Here’s a wee brainteaser for you to while away ninety minutes with.
For each positive integer n, the Bank of Cape Town issues coins of denomination 1/n. Given a finite collection of such coins (of not necessarily different denominations) with total value at most 99 + ½, prove that it is possible to split this collection into 100 or fewer groups, such that each group has total value at most 1.
You can download all six problems in the language of your choice, from Afrikaans to Vietnamese, here. There are worked solutions here. Participants were given three problems on July 8th, three on the 9th, with four-and-a-half-hour sessions each time—average an hour and a half per problem. So if you can make fair progress on that one above in ninety minutes, and are less than 20 years old, you are IMO material.
I have put up occasional blog posts about the IMO before (this one from last year, for example) and the national-level USAMO (2012 winners here) as a matter of minor interest to human-biodiversity mavens. I thought I’d try something a bit more ambitious with this year’s IMO.
In doing so, I was diving into a crowded pool. Analyzing IMO results is a popular pastime among the statistically inclined—so much so that after browsing thirty-odd websites on the topic I began to feel that crunching IMO results data deserves an Olympiad of its own—an IMOO, perhaps.
Some names familiar to VDARE.com readers show up in those websites. Ron Unz waded into the pool last year in one of his meritocracy pieces (four paragraphs into here). Fred Reed used IMO results to give his Hispanophilia an airing over at Taki’s Magazine back in March. The blogger Occidentalist demolished Fred here, with a good combative comment thread … and so on, and on.
As I said, it’s a popular pastime.
The Olympiad anyway lends itself to this sort of thing. It is, after all, run by and for mathematicians. The IMO publish excellent tables for the results, cut several ways—I’ll get to them in just a moment.
The event has been held since 1959, so there’s a good historical trail, made use of for example by Heiner Rindermann in a well-known (here in the pool, I mean) 2011 paper titled “Results in the International Mathematical Olympiad (IMO) as Indicators of the Intellectual Classes’ Cognitive-Ability Level,” published in a festschrift for German psychologist Kurt Heller.
(Rindermann’s paper points out, with no irony I can detect, that “It may be hard to believe, but there are no IQ measurements of IMO participants”—page 314 of the festschrift.)
Here I shall only look at this year’s results.
And then, there is a straightforward mathematical elegance to the contest. Each of the six questions gets marked with from zero to seven points, for a possible maximum 42 points.
More than 28 points gets you a gold medal. From 22 to 28 gets you a silver; from 16 to 21 a bronze; from 7 to 15, an honorable mention (with some judges’ discretion).(Update: it’s even more meritocratic than that–see here.)
Each national team is supposed to be six members, and most are—all but 14 of this year’s 101 national teams.
The basic result table is here. You can sort the whole table on any column by clicking the column’s heading. The “Contestant” column can be re-sorted by first or last names; and it can be reduced to onlyfemales or only males.
There is the first HBD point: Of the 560 participants this year, only 56 were female. That ten percent is, according to Rindermann, historically normal. In this year’s IMO, 58 of the 101 participating countries fielded all-male teams. Among the 58: the U.S.A., Canada, Australia, New Zealand, the U.K., China, Japan, both Koreas, Russia, and host country South Africa.
Much ink has been spilled over the reasons for this disparity. The Ron Unz column I linked to above has some interesting links of its own.
Testosterone may be a factor: the greatest female mathematician of the last century, Emmy Noether, was so high-T her male colleagues at Göttingen referred to her as “Der Noether,” using the masculine form of the definite article.
Her colleagues regarded her with awe and affection, though since they were all male, and Kaiser Wilhelm’s Germany was only a dozen or so years in the past, the affection expressed itself in ways that would not be accepted nowadays. Noether did not at all conform to the standards of femininity current in that time and place—nor, it has to be said in fairness to her colleagues, any other time and place. She was stocky and plain, with thick glasses and a deep, harsh voice. She wore shapeless clothes and cropped her hair. She had a rough temper, and her lecturing style was generally described as impenetrable.
Hence all the disparaging quips, not meant unkindly at the time, that have become part of mathematical folklore. Best known is the reply by her colleague Edmund Landau, when asked if he did not agree that Noether was an instance of a great woman mathematician: “Emmy is certainly a great mathematician; but that she is a woman, I cannot swear.”
[Lady of the Rings, by me, National Review Online, April 21, 2005.]
If testosterone is necessary, though, it is not sufficient. According to the late Philippe Rushton, testosterone levels follow the Rule of Three, with blacks highest, East Asians lowest, and whites intermediate. Mathematical talent cuts the opposite way.
That’s the other big takeaway from the IMO results. Of the three participants who got the maximum 42-point score, two are Chinese. Of the 49 gold medal winners, 31 are East Asian and 18 are white European.
Down at the other end, of the 17 participants scoring no points at all, one is West Asian, two are Indios (that is, Latin American aboriginal), and the other 14 are black African.
I am told that because this was the first IMO held in Africa, black African countries tried hard to make a good showing. Yet the highest-ranked black African nation among the 101 nations participating was South Africa at #67, followed by Nigeria at #91.
And the South African team contained no blacks!
(I should say that on my own spreadsheets I normed the national scores to allow for teams of less than six. Venezuela, for instance, had only two participants, so I tripled their points.)
So far as I can discover there have been only three black African IMO medalists in recent years: Chigozie Henry Aniobe of Nigeria with a bronze in each of the last four years; Puis Aje Onah of Nigeria with a bronze in 2010 and Isaac Jean Eliel Konan of Ivory Coast with a silver that same year. (Konan is rather light-skinned, possibly a mulatto.)
It’s a poor showing for a continent that has had established universities for decades.
The orthodox explanation for this quite dramatic black underachievement at the highest levels of math is of course RACISM:Charlie deliberately keeping the black man down.
One specimen of this orthodoxy showed up two years ago in the leftist British newspaper The Guardian in response to a passing remark I had made in my infamous 2012 “Talk” column.
I had said the following thing.
There are black geniuses and black morons. There are black saints and black psychopaths. In a population of forty million, you will find almost any human type. Only at the far, far extremes of certain traits are there absences. There are, for example, no black Fields Medal winners.
This drew a column in response from black American mathematician Jonathan Farley, who asserted that:
Black mathematicians face career-retarding racism that white Fields medalists never encounter. Three stories will suffice to make this point.
[Black mathematicians: the kind of problems they wish didn’t need solving, by Jonathan Farley, The Guardian, April 12, 2012.]
He actually tells us four stories. The first two concern minor acts of discrimination against black Americans in, respectively, 1951 and 1941. The Fields Medal was first awarded in 1936, so the dates of these incidents stand 19 percent and 6 percent, respectively, along the timeline of Fields awards.
(The victim of the 1941 incident was hired as a Professor at Berkeley in 1954, and spent the last 35 years of his career happily teaching there.)
Farley’s third story is “that in 2002, after I wrote an article about Confederate remembrance, supporters of the Ku Klux Klan sent me death threats, forcing me to leave my home and my permanent job at Vanderbilt University.”[VDARE.com note: When Farley said “every Confederate soldier … deserved not a hallowed resting place at the end of his days but a reservation at the end of the gallows.” in 2002, it was addressed here in by Paul Craig Roberts, Sam Francis, and James Fulford, all of whom felt that Farley was calling, retrospectively, for the execution of over a million white people.]
I’m sure we all remember what a mighty and terrifying force the KKK was in American life twelve years ago, and how hazardous it was to criticize Confederate remembrance in those dark times.
The fourth story concerns some argy-bargy at a conference in 2009, as a result of which, says Farley, “a job offer that had been previously discussed disappeared.”
With only Farley’s side of the story to go on, it’s impossible to know what happened there, but the idea that race prejudice is keeping black mathematicians out of jobs is beyond preposterous. If you believe that, you will believe, as one of Farley’s approving commentators does, that Euclid and Eratosthenes were black.
(The Guardian heads up Farley’s column with a picture of Euclid. He lived in Alexandria, see? Alexandria’s in Africa!)
As I’ve noted elsewhere, based on several conversations with mathematicians in our diversity-addled universities:
I am reliably informed that math departments fight like cats to acquire the tiny numbers of black and Hispanic doctoral recipients produced each year.
[Quarterly Potpourri, Taki’s Magazine, April 17, 2014.]
Chike Obi. He took a London B.A. from West Africa, mathematics not a subject. He wrote asking for the mathematical books he wanted to learn, including Poincaré on Celestial Mechanics, and taught himself. He managed to get accepted in Cambridge for a Ph.D. (turned down in London), and then struck a modest, but quite genuine, vein of oil (making some experts on differential equations look quite silly). He had no idea whatsoever how to write, and I had him for a year—one term I had him for 90 minutes a day every other day. (Each session began by my removing trumpet parts from the orchestration.) He had a curious belief that he could get something out of nothing by a transformation x = εy and thenusing the fact that epsilon was small. I finally said this “was a belief in ju-ju” (which went off all right, if rather daring). I also said he alternated classical off-drives with pure cow-shots, and got an understanding grin.
There was a film about this time about an intellectual negro going back to Africa and all but succumbing to a witch-doctor. The English Resident whispered in his ear when he lay in a coma “Africa needs you.” Obi was the image of the witch-doctor. (“Obi” means “witch-doctor.”)
[Littlewood’s Miscellany, p. 122 (1953).]
Politically incorrect, no doubt, but not malicious, and Cambridge was obviously hospitable to the Nigerian Obi (as, later in the 1940s, was MIT).
We should therefore be skeptical of explanations involving racism. Most claims to have been disadvantaged by racism in the past fifty years amount to nothing more than rent-seeking on the part of educated blacks.
For a better handle on the racial aspect of the IMO results, I went through the descriptions of the 560 participants assigning each to a broad racial category with no regard to the nation they are representing. My categories are: white, black (including one mulatto), West Asian (Iranian, Arab, etc.), South Asian, Indio, Mestizo, East Asian, and Austronesian (Indonesian, Polynesian, etc.)
This is an approximate art, not helped by the fact that seven participants post no photograph. There has been a fair amount of East Asian settlement into Latin American countries, so untangling Indios from East Asians is nontrivial. Thais are basically Austronesian (according to Cavalli-Sforza) but there is a big assimilated Chinese population, all using Thai names…One does one’s best.
Doing my best, I got the following breakdown:
|East Asian males||114|
|East Asian females||6|
|West Asian males||37|
|West Asian females||6|
|South Asian males||28|
|South Asian females||1|
UPDATE: See new and improved tables here.
I also wanted to get a handle on which countries are punching above their weight. Population is of course a factor here, the more so as we are operating at the far right extreme of a bell curve.
To take a very simplified model: Suppose the cutoff for participation in an IMO team is an IQ of 172 or more, and suppose all countries have mean IQ 100 and standard deviation 15. Then a country with ten million high-schoolers will have eight beyond the cutoff—just enough for a team! A country with a hundred million high-schoolers, on the other hand, will have 79 candidates, enough for some higher-level selecting.
Ignoring these niceties, just to get a rough picture I took my normed country scores and scaled them by each country’s population to get a number for IMO points score per million of population. The South Korean team, for example, scored 172 points for a population of 49 million, or 3½ points per million South Koreans.
On that basis the rankings show tiny Liechtenstein way out ahead of the pack with 3,568 points per million, followed by Luxembourg (157), Iceland (148), Macau (125), Montenegro (65), Cyprus (45), Estonia (41), Slovenia (39), Armenia (36), and Mongolia (35). Uncle Sam is at 0.6, between the Philippines and Brazil … but this method is probably unfair to big countries.
Culling off small (less than five million) and big (more than fifty million) countries and ranking the rest by IMO points per million of population, punching hardest above their weight are Singapore (29), Slovakia (22), Hong Kong (20), Israel (18), and Serbia (18) …
And while the big disparities of sex and race are hard to ignore, there are adscititious factors operating at the next level down.
Probably the most important is different national methods of training and selection. The U.S.A. team emerges from the famously grueling Mathematical Olympiad Summer Program (abbreviated MOSP but known to everyone as MOP). From its website:
The combination of these [program elements] makes MOP an extraordinarily intense experience. One participant at 2007 MOP calculated that by the end of the second week members of Blue MOP had already spent more time in a classroom than most calculus classes do in a year, and by the end of the third week participants had spent 170 hours over 19 days either in class or taking practice test for an average of roughly 9 hours a day of math—and that’s before time spent doing problem sets and working on the team contest outside of class is included.
A particular secondary factor this year was temperature. Cape Town is cold at this time of year, and the IMO tests were conducted in a large unheated sports center. Not all participants were prepared for this, and there was some grumbling about it.
A modest feast for statistics geeks there, then, and some in-your-face HBD facts. Math, like sport, is coldly meritocratic: you can do the stuff at these high levels, or you can’t. (I, by the way, can’t. After wrestling with that opening question for an hour, I looked up the worked solution.)
My congratulations to the U.S. team on their placing second in the country tables: 193 points, five golds and one silver.
Next year, Thailand. I once spent July in Thailand. Trust me, cold won’t be a problem.
Describing the scoring system for the International Math Olympiad, I said:
From 7 to 15 [points gets you] an honorable mention (with some judges’ discretion)
In fact the scoring is even more straightforwardly rule-based than that. There is no judicial discretion.
Participants who do not win a medal but who score seven points on at least one problem receive an honorable mention.
That’s from Wikipedia, which I didn’t check because I don’t trust it. In this case, however, Wikipedia is supported by the data. For example: Anthony Flores of Ecuador got an Honorable Mention with scores 0-0-0-7-0-0, but Matteo Migliorini of Italy with scores 6-6-0-1-0-0 didn’t, in spite of having nearly twice Flores’ total score. Tough tetrahedra there, Matt.
I apologize for the error.
I have improved the table in my piece on the International Math Olympiad to show point and points per participant for each race.
|East Asian males||114||2702||23.7|
|East Asian females||6||85||14.2|
|West Asian males||37||461||12.5|
|West Asian females||6||74||12.3|
|South Asian males||28||392||14.0|
|South Asian females||1||3||3.0|
It can be seen that—with, of course, all due allowance for size of countries and different training regimes—East Asian males run away with the points per participant score, followed by white males, East Asian females, South Asian males, and West Asian males. Consolidating West Asians with whites, which is reasonable on phylogenetic grounds, doesn’t affect the rankings.
If you consolidate the sexes by race the points per participant rankings go:
If you consolidate the races by sex: