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. Various studies 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: **

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This post had me cheering all through it. I haven't noticed any gender differences in math learning. And I'll just use this opportunity to plug the JUMP math program--which I have no personal connection with other than using it with my own kids. I recommend it highly both for kids who love math and kids who struggle with it.

Women also self select themselves out in favor of being full time moms. Let's just say that women who can really excel in math are smart women. Smart women who really want to be stay home moms will make decisions that lead to their goal. The will satisfy their parents' expectations and go to college and start careers. However they will not allow their own aspirations to take a back seat forever. Now this is only a percentage of women, but I would say there is a greater percentage of women than men who have talent and actually quit. I know women who have advanced math and science degrees who have quit to stay home with their family. I know some others who said they wanted to. I don't know any men like that.

I'm going to play Devil's Advocate.

Hyde and Mertz attempt to distinguish differences in those at the top of the field by crunching the numbers on children at the top of their classes. All of the data, in fact, appears to be from the schoolroom (although I only read your review, not the article itself).

Having done very well in school, but hit my 'math wall' -- the point of conceptual difficulty I could not overcome -- with advanced quantum mechanics and group theory, I can myself provide a example showing that the link between school performance and high level performance is not in all cases straightforward. Consequently, statistics using a body of school students to judge high-level ability are of dubious reliability.

The only data I'd really trust on this would be a study of experts in the field, from a society free for at least a generation of any kind of gender bias. Realistically, this isn't going to happen, since the energy and time investment required for pregnancy is going to skew any large sample size away from women. One would have to adjust for that very carefully. And even in relatively enlightened western countries, gender bias is still a reality in any number of situations, for both sexes.

In the end, we should probably trust our intuition on this one. Irrespective of any small variations between the sexes -- if any really do exist -- the fact remains that both sexes can potentially achieve greatness in mathematics (and, indeed, all fields of endeavour). One example is sufficient to prove potential. Every field has one example or CAN have one. And it's this potential we should protect.

PS Girls kick ass, it says so on a t-shirt.

Ah, if only you'd had this posted in time to be nominated for the contest to be judged by Steven Pinker. . . .

/me is a sad little Puck

Boy, I can't wait to see this study spread out on a full page in the newspapers and covered by all the networks!!! I mean, a large scientific study saying ability is fostered by society and not innate - that gets to the top of science news evere time doesn't it?

Is it in the papers yet?

How about now?

Maybe later...

Great work Ed, and GREAT work Janet and Janet!

I wonder how much of this is fully their choice, though. Children are still considered primarily the responsibility of the mother. Girls grow up with wonderful stories of being a stay-at-home mom and how it's just what's best for the kids. Men do not get these same messages, so they are less likely to "choose" to be stay-at-home dads, even though it could easily be just as fulfilling for them. As long as we still expect mothers to be more responsible for childcare than fathers, more women will have an extra burden that might make them "choose" to give up a career. Even when no children are involved, women are still expected to do more domestic chores than men are, although the situation is certainly improving. The problem isn't that women "choose" full-time parenting over a strong career. The problem is that they often feel like they have to choose because they don't have enough support from their husband to have both. Men rarely have to face this choice.

Thanks for posting on this - awesome job. ArchAsa, your comment made me LOL! So frickin' true.

I suspect the conclusion of this essay is correct, but the argument is weak, starting from the beginning--Hypatia and Ada aren't great compared to the male mathematicians of their ages, and there are problems with the paper as well, which one poster begins to illustrate.

Having done very well in school, but hit my 'math wall' -- the point of conceptual difficulty I could not overcome -- with advanced quantum mechanics and group theory, I can myself provide a example showing that the link between school performance and high level performance is not in all cases straightforward.

The difference is actually deeper than this--elementary math classes like calculus are typically taught from a calculational perspective, whereas the work of a mathematician and later math classes focus on theorem proving. Historically, middle school geometry focused on proofs at an elementary level, but that's no longer the case in most US schools any longer.

ArchAsa - that's a *really* good point. I (perhaps naively) assumed that this would get quite a lot of coverage but Google News says otherwise. Newsweek, LA Times, couple of others. Looks like similar results for similar important studies in the past, like the chess grandmaster one I linked too.

Bad show.

Great post, Ed. Don't know if you knew this and included it on purpose or not, but I believe the second image you posted is actually a man -- the self-portrait of Raphael from The School of Athens (the art featured in all the Two Cultures Ads). Growing up, though, I did always think he looked like a girl in this image. Just thought I'd mention it! : )

Interesting. Any data on how involved fathers in Denmark, the Netherlands, etc. are in their children's care?

#8, I'm a little confused by your comment. I was simply using my own limitations as one example, not claiming it was the only example. We agree regardless: mathematics at the higher level is significantly different from school-level mathematics, rather than just 'scaled-up in difficulty'. So that stats done in this study can't really be seen to apply particularly well.

It's also interesting to see this post in the light of today's estimate that the medical profession in Britain will be majority-female within eight years. I can imagine doctors forty years ago shaking their heads and saying "well of course _some_ girls have what got what it takes to be doctors, but statistically those qualities are more common in boys" or words to that effect.

Azkyroth: I'm a father in Denmark, but this doesn't me make well-placed to make _comparative_ judgements with other countries. However based on my experience I would say that what makes Denmark a relatively good place for families in general, including career women, is

i) the expectation that good employers will be family friendly - e.g. offering family sick leave, flexitime, and work from home.

ii) guaranteed parental leave

iii) universal provision of childcare after the end of parental leave (including after-schools for school-age children)

iv) six weeks paid holiday per year (five standard weeks + an extra week for many employers)

These factors make it easier to be a mother but also easier to be a hands-on father.

A clear explanation of the math gender gap.

http://www.lagriffedulion.f2s.com/math2.htm

"Clear" does not mean "flatters my preconceptions."

Has anyone ever just asked how much everyone likes math? I feel like a far easier explanation the people rarely talk about in issues of this type is the distinction between selecting away and selecting towards. There are things I am talented at that I would never pursue as a career because I have other things I like more. This gap could almost certainly could be partially explained by women simply choosing other fields because they enjoy them more.

NICE

To Zach:

I believe there's been a fair bit of research done on why women choose to leave mathematics.

I googled "women leave mathematics" and it came up with quite a few theories (no really decent links though) which included: they wanted to do something that "served" the community, they lack confidence, the stereotype of the mathematician clashes with their self-image, and they don't think they can have time for their family and also a mathematical career.

It seems that a lot of women like mathematics enough to study it for their undergraduate degree, but choose not to pursue a career in it (according to this article, http://www.springerlink.com/content/j480476u75rk8683/ )

Personally I like mathematics, and I've progressed until the postdoc stage, but I think about quitting everyday. The reason is something which perhaps affects women more than men. I work at an international institute. Most of the people here (and they're mostly men) are from somewhere else. A surprising number of the men have their wives or girlfriends here with them, a lot of whom don't work because it's really hard to find a job in foreign country. On the other hand I've been told that out of the women working only one has their partner here, because he works at the institute! I'm one of the women whose partners live somewhere else. I can't imagine asking my boyfriend to give up his career to come stay with me, and so we live on different continents. Everyday I think maybe I should just quit, go home to my small country and work in a shop or whatever so we can live together.

Looking at the best 1% or best 5% (like the studies referred to in the article above) is nonsense when trying to address the gender gap issue in top talented young mathematicians.

The international mathematical olympiads consist of a very difficult math problem-solving competition bringing together each year the most brilliant teenager mathematical talents in the world (the 6 best in each country). For big countries like Russia, the US or China, this means not the 1% best (best one in 100) but the few best ones amongst millions of competitors.

Even in the countries which most favor female participation at the mathematical olympiads (like Russia or Bulgaria) there are only 12% to 24% females, which means that males still make up 76% to 84% of exceptionally talented young mathematicians, much more in other countries. On a combined international basis, nearly all golden medals at the mathematical olympiads go to boys. At the international physics olympiads the boys superiority over girls is even more overwhelming. Girls just cannot compete against boys at these levels.

The reason why there is such an overwhelming male representation in fields like top level mathematics, theoretical physics or astrophysics is actually very simple. It can be explained by the the fact that you need a IQ of at least 3 or 4 standard deviations above the mean of 100 (in other words a IQ of at least 150 or 160) to master the most advanced topics in these disciplines. Now there are numerous studies showing that the standard deviation of males IQ is significantly larger than the standard deviation of females IQ. If you add the fact that the IQ distribution is approximately normal (or gaussian) then you have a very simple explanation of the huge male over-representation in those areas.

Note that exactly the same factors probably explain why there is a huge male over-representation at top levels in games of pure abstract intelligence like chess or checkers. For example, according to the FIDE database of April, 2009 (available free online) there is only 1 female in the best 100 chess players worldwide (1%) and 21 in the first 1000 (2.1%) whereas females represent 7.6% of the overall FIDE chess rated population of about 100,000 players. All the big chess tournaments (like world championships for example) are open to both genders but as the result of the huge gender gap female-only chess tournaments had to be set up in addition to all the other ones open to both genders.

incidentally this male imbalance is not restricted to humans. For example male rats perform more accurately than female rats on tasks that require spatially organized representations. No social factors can explain better male rats performance, certainly not male rats chauvinistic behavior.