Larry Summers, the president of Harvard University, speculated last month that there might be biological factors that help explain the relatively small number of women who go into careers in mathematics or science. Summers did not say that women who have succeeded in these fields differ from men or that women don't make first class scientists (although the transcript of the meeting hasn't been released so we can't be sure).
What he seems to have said is that the statistical distributions of the test scores of the sexes differ and that these differences may be, at least in part, biological.
That the scores differ is not disputed. For example, on the math SATs, the average boy's score is slightly higher than the average girl's score, but, perhaps more significantly, the variability of boys' scores is greater than that of girls' scores.
To appreciate the role of variability, we can imagine 1,000 women taking a math achievement test. Absurdly exaggerating for the sake of clarity, let's stipulate that 200 of them score around 75 on it, 600 of them score around 100, and 200 of them score around 125. In contrast, we can imagine 1,000 men taking the test, but now we stipulate that 200 of them score around 25 on it, 600 of them score around 100, and 200 of them score around 175.
Both groups' scores would average 100, but there is no doubt that the men would be disproportionately represented in institutions of higher learning as well as in institutions of other sorts.
Even with more realistic statistical distributions of talent in which women score at the very highest levels (and, of course, many do), the extremes and not the averages of the distribution often determine how many enter a technical field. Whatever the source and permanence of these distributional differences, nothing in them justifies any sort of discrimination against women, either as individuals or as a group.
So what does bring about the difference in the distribution of scores? Psycho-social factors? Biological differences? Educational practices?
Undoubtedly social conditions play an important role. It can't be denied, for example, that sex discrimination, sometimes overt, but more often subtle, remains a serious problem in many places (especially in university hiring and promotion). Neither can it be denied that because of their socialization very many women simply have no interest in mathematics or science. There is some evidence that the abstraction of mathematics poses more of a social challenge for women than it does a cognitive challenge. For whatever reason women have a relatively greater preference for involvement with others.
And biological differences? Summers' remarks (or, rather, crude versions of them) caused an indignant uproar. But there are many biological differences between the sexes, and there is no reason why these should not extend to matters mathematical. In addition to the SAT and other test data, well-known studies have shown that across cultures and on average men do better in navigating through three-dimensional space and visualizing objects therein.