The recent push to promote the notion of gender equality in mathematical aptitude, contrary to the overwhelming bulk of psychometric data, is itself ironically a demonstration of mathematical illiteracy. Just as it is horrible scientific practice to cherry pick studies indicating the desired result while ignoring all others, so it is terrible mathematics to make inferences about statistical variance from facts about the mean. Allow me to clarify.
Large-scale psychometric analyses have consistently found a stable discrepancy between males and females in cognitive test performance. The difference in the statistical mean or average is small, favoring men by about 2.5 IQ points according to the best analysis, but the most marked difference is not in the mean, but in the variance. There is significantly greater variance among males than among females. This means males outnumber females at both ends of the spectrum, so there are more male dullards and geniuses, a fact consistent with most people’s recollection of their classmates.
The current Science study touting gender equality actually confirms that male variability in math ability is greater, by a factor of 1.11-1.21, consistent with results back in 1960 (variance factor: 1.20, mean difference 0.12 std dev, N=73,000 15-yr olds). This aspect of the study is downplayed by the media, even among scientific journals, since it leads to some politically undesirable facts.
As the authors of the Science paper admit, the gender discrepancy in variance means that at about two standard deviations above the male mean, there should be twice as many males as females. So if the threshold for performance in a science or engineering program was at two standard deviations above the mean, we should expect there to be twice as many males as females, based on mathematical aptitude alone. In reality, the most demanding physics and engineering programs only accept people three to four standard deviations above the mean, which would make the male to female ratio even greater, consistent with the 85%-15% male-female split in most top science and engineering programs. Harvard President Larry Summers made precisely this point in the infamous speech that cost him his job, at the instigation of feminist faculty who ironically displayed their own mathematical ineptitude.
All of this contradicts contemporary social dogma, yet is entirely consistent with common sense. It is far more credible that the consistent discrepancy in variability, seen across cultures and time periods, is the result of a real difference in aptitude rather than the product of discrimination. Indeed, gender stereotyping is more likely to take place in the home than at liberal institutions of learning, especially at the highest levels. If social factors were the cause of gender disparity, we should expect this to diminish as students progress to higher levels of university education, becoming further removed from their family’s influence and more engaged with socially liberal university culture. In fact, we see the exact opposite, as the gender disparity becomes more pronounced as students progress to higher degrees. Thus feminists are left with the absurd accusation that science and engineering departments are biased against females. Anyone familiar with university life should know better than to believe such nonsense, as faculty and administrators take special care to offer opportunities to females and minorities.
The disparity between male and female mathematical aptitude is barely noticeable at the median level. A little extra industriousness would be enough for females in the middle of the pack to perform equally with males in math class or even a bit better. In fact, in cultures where girls are academically industrious, we do see slightly better average grades for females in primary and secondary math class, probably owing to better study discipline, again consistent with common observation. However, at the highest levels, the aptitude disparity is too great for very many females to compensate with greater effort. The gifts of mental quickness and astute intuition are needed in order to do math at a high level with the facility required in a fast-paced working environment. The difference in gender variability may be used to calculate the expected male-female split among mathematicians in the National Academy, Fields medalists, and Putnam competition top performers. The computed values correspond closely with reality, comporting with the hypothesis that membership in these categories is indeed merit-based.
It is striking that the Science study still shows the same discrepancy in variability by gender, despite the fact that it uses the SAT, which was redesigned in 2002 to be less of an aptitude test and more of an achievement test. Verbal analogies were eliminated, since minorities performed poorly on these, and the math section now places less emphasis on speed and intuition, instead focusing on mastery of course material. This emphasis on achievement gives industrious females an advantage at the middle of the pack, accounting for the disappearance of the difference in mean, which still persists on true cognitive tests. Yet extra study is no substitute for genius, so there is still a pronounced gender discrepancy at the high end of SAT math performance, as the mathematically gifted can breeze through the exam with ease.
The only reason to protest these findings is political, not scientific. The gender disparity in math performance is no less well established than a reverse disparity favoring females at reading. No one questions the latter finding, in fact many feminists are proud to point to it, evincing their strange notion of equality. Similarly, race-based cognitive differences, which are even more pronounced than gender differences, even after controlling for socioeconomic status, are strictly taboo, unless perchance they are in favor of the supposedly oppressed minority.
This deep hostility to any finding that contradicts the contemporary myth of equality of aptitude across demographic categories is misguided. Gender- or race-based disparity in math and science aptitude is no cause for dismay or bigotry, if we understand what statistical statements about groups signify. We are making general statements about groups via statistical averages and variances; there will still be many individual women who do well in math and science, and even some geniuses. It would be a mistake to judge an individual based on that person’s demographic group; individuals are the basis of statistics, not the product of statistics. However, it is disastrous social policy to try to “correct” aptitude-based inequalities, not only because it results in unjustified accusations of discrimination, but because it may direct individuals away from the field they would have chosen for themselves based on their aptitude and inclination. Once outside of academia, graduates will find that performance is what matters, and they will be ill-benefited by having been protected or coddled by grade inflation or some other esteem-building measure to impose a false equality.
I understand that the desire to prove equality of aptitude by race and gender is motivated by the belief in the moral equality of all people, yet neither of these equalities implies the other. Even if we admitted that all races and genders were equal in every aptitude, with the same mean and standard deviation for all groups, we would still be faced with a real variation of aptitude among individuals within each group. What then of human equality? Does a genius have greater moral, social, or political rights than a dullard? If not, then it is clear that moral equality does not depend on equality of aptitude.
The confusion between equality of human worth and equality of ability can only come about in a society that values people primarily for their abilities. This instrumentalist notion of humanity, so unworthy of human dignity, can be a constant temptation for capitalist societies, where people are valued based on what they can produce. This perverse moral philosophy can be given a social Darwinist rationale, declaring that the only attributes with value are those that have some adaptive advantage. Only when we move beyond this crass instrumentalism will people be able to face their congenital inequalities with maturity and not be perturbed by them, nor use them as an excuse to lord over one’s fellow human being, for we have human worth for who we are, not what we can do.