With regards to top mathematicians being male, it's understood that the variance in male IQ is much greater than for females, so men end up over-represented in both the top and bottom tiers of intelligence.
But society factors do have an effect. In one study with asian american women asked to do a difficult math test, those primed to remember that they were asian did better than those primed reminded that they were female: http://pss.sagepub.com/content/10/1/80.abstract
I'm sorry about nitpicking, as I think your heart is in the right place, but I believe you're incorrect regarding the variance in male IQ vs female.
It is a conventionally believed thing, but I think it is conventionally misunderstood. The IQ tests don't even have validity well outside 2 s.d. (how could they without much more testing outside the sample?) It's not even a particularly valid statistical idea to be contemplating very high IQs beyond the normed values of the tests (how are they supposed to calibrate the scale?) nor is there good evidence that whatever the measures are that we're given are normally distributed. I have personally known several people with "measured IQs" above 200; that is statistically not supposed to happen. There are a lot of conceptual and practical problems with the idea of IQ.
Regarding mathematical ability, please see this paper by the former USA IMO coach Titu Andreescu.
They make a very good case for cultural specific factors in the development of mathematical skill, at least as far as Olympiad maths goes. The presence of women in the competition varies dramatically depending on the culture (and even the team)
> IQ tests don't even have validity well outside 2 s.d.
An easy way to measure above +2 z-scores is to administer an IQ test at a much earlier age than usual. That's what the famous Study of Mathematically Precocious Youth did. It has proven to be super effective even at the extreme right tail of the curve.
> I believe you're incorrect regarding the variance in male IQ vs female.
Belief doesn't enter into it. Many studies report higher male variance and it is widely known in the psychological community. While people try and attack this as a recruitment pattern problem (see [2]) or try to prove that it is partly cultural (see [3]), only people unfamiliar with the literature would outright deny it.
To be clear, I think that the stated belief that there is higher male variance is possibly true. I think it has a good chance of being false, but that's not the point. Statistically, for example, the male population has a greater chance of genetic disease and indeed lives shorter life; this is supposed to be in part because of the lack of two x-chromosomes, which, as a mosaic, both express themselves in the ordinary female body.
What's emphatically not true is assuming a normal distribution -- specifically out to the tails. It's not even clear that the variance doesn't turn around at some point to have higher female variance at the top end of the curve. It is extremely easy to synthesize violations of a normal distribution of ability for female subjects -- there seems to be a powerful threshold effect that, in addition to cutting out large numbers of young women in certain cultures in mathematical competition, tends to preferentially spare the very top. If things were normally distributed, of those women that compete in mathematics competitions, almost none would make it to the very top of the competition, mathematically. That has been proven empirically false.
Few scholars directly assert that the normal distribution is a perfect model for intelligence, but people seem to take the implications quite seriously.
An easy way to measure above +2 z-scores is to administer an IQ test at a much earlier age than usual.
Your graph shows that this study administered a SAT Math test at a much earlier age, not an IQ test.
The study itself says: "Before age 13, these participants scored within the top 0.01% for their age on either SAT mathematical reasoning ability (SAT-M 700) or SAT verbal reasoning ability."
I'm unconvinced that this shows either way if "IQ tests [don't] even have validity well outside 2 s.d"
Thanks for sharing data, that's a pretty good case for cultural factors making up a large part of the discrepancy, as I suspected.
As for the IQ test variability, do you have any papers or research on that? Citation 19 in this wikipedia article doesn't seem to actually address the issue of variance, only the question of absolute ability: https://en.wikipedia.org/wiki/Sex_differences_in_intelligenc...
If I just suggest a reference without a suggested change in "point of view" you're likely to get very confused.
May I recommend as a starting point:
Be skeptical about the idea of a single number characterizing intelligence. We don't even do that for the weather.
Next, learn about the genesis of the entire IQ concept, and later efforts to academically justify past ideas about intelligence. The first really popular writings were by Galton
Afterwards, Binet and Simon, and Terman (at Stanford, the Stanford in Stanford Binet) get at it.
Back then, IQ was really a "quotient," "mental age" divided by actual age. The concept only really makes sense in a developmental context -- after all, how are we supposed to believe that a "developmentally baseline" 23 year old is actually the pinnacle of intelligence?
Only after this did the Weschler Adult Intelligence scale come in. Read (some) of the criticisms Weschler had of the Stanford Binet here.
This was devised as a clinical scale. This is still one of the only widely administered and normed tests. The norming takes place only over a few thousand individuals. The types of abilities typical in an international IMO context are simply unlikely to show up in these cases, much less register statistically in the test!
and the mathematics behind what suggested it, "Factor Analysis," which has many capabilities but is worthy of many criticisms, including particularly that there is no obvious weigh to norm or weight any of the tests, so ultimately you end up with a judgement call for which tests to include, and how much to gather from their results.
A far more enlightening study of genius, I have found in the book "Human Accomplishment", by Charles Murray. When you're sample is all of those humans who have left a mark on history, and your measure is impact, and our remembrance of it, you learn far more about the heights of human capability, I believe, than by scoring how well people match patterns to a preconceived idea of the "right answer" on a test.
> Intelligence exists and is accurately measurable across racial, language, and national boundaries.
> Intelligence is one of, if not the most, important factors correlated to economic, social, and overall success in the United States, and its importance is increasing.
> Intelligence is largely (40% to 80%) heritable.
> No one has so far been able to manipulate IQ to a significant degree through changes in environmental factors—except for child adoption—and in the light of these failures, future successful manipulations are unlikely.
> The United States has been in denial of these facts. A better public understanding of the nature of intelligence and its social correlates is necessary to guide future policy decisions.
And who then went on to argue in Human Accomplishment that the most important humans were European males based on a biased application of Pagerank on modern encyclopedias written in English?
This is the response to the reply above; I'm unable to directly respond to a comment that deep.
I thought similar things about Charles Murray, and I don't think that the Human Accomplishment book is without flaws -- it has many. Nonetheless, the whole book is worth reading. Honestly, I think it faces some serious facts on the distribution of impact on civilization.
The fact that some cultures, like classical Athens and Elizabethan and Enlightenment England, have had an outsized impact on modern science and civilization, that we have a massive debt to particular thinkers from Europe of the past few centuries, is a fact I think a serious study of great scientists needs to come to terms with. That being said, past contribution is not a good indicator of genetic, racial superiority! We should do well to ask what made those contributions possible, from nurturance, to growth, to self belief, and belief in the idea of progress.
Just FYI the lack of comment button is based on time, and is meant to prevent deep threads that become flamewars, or devolve into arguing over semantics.
> nurturance, to growth, to self belief, and belief in the idea of progress.
I'd also guess: encouraging risk taking; valuing radical ideas, or at least individualism; and a safe environment, or at least a sufficient military.
But society factors do have an effect. In one study with asian american women asked to do a difficult math test, those primed to remember that they were asian did better than those primed reminded that they were female: http://pss.sagepub.com/content/10/1/80.abstract