The nature versus nurture argument over aptitude for science and math seems to resurface every few years, but recent studies are providing strong support for the argument that any gender gap is cultural rather than biological. A new report looks beyond standardized tests of mathematical skills to see what happens in the world of exceptional mathematical ability, and it finds that the same thing applies there. The report's authors, reasoning that we could use any talent that's out there, make some suggestions as to how to eliminate the people who get lost due to this cultural math gap.

The study (PDF) is published in the Notices of the American Mathematical Society, which is an open access publication, meaning anyone can read the paper. The authors start by reinforcing the general conclusion that advanced math skills do not exhibit a biological gender gap. Administering the SAT math test to 13-year-olds 25 years ago resulted in top scores skewed thirteenfold in favor of boys. By 2005, males outperformed females by less than threefold, and the rate was still dropping.

But the bulk of the report focuses on exceptional achievement, examining performance in tests like the Putnam Mathematical Competition and the International Mathematical Olympiad. For these competitions, mathematical problem skills are nowhere near sufficient; students are tested on the ability to generate elaborate proofs of complex mathematical concepts. Most students who attempt the Putnam, for example, fail to handle any of its dozen problems within the six hours allotted. Those who excel here are, in the authors' view, literally one in a million.

Unfortunately, given their rarity, it's hard to do a robust statistical analysis of these exceptional talents. Still, the authors can detect a number of trends when it comes to gender, ethnicity, and social factors, and their connections to mathematical achievement. Their first point is that people from Asian nations and Central Europe do extraordinarily well, and this often includes the women from these nations. This isn't uniform, however; Japan has only put a single woman on its team in recent decades. However, she happened to be an exception that supported the authors' contention that gender has nothing to do with it, since she was that team's top scorer.

Money and a large starting pool of talent also seem to have little impact. Bulgaria and Romania consistently did well, despite their small populations and economies. Meanwhile, none of the Western European nations were able to consistently score well over the last few decades. The US was an informative exception; it frequently did reasonably well, and the teams it sent often included women. But those women were often from Asian or Central European countries and, in many cases, had received much of their mathematical training overseas.

The authors conclude that the scarcity of women at the highest levels of math "is due, in significant part, to changeable factors that vary with time, country, and ethnic group." They estimate that, globally, the lower bound for female achievement would see them account for somewhere in the neighborhood of 20 percent of the highest honors, even without compensating for the cultural issues they face.

With that in mind, they attempted to identify the cultural issues that were holding women back in the US. For both males and females, family culture played a big role, as the children of first-generation immigrants from Asia and Central Europe did well; so did Jewish students.

Since the gender gap first appears on math tests in middle school, the authors examined factors that might protect students form social pressures at this age. They found that high achievers often came from towns populated by the faculty of nearby academic centers; several of them were also home schooled, which isolates them from social pressures. Finally, many of them engaged in extracurricular mathematical education, such as programs hosted at local colleges, and some even engaged private tutors.

The authors argue that we can't afford to have social factors rob us as a society of the people who have the most to contribute to math, either directly or through its application to science and technology. To foster a better environment, they provide a list of recommendations. Some of these are fairly standard—improve early math education and foster a better public image for math. But they also argue that we need to expand access to high schools dedicated to high achievers in math and science and provide greater access to programs that place advanced public school students at local universities.

Due to the small population of high achievers, a lot of the information in the study appears somewhat anecdotal. Still, its authors present a compelling case that, even at the highest level, mathematical achievement is largely a matter of cultural priorities.