<p>I need to correct myself. I didn’t realize Fields medal goes back to 1936. Mathematicians from Russia/USSR started appearing on the list in 1970. I bet part of it was that Soviet scientists were not receiving due recognition during the iron curtain. Since 1970, there are 9 Fields medalists from Russia/USSR, 8 from US, and 6 from France. USSR developed a unique system of developing mathematical talents, and contests like ARML are not part of it. It’s considering wasting precious time. I recall years ago a team of talented kids from Russia participated in ARML as guests. They didn’t do very well.</p>
<p>I never claimed and don’t think math competitions are particularly good measures of mathematical ability. However, using them seems to be a better method than random people on the internet making assertions without any evidence. For what it’s worth 10 of the past 18 Fields Medalists competed in the IMO so there does seem to be some correlation. In terms of number of high scorers, MIT blows away Harvard and other schools but typically chooses the wrong team [introspect] and thus doesn’t win (in 2011 29/81 of honorable mention or better were from MIT but MIT got 5th).</p>
<p>For the Duluth REU list of graduate schools attended the list you posted is 15 years old. Of the attendees in the past 5 years 24 have gone to graduate school (some are still undergrads) and 12 of those choose MIT, 4 choose Harvard, 2 choose Berkeley, Stanford and Chicago, and 1 chose Rutgers and Princeton. Of the 43 attendees in the past 5 years 16 were from MIT, 10 were from Harvard, 5 from Princeton, 4 from Caltech, 2 from Stanford and Notre Dame, and 1 from Penn, Carnegie Mellon, and Chicago. Is this the most important metric in making any sort of decision? Obviously not but it may be indicative.</p>
<p>UMTYMP student, you seem to have access to some very interesting statistics. I’m curious if you could share the source for IMO participants among Fields medalists. It’s very interesting. However, you didn’t address my other points about MIT and its changing demographics. I think it would be instructive to track winners of important mathematics awards (e.g., Fields Medals) and possibly include awards in related fields (Nobel prize in Physics) to their undergrad institutions. This would be an important measure of realized potential. However, the limitation is that it would be past potential not current. Again, I’m curious what will happen in 10-15 years when current MIT grads will be reaching their potential. I have a strong suspicion that the quality of current MIT pool is lower, on average, than it used to be.</p>
<p>I am not sure the high number of REU participants indicates high level of math research at a particular institution. One can make an argument that an institution that is able to provide research finding and high quality mentors to its undergrads doesn’t need to send them for opportunities elsewhere.</p>
<p>I got the data on IMO participation and Fields Medals from here [List</a> of International Mathematical Olympiad participants - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/List_of_International_Mathematical_Olympiad_participants]List”>List of International Mathematical Olympiad participants - Wikipedia). It has other math awards by IMO participants as well. I don’t think MIT’s changing demographics are that a big of a deal as the best students are still admitted. Even when some affirmative action and possibly a small preference for girls the very best students will still be admitted to MIT. The issue is Fields Medalists is the extremely small number of winners so noise would be huge. Physics Nobels has a similar problem and a huge time lag as most winners graduated from undergrad 30+ years ago. Another interesting stat would be placement at graduate schools but I haven’t been able to find any good students on that for math. It’s true that REU participation may be affected by the presence of research opportunities on campus but both MIT and Chicago offer excellent opportunities so it’s not clear why that would skew the numbers.</p>
<p>It’s an interesting discussion that raises many philosophical questions. What does it take to raise a mathematician? To start with, it has to be abilities, then early exposure, and then an opportunity to interact with others and especially a mentor who is already an established mathematician. To judge an undergraduate program, we need to evaluate many factors: availability of prominent mathematicians and their willingness to provide high quality mentorship is probably the most significant. What do we know about this for MIT and UChicago? Then, we could look at indicators of peer quality (e.g, IMO participation), realized potential (# of MIT grads who went on to become prominent mathematicians or simply earned a PhD in math and are leading successful math career even if not of Field’s medal caliber, etc). Then we need to find the same stats for Harvard, UChicago, and other known programs, and compare them, adjusting for the size of the program (is the # of math majors at MIT several times larger than that at UChicago?). </p>
<p>I agree the data suggest that IMO medalists have the potential to become prominent mathematicians. I’d like to know how many of the IMO participants who went to MIT actually became prominent mathematicians. </p>
<p>One little comment I’d like to make is that “possibly a small preference for girls” sounds counter to the reported data by MIT. Last year, MIT’s admission rate was 7.2% for boys and 15.6% for girls. That’s not “small preference”. However, I agree that it doesn’t mean MIT is not selecting just as many “best” students as it had in the past in terms of absolute numbers. Even though, the overall quality of the student pool went down recently, MIT can still have all the IMO participants it wants.</p>
<p>Interestingly, Chicago has an exceptional summer research program that makes it unnecessary for math majors to participate in outside REU opportunities.
<a href=“http://www.math.uchicago.edu/~may/VIGRE/[/url]”>http://www.math.uchicago.edu/~may/VIGRE/</a></p>
<p>
</p>
<p>You are assuming the applicant pools are the same quality. The admissions staff at MIT says the female applicants are much more self-selecting and thus accounts for the entire difference in acceptance rates. It seems plausible to me that the female applicant pool is much more selecting although I’m not sure it accounts for all the difference. Furthermore, if the preference was as big as you claim, females would make up the vast majority of poor students at MIT which doesn’t seem to be the case.</p>
<p>it’s not my claim, it’s the numbers that are reported by MIT in their common data set. I’m not sure how you can conclude that females make up the the majority of poor students. The stats in the common data set don’t include any indicators of income. I’m not buying the claim that females are that much more self-selective than males when it comes to MIT applications. In my town there are 2 high schools, both very good. I know about the kids who apply to MIT and I know who were admitted, rejected, and deferred in the past 4 years. In most cases, girls were much less qualified than boys. They were bright girls, no question, and some of them definitely belong to MIT. However, many of the boys who got rejected in the same years had more accomplishments than those girls. The same conclusion can be made looking at the stats reported here.</p>
<p>Your claim is that females receive a large preference in admissions. I’m pretty sure the Common Data Set does not say that. This entire discussion is ridiculously off-topic so I’m not going to comment more on this other than saying this topic has been beaten to the death in the MIT forum and those interested in it can find more information in many threads there.</p>