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Meritocracy: Almost as Wrong as Larry Summers

Several years ago, Harvard President Larry Summers spoke at an academic conference on diversity issues, and casually speculated that one of the possible reasons there were relatively few female mathematics professors might be that men were just a bit better at math than women.  Although his remarks were private and informal, the massive national scandal that erupted rapidly transformed President Summers into former President Summers, and coincidentally persuaded Harvard to name its first woman president as his permanent successor.

Now I am hardly someone willing to defend Summers from a whole host of very serious and legitimate charges.  He seems to have played a major role in transmuting Harvard from a renowned university to an aggressive hedge fund [1], policies that subsequently brought my beloved alma mater to the very brink of bankruptcy during the 2008 financial crisis.  Under his presidency, Harvard paid out $26 million dollars to help settle international insider-trading charges [2] against Andrei Shleifer, one of his closest personal friends, who avoided prison as a consequence.  And after such stellar financial and ethical achievements, he was naturally appointed as one of President Obama’s top economic advisors, a position from which he strongly supported the massive bailout of Wall Street and the rest of our elite financial services sector, while ignoring Main Street suffering.  Perhaps coincidentally, wealthy hedge funds had paid him many millions of dollars [3] for providing a few hours a week of part-time consulting advice during the twelve months prior to his appointment.

Still, even a broken or crooked clock is right twice each day, and Larry Summers is not the only person in the world who suspects that men might be a bit better at math than women. However, the notion that such vile and disgusting thoughts may be concealed in a few human skulls tends to agitate many ideologues, whose motives often seem to include a powerful emotional component.  For example, MIT Professor Nancy Hopkins told reporters [4] that she became physically ill at hearing Summers’ controversial remarks, and fled the auditorium, fearing she would black out or vomit if she remained.  Many of the other details of Summers’ defenestration may be found in the numerous columns [5] by bloggers such as Steve Sailer.


Perhaps Prof. Janet Mertz, a Wisconsin cancer expert, might fall into the same emotional category as Prof. Hopkins, given the peer-reviewed journal articles that she has published debunking the pernicious myth of gender differences in math ability, and rebutting the dreadful views of Larry Summers in particular.  In her first article [6], she and her co-authors explored the distribution of top math achievers, focusing especially on the participants in the International Math Olympiad, and although the 10,000 word academic study is a bit eye-glazing, their quantitative findings are helpfully summarized in Tables 6 and 7 (pp. 1252-53).

The first of these shows the gender-distribution of the 3200-odd Math Olympians of the leading 34 countries for the years 1988-2007, and a few minutes with a spreadsheet reveals that the skew is 95% male and 5% female.  Furthermore, almost every single country, whether in Europe, Asia, or elsewhere, seems to follow this same pattern, with the female share ranging between 0% and 12% but mostly close to 5%; Serbia/Montenegro is the only major outlier at 20% female.  Similarly, Table 7 provides a gender distribution of results for just the United States, and we find that just 5 of our 126 Math Olympians—or 4%—have been female.  Various other prestigious math competitions seem to follow a roughly similar gender skew.

Mertz and her co-authors seem to regard these results as a decisive refutation of Summers’ controversial remarks, and state as their “first and foremost” conclusion that “the myth that females cannot excel in mathematics must be put to rest” (bold-italics in the original).

In a more recent 2012 article aptly titled “Debunking Myths about Gender and Mathematics Performance [7],” Mertz and her co-author revisit the same topic.  They open their discussion by noting in the very first paragraph that every single one of the fifty-odd winners of the Fields Medal—the “Nobel Prize” of mathematics—has been male.  But this seemingly dispiriting fact is followed by 10,000 words of extremely dense verbiage, laced with mind-numbingly complex statistical analysis, ultimately allowing them to conclude that purported gender differences in math performance are largely due to differences in socialization and schooling, as well as outright bias.  As a result, they end with a ringing call for the total elimination of gender-discrimination in mathematics.


But Prof. Mertz is hardly a narrow ideologue, focused solely on gender issues.  Having successfully demolished Summers’ male-chauvinistic views by demonstrating that 95% or more of all the world’s top math students—both American and foreign—have always been male, she has recently turned her attention to similarly debunking my own claims regarding the recent pattern of ethnic performance in America.  A few days ago, she produced a 3,500 word rebuttal [8] promoted by Prof. Andrew Gelman on his blogsite [9].

As it happens, she and her co-authors had exhaustively researched the ethnicity of the 1988-2007 American Math Olympians in their aforementioned 2008 article, and through a combination of extensive biographical research and confidential personal interviews had determined the exact number of full-Jews and part-Jews among those 120 individuals, publishing the results in their Table 7 mentioned above, together with the broader racial categories.

Given that I had produced my own ethnic estimates for those same students based on perhaps five minutes of cursory surname analysis, while Mertz and her associates seemingly devoted five weeks of research to the same task, I readily acknowledge that her results are certain to be vastly more accurate than my own.  Indeed, if we regard the Mertz figures as the “gold standard,” then comparing them with my own numbers provides a useful means of assessing the overall quality of my direct inspection technique, a technique that constituted a central pillar of my entire study.  This allows us to decide whether my approach was indeed just the worthless “guesswork” that she alleges.

Her peer-reviewed journal article determined that the 120 American Math Olympians from 1988-2007 consisted of exactly 42 Asians, 26 Jews, and 52 non-Jewish whites.  My crude surname estimate had been 44 Asians, 23 Jews, and 53 non-Jewish whites. Individual readers must decide for themselves whether these estimation errors seem so enormous as to totally invalidate my overall conclusions, but personally I would be quite satisfied if they remained in this range across the tens of thousands of surnames I had inspected throughout the rest of my paper.

Obviously, such estimation techniques may be completely incorrect for tiny handfuls of names, and should only be relied upon across substantial lists.  For example, in one sentence of my 30,000 word article I stated that just 2 of the 78 names of Olympiad winners since 2000 seemed likely to be Jewish, and Mertz has repeatedly attacked me for this claim, now pointing out that I had missed the Hebrew name of winner “Oaz Nir.”  She is correct, and since Nir was a double winner in 2000 and 2001, this single surname error on my part accounts for virtually the entire discrepancy between my own 1988-2007 Olympiad results and those produced by the exhaustive research undertaken by Mertz and her three academic co-authors.


The bulk of Mertz’s criticism relates to these surname estimation issues, and now that I have used her own data to determine the likely error rate of my own technique, let me respond to some of her other major arguments.

She claims that my Asian-American enrollment percentages at the Ivies and other elite universities are distorted by inclusion of part-time students in the governmental NCES database.  However, this is completely incorrect.  If she had bothered examining either the NCES database or my own description of the dataset, she would have noticed that I was quite careful to restrict my results to full-time students only.  Anyway, with the notable exception of Harvard, almost none of these elite schools contain significant numbers of part-time students.  She should have examined the NCES data before she made those spurious charges.

On another matter, she argues that the Jewish enrollment numbers provided by Hillel cannot possibly be correct because they are relatively constant from year to year.  Now I have never claimed that the Hillel numbers are exact, and indeed have always suggested that they were probably mere estimates.  But consider that the Asian enrollment figures are based on exact racial reporting as required by the federal government, and those numbers tend to be roughly as constant as the Hillel Jewish figures.  Since the Asian figures are surely precise, how can the mere relative constancy of the Hillel numbers be taken as proof they are obviously fraudulent?

Next, she raises the question of whether the number of estimated Jewish NMS semifinalists is artificially depressed by their concentration in states with especially high thresholds, an issue that I had already discussed at length both in my main text and in my Appendix E [10].  Although this issue cannot be fully resolved given our limited data, I doubt this is the case, and I actually suspect that the opposite is true, namely that the number of high-performing Jews is somewhat over-estimated.  The reason is that Asians tend to dramatically outperform Jews, and a large fraction of all Asians are located in California, where they must compete against each other and face the highest state thresholds, thereby artificially restricting their numbers.  For example, high school Asians in California outnumber Jews just 4.5-to-1, but are over 13 times as numerous among high-performing students.  Meanwhile, a hugely disproportionate number of Jewish NMS semifinalists come from states with far lower thresholds such as Arizona, Florida, Pennsylvania, and Illinois; if a single national standard were in place, many or most of those Jews would probably have been replaced by higher-scoring Asians from California.

In any event, Mertz cites various arguments to suggest that my estimate that Jews constitute about 6% of national NMS semifinalists is too low, and that the correct figure should be 7%.  Since I have already stated [11] that I am reasonably comfortable with any figure in the 5.5% to 7.0% range, perhaps our differences are not so enormous in this particular item.  But if she accepts that 7% figure, then the over-representation of Jews in elite academic institutions remains just as suspiciously high as I had originally claimed.


Given that two of Prof. Mertz’s greatest areas of policy interest seem to be the relative rate of elite performance by gender and by ethnicity, I notice a curious mismatch in her analysis.

She notes the large over-representation of males in math achievement, and strenuously argues that this is merely an artificial byproduct of social conditioning or even unfair gender bias, which distorts the inherently near-equal abilities of males and females. Therefore, she advocates major policy changes to bring the numbers of men and women in elite mathematics into much closer equality.

Yet at exactly the same time, she seems perfectly comfortable with Jews being over-represented at elite academic institutions by perhaps 3,000% relative to non-Jewish whites, and totally disproportionate to their apparent academic ability.  I also suspect that she would be unwilling to endorse social policies aimed at bringing Jewish elite representation into much closer alignment with their 2% share of the national population.

Although I cannot explain this puzzling inconsistency in her logical positions, I can only note the curious coincidence that she herself happens to be a Jewish woman.


On a totally different matter I stepped off the plane in DC Tuesday evening and immediately found a message notifying me that my Wednesday Aspen Institute panel on federal minimum wage issues had been cancelled due to a looming snowstorm.  Given that no ordinary snowstorm had ever cancelled a scheduled event during the years I lived in New York City, I braced myself for the blizzard of the century.  Instead the next morning there were just a few very light snow flurries, without any of the scattered flakes surviving on the ground, but the government remained mostly shut down.  I suppose the next step will be to close all government offices and allow workers to remain home on days that are rainy or overly warm.  Such is the remarkable competence and grit of the capital city of our American World Empire.

The Aspen panel should be rescheduled for the near future, perhaps as early as March 15th, presumably subject to cancellation due to snow, rain, sleet, wind, or gloom of night.

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Comments Disabled To "Meritocracy: Almost as Wrong as Larry Summers"

#1 Comment By EliteCommInc. On March 16, 2013 @ 4:20 am


I take Farrell’s work at face value. I think his motive is simple and clear. Where as men have been indicted on their abuse of women. The historical data as he presents it, and I agree is quite the opposite. That men have paid a fair price on behalf of women and in protection of women.

I won’t go further, because what prompted his text was his work with men on anger issues. And I would not deny, it is a defense of manhood being a man and what that means.

I appreciated your comments. I don’t think it is simple as it is played out, but a quick anecdotal observation. From the moment male issue ascends the pathway to egg. It is on a very risky journey frought with benign and unbenign attempts to prevent success.

#2 Pingback By Unz on Meritocracy: Dangerous Cancer Statistics | Ron Unz – Writings and Perspectives On March 16, 2013 @ 6:10 pm

[…] focus of her article was a worldwide gender analysis of top performing math students aimed at refuting the controversial speculations of former Harvard President Larry Summers, who had suggested that men might be better at math than women, at least at the very high end of […]

#3 Pingback By Meritocracy: Dangerous Cancer Statistics | The American Conservative On March 16, 2013 @ 6:11 pm

[…] focus of her article was a worldwide gender analysis of top performing math students aimed at refuting the controversial speculations of former Harvard President Larry Summers, who had suggested that men might be better at math than women, at least at the very high end of […]

#4 Comment By Janet Mertz On March 18, 2013 @ 10:11 pm

I have now posted my official 3-page response to Unz’s above March 9th post. It is available at:

#5 Comment By linert On March 19, 2013 @ 9:15 am

Mertz’s response to this latest defense eviscerates Unz’s argument. It is now difficult to believe that Unz in debating in good faith and it is rather ironic that Unz accuses Mertz of being emotional. Unz states that his count of Jewish Math Olympians from 1988-2012 was only wrong by 2. Well, yes. But what he doesn’t mention is that he accidentally stumbled on the right answer by grossly over-counting Jewish representation on the 1970 teams and gross under-counting representation on the 2000-2012 team. After you adjust for Unz’s errors, the change in representation is only about 5%, very far from the collapse in Jewish achievement that Unz claimed. His thesis completely falls apart.

It is telling that Unz, who claims to objectively follow the statistics, refuses to acknowledge these errors and reconsider his findings in light of the new evidence.

Andrew Gelman, the highly respected Columbia University statistician who was originally favorable inclined to Unz’s argument has reversed course after reviewing the numbers and the Mertz rebuttal. And no wonder – Unz’s errors are devastating.

#6 Comment By Crown On April 3, 2013 @ 11:48 pm

Mertz’s work is flawed at best, as it does not take biological factors into account at all. This constant drivel of words like “social conditioning” and “gender bias” stems purely from emotion with an insistence that masks biological affinities. The male and female brains (and bodies) evolved differently and are built for different things. This is one of the more recent documentaries that exposed the paradox: [13].

The national “outrage” that followed Summers is no different from the feminist tactics of bullying institutions and attacking men in order to feed emotional failures. It is the same tactic that skews domestic violence or sexual harassment reports: [14] or [15]. Mertz’s work follow the same forced, unscientific method of appealing to feelings rather than facts. Just like most feminist “research”, this is just another card to the pile of rubbish that insults the scientific method. Stop trying to reform biology.

#7 Comment By Malcolm James On April 19, 2013 @ 3:50 am

Research has found that male and female brains are ‘essentially’ the same (Cordelia Fine). Unfortunately ‘essentially’ is a weasel word because it doesn’t preclude one gender having a very slight edge in a particular area – and that is all it takes to dominate in the very highest echelons. In tennis, the absolute difference between Djokovic and the player ranked 50 in the world is, in absolute terms, miniscule and the latter is a superlative player by all but the very highest standards. However, in an intensely competitive situation, the tiny edge which Djokovic possesses is sufficient to ensure that he will prevail the great majority of the time.

#8 Comment By Nancy Hopkins On May 20, 2013 @ 6:56 am

Just stumbled on this interesting set of comments.
Here is a response:

I am constantly astonished by people who wish to claim and imply that men’s and women’s brains are different and therefore women can reasonably be expected to be less good at math. If these people had any interest whatsoever in understanding the biological basis of math ability, they would be interested in comparing the brains of women who are great mathematicians to women who aren’t, or the brains of men who are great mathematicians to men who can’t do math at all. But they never do, Why?

I assume for the same reason that Mr. Unz selects only data that fits his preconceived ideas (while Mertz – a scientist – feels obliged to get every data point correct before making her conclusions.) ps Mr. Unz, Larry Summers was just as wrong when his ideas DON”T agree with yours, as he was when they do. He is one of those very smart people who lack common sense and wisdom.