Mathematical achievement doesn't fit a gaussian, and neither do the gendered groups of your conception. And if mathematical ability were distributed as a Gaussian, and genetic, women couldn't be ascending so rapidly.

See for example Lisa Sauermann, the all time best performer in the international math olympiad:

http://en.wikipedia.org/wiki/Lisa_Sauermann

As I wrote four years ago:

http://news.ycombinator.com/item?id=65494

The thing is that intelligence isn't some kind of nice, statistically normed quantity. There's more to most variables than a mean and a standard deviation -- so I don't know why people seem to always think that you can restrict a discussion of intelligence to such concepts.

...

But intelligence isn't a gene. Researchers have, since the time of Galton, tried to find a simple, biological basis for genius. You know, memory capacity, reaction times, brain size, brain structure convolution, etc. They haven't found anything -- literally everything has turned out to be a false start, even brain size, which, has been shown, within families does not even predict g.
In the mid ranges, there are greater standard deviations, yes. But every single normed test is normed on a sample on the order of 1000. They're designed for regular people. The designer of the Weschler has adamantly opposed the use of IQ tests for anything other than clinical settings, for this reason. It's just no good at drawing conclusions on the extremes of ability.
A better guide might be actual performance. The IOI this year had more girls than ever before -- 11. That's nearly 300% more than last year, where they had 4, and one medal. They are:
Emina Bukva (Bosnia and Herzegovina) Constanza Contreras (Chile) Anna Currel (Spain) Romina Huenchunao (Chile) Vaiva Imbrasaite (Lithuania) Taksapaun Kittiakrastien (Thailand) [Silver] Sepideh Mahabadi (Iran) [Gold!] Radwa Metwali (Egypt) Katie O'Mahony (Ireland) Phitchaya Phothilimthana (Thailand) [Silver] Ye Wang (USA) [Silver]
Sepideh Mahabadi had one of the best performances of anyone. If you're familiar with IOI scoring, only the top 1/12 are to get golds, and 2/12 to get silvers, thus 1 gold and 3 silvers out of 11 implies that they did at least as good as the boys, and in fact somewhat better.
Were the 'standard deviation' explanation correct they should have, instead, had 0.4 girls earning maybe 0.01 medals. It just doesn't work.

And three years ago:

http://news.ycombinator.com/item?id=244449

Why is it sexist to say we show up more frequently in science departments because we have also been designed by evolution to be better at math?

Because compared with bench-pressing, claims of mathematically ability being better in men (and partially ordered, to boot) is seriously jumping the gun.
We know what's involved in a bench press. We understand how testosterone stimulates the production of muscle. We are nowhere close with mathematical ability. We have no theory of mathematically ability -- we really don't know what it means, or if the simplest metrics are even useful for higher level math. We have no experimental results, because we have no controlled variables. We have few pieces of data, none of which are conclusively disentangled from cultural and historical influence.
In the past two decades, the number of women scoring highly on the IMO, the IOI, the Putnam, and SMPY has gone up by roughly a factor of six. Doubtful that the number of girls with 'math talent genes' have sextupled that quickly. Isn't this evidence that we should hold off on our conclusions?

And four years ago:

http://news.ycombinator.com/item?id=65524

"Brain size does not predict general cognitive ability within families"
http://www.pnas.org/cgi/content/abstract/97/9/4932
You can't discount that IOI statistic becuase it's an outlier. Every single participant at the IOI is an outlier in cognitive ability. Do you know about the theory of outliers?
There's this thing called the central limit theorem. It says that if you have a lot of small independent variables, randomly assigned some value, then the mean of all these variables (or, by the same token, the sum of the variables) is distributed approximately normally. But suppose the variables are not small, or they're not independent. Then the central limit theorem doesn't hold, and what you have, almost all of the time, is an outlier -- that's why there are often many more outliers than you'd predict in a given population, using a small sample.
Now, I'm not saying that g is zero. I said that psychometrics is a non-science, in the same sense that a lot of the social sciences are non-sciences (you can find papers which try to show a causal effect of insurance regulation on premium prices, ignoring profits entirely, for example).
The fact that g is non-zero can be readily explained by the following simple observation -- most academic subtests, including IQ's, rely on skills that are either practiced as a group, or on skills that are shared between subtests. One example is focus, in general. Another is visualisation. Another is working memory. And so on and so on.
Many of these skills are also practiced in situations, like school, where if one does well in one area, they do well in another. If you're the teacher's pet, you get more attention. If you're known as the bad kid, you're immediately discounted (and I've been on both sides). If you're poisoned against a learning environment, you just won't put any effort in.
So it's no mystery to me that g is non-zero. The point is that the field of psychometrics is totally absent of content. There's no objective test for the validity of a test, for example -- the best they have is g-loading. Over the years, this means that tests have become higher and higher g-loaded. Now this could mean that the tests are getting better, or it could be that the subtests only look different, they are becoming more similar in content.
I've been studying these tests, the actual tests, since I was twelve. It didn't take long before I figured out how poor they were at answering research questions, or questions of individual ability. If you get the chance, try to look up the history of the Stanford-Binet, or Terman's kids, or actually take a look at the scoring method behind most of these things. They're totally full of crap...