History has had no shortage of outstanding female mathematicians, from Hypatia of Alexandria to Ada Lovelace, and yet no woman has ever won the Fields medal - the Nobel prize of the maths world. The fact that men outnumber women in the highest echelons of mathematics (as in science, technology and engineering) has always been controversial, particularly for the persistent notion that this disparity is down to an innate biological advantage.

Now, two professors from the University of Wisconsin - Janet Hyde and Janet Mertz - have reviewed the strong evidence that at least in maths, the gender gap is down to social and cultural factors that can help or hinder women from pursuing the skills needed to master mathematics.

The duo of Janets have published a review that tackles the issue from three different angles. They considered the presence of outstanding female mathematicians. Looking beyond individuals, they found that gender differences in maths performance don't really exist in the general population, with girls now performing as well as boys in standardised tests. Among the mathematically talented, a gender gap is more apparent but it is closing fast in many countries and non-existent in others. And tellingly, the size of the gap strongly depends on how equally the two sexes are treated.

Hyde and Mertz used a wide range of data sources, including the standardised maths tests that all US children must sit as a result of the No Child Left Behind Act. Last year, Hyde reviewed data from 7 million children across 10 states and found that neither gender had the edge in performance, regardless of ethnicity or grade, even in schools which had seen disparities in past decades. The duo also looked at data from the National Assessment of Educational Progress (NAEP), a programme that tests a random sample of students every year, and found that male and female 12^th-graders had only "trivial differences" in terms of complex problem-solving.

These results address an issue raised by past work from Hyde's group. In 1990, she did a meta-analysis (a statistical fusion of the results from many studies) that found no overall performance differences between the two sexes, but that high-school boys has a slight edge in terms of complex problem-solving. A similar study in 1995 found similar results, but this might be down to a difference in training rather than innate ability. The new analyses suggest that this explanation is correct.

At the time, girls were less likely to take advanced mathematics, chemistry, physics and other high school courses that teach complex problem solving. Since then the onset of the 21^st century, the number of girls studying calculus has dramatically increased, providing Hyde with new data to analyse. Her newest research suggests that in this more equal environment, girls are matching boys even in the most difficult of intellectual tasks.

Of course, that's in the general population; what of the mathematically talented, those who are most likely to make an impact in the field? Since 1894, some scientists have suggested that men have a greater variability in intellectual ability than women, a simple statistical quirk that would result in more male prodigies. This was the controversial hypothesis that Lawrence Summers mentioned in his now-infamous speech at the National Bureau of Economic Research Conference in 2005:

"Even small differences in the standard deviation will translate into very large differences in the available pool substantially out... In the special case of science and engineering, there are issues of intrinsic aptitude, and particularly of the variability of aptitude, and that those considerations are reinforced by what are in fact lesser factors involving socialization and continuing discrimination."

To test that, Hyde looked at data from maths tests in Minnesota and compared the numbers of boys and girls who scored in the top 5% of their year. The ratio was 1.45, meaning that for every two girls in this elite group, there were around three boys. In the top 1%, the ratio was 2.06, meaning two boys for every girl. That seems to vindicate the Variability Hypothesis, but those figures only applied to white American children. In other ethnic groups or, indeed, in other countries, the picture was very different.

For Asian-Americans the ratio was actually 0.91, meaning more girls than boys in the top 1%. International studies have found similar trends. One analysis of tests from the Program for International Student Assessment (PISA) showed that 15-year-old girls matched or outnumbered their male peers in the top tiers within Iceland, Thailand and the UK. Two studies found that 15-year-old boys and girls were equally varied in their mathematical skills in most of the countries taking part in PISA and the Trends in International Mathematics and Science Study (TIMSS). In some, like the Netherlands, girls actually turned out to have the wider range of ability.

So much for the idea that a greater variation in ability underlies the larger number of men in the top ranks of mathematics - if that had any biological basis, it should apply to all populations regardless of ethnicity or nationality. Clearly, that's not the case. Instead, the evidence suggests that whatever gender differences exist are mostly down to social factors.

There's plenty of evidence to suggest that, given the right social environment, the gender disparity in maths becomes vanishingly narrow. Variousstudies have found that countries with the poorest degrees of gender equality also have the widest gulfs between male and female mathematical performance. And in their own analyses, Hyde and Mertz found that a country's gender inequality gap significantly correlates with the ratio of boys to girls in the top 5% of PISA test scorers, and the proportion of girls competing in the International Mathematics Olympiad - an incredibly challenging competition where the top scorers have one-in-a-million ability.

It's no coincidence that countries like Denmark, the Netherlands, the UK and Iceland, where equal numbers of girls and boys populate the top 1% of the PISA results, are also in the top dozen countries in terms of gender equality. (The US, for the curious among you, is ranked 31^st, between Estonia and Kazakhstan) These international comparisons point the finger at gender inequality, rather than greater male variability or aptitude, as the main reason behind the lack of women at the highest levels of maths in some countries.

Obviously, that includes a multitude of sins that will need to be addressed - lack of attention or encouragement, the effects of stereotypes, a lack of female role models, wilful misogyny and unconscious biases, hostile work environments, and so on. Addressing these issues is no easy task but at the very least, this review summarises firm evidence that attempts to do so will see female mathematicians rivalling their male counterparts at every level of the discipline.

Reference: Hyde, J., & Mertz, J. (2009). Gender, culture, and mathematics performance Proceedings of the National Academy of Sciences, 106 (22), 8801-8807 DOI: 10.1073/pnas.0901265106

More on gender issues in science and maths: