton and Harvard get the highest number of mathematicians.
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Sorry, but this is utter rubbish. You don’t even get as far as the interview stage at Oxford or Cambridge unless you can show As or even A* at A-levels in the subjects related to the field you want to study AND, in most cases, an entrance examinations, both of which go far beyond AP exams. In the interview, you demonstrate your potential to go even further.
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Thank you, thank you for finally defining holistic admission in two words, easy enough for even the dense, like me, to understand. It’s about “brownie points”.
Seriously, it’s such a common complaint that students choose their schools on the “prestigiosity” of the name or athletic conference, but if you’re supposed to disregard both the field the student wants to study (because students must be able to go in “undecided”) and prior achievements and demonstrated ability in the field, there is not much left other than “prestigiosity” and lifestyle (ie “Dartmouth and Penn are so different because one’s in a small town and one’s in a big city! If you have no preference for one or the other it must be because you are a shallow person!”)
Every time some sort of standardized tests (academic Olympiads, IQ test, SAT or college entrance exams, etc.) are discussed, there seem to be passionate reactions. From both sides of the spectrum!
@Tigerle I don’t disagree with you that these exams/tests play an important role in Oxbridge admissions. In fact, we discussed upthread that these tests help reduce the number of eligible candidates to a manageable level so faculty involvement (whether interviews or some other types of involvement) becomes feasible. I’m not even sure you disagree that faculty involvement is critical in Oxbridge admissions. Do you?
@MWolf Again, no one has said either an IMO medal or an high IQ guarantees high accomplishment. However, there’s high correlation between them. I don’t think Terence Tao prepared (or “trained”) for his IQ test when he tested 230. Do you? In an IMO, every single problem tests a different area of mathematical aptitude. At the IMO level, preparation is certainly necessary, but it’s far from sufficient. The difficulty level of the test made it highly unlikely anyone could solve every problem. In fact, perfect scores are rare. Many/most qualified to participate managed to solve zero problem over the two-day period of the exam. So it shouldn’t be a surprise to Terence Tao or anyone else that he wasn’t able to solve every problem at the young age of 13.
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