After posting my note on Math and Gender Bias, I received numerous comments which indirectly echoed Larry Summers' famous remarks in 2005 suggesting that innate biological differences limited the role of women in mathematics and science. Even in 2005, Summers' remark was somewhat disconnected from the data. I thought it might be useful to compile a few relevant numbers to dispel misconceptions about the role of women in mathematics.
According to the Notices of the AMS, (vol 51, no. 7), by 2003, women received 21% of Ph.D.s granted by the top 48 U.S. mathematics departments (as ranked by the National Research Council), 27% of the Ph.D.s granted by the next (ranked) 56 departments, and 26% of all mathematics Ph.D.s. Last year, 16% of the (over 800) job applicants to our department were female, and women comprise receive a comparable percentage of our job offers.
What do these numbers suggest about biology and mathematical ability? For the ten years preceding 1991, women received approximately 17% of doctorates in mathematics. Anyone positing that the fact that women represent only 26% of all mathematics Ph.D.s is evidence of a significant biological difference must also argue for dramatic genetic changes over a 12 year time period leading to a 50% increase in women's representation among Ph.D. recipients. It is hard to avoid the conclusion that social influences play a dominant role in these numbers.
Looking beyond these numbers, it is also true that there are ever more women who are the - or among the - leaders in their fields. So, the numbers are not merely evidence of competence. The impact of women on the field is continuing to grow.
The hot political question is: "Do universities discriminate either for or against women in their hiring?" I have certainly not seen evidence of institutional discrimination against women. A decade or more ago, I was occasionally annoyed by letters of recommendation which compared female job applicants only against other women. These were probably clumsy attempts to aid women, which I viewed as counterproductive. I haven't seen such letters in recent years. I do believe that there is a premium paid for female candidates. There are two simple ways to pay such a premium: cash or prestige. A candidate may earn a higher salary or gain a more prestigious position than might be predicted by research accomplishments alone. There is no reasonable way to measure the latter; so, I will not consider it here. I have, however, heard university administrators advocate the cash premium. My conservative colleagues can have little quarrel with this premium. There is competition for the best female job candidates, which drives up their salaries. A university donor, a trustee, or tuition paying student may argue whether or not having more women on the science faculty is worth a small salary premium, but if the premium is not paid in prestige, it does not affect the department's research reputation. I think this is ultimately a nonissue, not really deserving significant attention from conservative thinkers.