No, for the simple reason that it's just not possible to control for all the cultural factors, so you can't do a study using a control group that does not exist.
However, we DO know that cultural attitudes about gender stereotypes have been changing over time, and we've seen that the performance gap changes over the same time period. We also know that cultural attitudes about gender stereotypes are different from culture to culture... and sure enough, we find that the performance gaps reflect those different attitudes as well.
So basically, we've proven beyond reasonable doubt that stereotypes play a significant role in gender differences in math, and in chess. We know that as attitudes skew closer to equality, the performance also skews closer to equality. That's a closed case.
All good points. I agree with most of what you said.
The question I have is whether there is still gender stereotyping going on in math today (leave chess aside for a moment), given that girls outperform boys in school. My limited view is that there is no longer gender stereotyping in math today. In our high school, there are as many girls in honors math as there are boys, and perhaps even more girls get As than boys. But interestingly, when it comes to competition math, the boys still dominate. And nationally, on the SAT, the mean score for boys is about 30 points higher than girls. I can't explain that either.
All that's left now is to hypothesize about an imaginary culture in which no gender stereotypes exist, would some biological factor pre-select males for dominance at the very highest echelons of math and chess?
My hunch is: no.
I have no opinion of what "truth" actually is. I would happily accept that there are no differences, or that there are inherent differences.
