A marginally relevant point is that biological differences leading to a greater likelihood of mathematical talent are not always desirable. Autism and related disorders, for example, strike four times as many boys as girls, and there is some indication that a mild Asperger's syndrome, one of these related conditions, is not rare among research mathematicians.
Neither are psycho-social factors that lead to a greater likelihood of mathematical talent always desirable. It's anecdotal to be sure, but consider the behavior seemingly typical of many successful math and science graduate students. How appealing is subsisting on candy bars, take-out food and coffee while wearing the same clothes for days on end and focusing monomaniacally on some technical detail or other. And how appealing is the jockeying for dominance that often characterizes mathematical and scientific research.
Again people vary in their tolerance for such conditions, but arguably proportionally fewer women than men will find them congenial.
Finally, even if it turns out that important biological differences underlie some of the difference in the distributions of mathematical talent, their effect may be quite small compared to the effect of these psycho-social factors. Vanderbilt professor Camilla Benbow, a specialist on gifted children, stresses the mutability of some of these factors. She points out that where there has been a concerted effort to encourage girls in mathematics, the ratio of mathematically high-achieving boys to mathematically high-achieving girls declines considerably.
The bottom line is that we can do much more to induce girls and women to study mathematics. We can make pedagogy and applications more palatable and stress the beauty and utility of the subject as well as its algorithms and calculations. Moreover, whether students of either sex go on to careers in science or not, there is compelling evidence that if they take more math, they will considerably increase their likelihood of finding higher-paying, more rewarding jobs.
-- Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books, including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNEWS.com appears the first weekend of every month.