Doing the Math

The Harvard president's little "gaffe" about there being fewer women in math-intensive posts has resulted in a lot of huffing and puffing. But now it has also resulted in Sex Differences in Mathematical Aptitude.

The pool of competitors is roughly the number of Americans between the ages of 25 and 85, approximately 190,000,000. Setting N  = 190,000,000 (the precise value is not important³) and the number of slots N_S  = 143, the competitor to slot ratio, N /N_S , is 1.329 million. With this value in (3), we find that the most probable number of women in the group of 143 Academy mathematicians is 7.1. (I choose not to round to the nearest integer.) At this time there are precisely 7 women in the mathematics sections of the Academy. (The agreement is almost embarrassing.) The 95% confidence interval⁴ is [2,12]. The minimum mathematical ability among the 143 Academy members is 4.68 SD greater than the male population mean. This is indeed an elite bunch!