Even the most hidebound male chauvinists have been forced to admit that girls are as good at math as boys, on average. Boys no longer start outperforming girls at age 12 or 13, as they did as late as the 1970s; in the U.S., high school girls now take calculus at the same rate as boys;  tests mandated by No Child Left Behind show that girls have reached parity with boys in math achievement through high school; and tests of complex problem-solving (which NCLB doesn’t measure) find that girls have now pulled even with boys through 12th grade on this skill, too.

But the stereotype that females lack the innate ability to match males at the highest levels of math lives on. A new study comes as close to burying it as anything yet.

In a paper posted this evening in the Proceedings of the National Academy of Sciences, researchers describe analyzing data on the highest level of math achievement. These problems are not multiplication calculations, not even second derivatives; they’re more like calculating the necessary relationship between N and epsilon for a uniform continuity proof. There are certainly hints that more males than females have what it takes to excel at math, “and there is an ingrained belief among very well-educated people that [the idea of superior math achievement among males] is true,” says Janet Mertz, professor of oncology at the University of Wisconsin, Madison . In the U.S., men earn 70 percent of the Ph.D.s in the mathematical sciences, though that’s down from a high of 95 percent in the 1950s. No female has ever won the Fields Medal, math’s Nobel Prize. A study of mathematically precocious young people finds that boys outnumbered girls 2.8-to-1 in 2005, though that was down from 13-to-1 a quarter-century before, UW psychology professor Janet Hyde and Mertz report in PNAS.

“On average, girls have reached parity with boys in the United States and some other countries, and the gender gap at the high end is closing,” says Hyde.

The question, then, is what accounts for the disparity in math geniuses. Here, international data are crucial. In the U.S., tests typically show that, among students scoring in the 99th percentile for math achievement, boys outnumber girls 2-to-1. But that’s only among white students. Among Asians in the U.S., girls outnumber boys very slightly, as they do in Britain, Iceland and Thailand. That suggests that males’ superior math ability does not hold true across the world, which is always a strong clue that social and cultural forces are involved.

“We concluded that the main  reason many fewer females than males excel in math in most countries is not lack of innate ability or ‘intrinsic aptitude’ but gender inequality,” says Mertz. “Nations with greater gender equality typically have a smaller math gender gap.” (Gender equality, as measured by economists, reflects the number of women holding political office, the difference in men’s and women’s pay and the like, and is calculated by the World Economic Forum. The U.S. currently ranks 31st, with northern and western Europe dominating the top spots.) That suggests that the root of gender disparity in math is sociocultural factors, not anything unchangeable that girls are born with. Society either sends a message that girls can excel at math, that they will be rewarded for doing so—or it doesn’t.

Gender equality also comes into play with what’s called the “greater male variability hypothesis.”  This is the idea that then-Harvard president, and now White House advisor, Larry Summers was referring to in the infamous 2005 speech in which he posited that the dearth of women among Ivy League math departments and other top echelons of the field reflected a lack of “intrinsic aptitude” and, in addition, “the variability of aptitude.” The last is a technical term for the idea that there are a greater number of males who are math dunces—but also a greater number who are math geniuses, while girls are clumped in the muddling middle.

Mertz and Hyde looked for evidence of this imbalance—more boys than girls at the extremes of math ability—in international data, too. Again, they found that in some countries as many girls as boys score above the 99th percentile, and in others more girls than boys are extreme math dunces or math geniuses. In both cases, countries with as many or more girls at the upper extreme tend to be those with the greatest gender equality, such as Germany and the Netherlands. If the greater male variability in math performance that Summers cited as an explanation for the low numbers of women among math geniuses is not ubiquitous across the world, then “the occurrence of greater male variability and scarcity of top-scoring females in many, but not all countries .. . must be largely due to changeable sociocultural factors,” the scientists write, “not immutable, innate biological differences between the sexes.” If the differences were innate, they should show up in every culture.

For anyone who still believes that innate factors explain the math gender gap, as I wrote last year, look at countries with a common gene pool. East Germany regularly sent many more girls than West Germany to the International Mathematics Olympiad by margins of 5-to-0; Slovakia sent more girls by a margin of 3-to-1; Korea topped Japan by 6 to 0. As I wrote then, “It’s hard to see that as anything but the result of the starkly different social and other environmental forces in each country, not intrinsic biology.”