How much of the math gender gap is due to culture?

Natalia Nollenberger, Núria Rodríguez-Planas, and Almudena Sevilla have a paper on this topic (click on the AEAweb pdf), presented at this year’s AEA meetings, the core result is this:

This paper investigates the effect of gender-related culture on the math gender gap by analysing math test scores of second-generation immigrants, who are all exposed to a common set of host country laws and institutions. We find that immigrant girls whose parents come from more gender-equal countries perform better (relative to similar boys) than immigrant girls whose parents come from less gender-equal countries, suggesting an important role of cultural beliefs on the role of women in society on the math gender gap. The transmission of cultural beliefs accounts for at least two thirds of the overall contribution of gender-related factors [emphasis added by TC].

I believe we will learn more yet when women stop improving, relative to men, at chess.  But so far that has not yet happened.


This is actually a pretty weird result. Overall, gender *inequality* is a strong predictor of having *more* women in math in the home country. Gender equity is positively correlated with an increase in both male and female math scores, but the effect is stronger for males.

But among the children of immigrants this effect completely reverses. That's pretty weird.

Well, this study shows gender inequality associated with more women in math; but in the introduction they refer other studies showing the opposite (even one study saying that including or not the muslim countries can change the signal of the relation). Thet even say that the results for the effect of gender inequality are "not reproducible".

Then, I think we can's say that «Overall, gender *inequality* is a strong predictor of having *more* women in math in the home country.» (seems more a kind of noise that can appear in some studies but not in others).

My vague impression is that girls often study harder than boys in some male chauvinist Muslim countries. Math is too much hard work for boys, so they treat it as a girl thing.

Anecdote: an Iranian female recently became the first woman to win the Fields Medal: Maryam Mirzakhani

"an Iranian female recently became the first woman to win the Fields Medal: Maryam Mirzakhani."
In the same group of medalists, there was a Brazilian. Brazil has produced as many Fields Medal winners as all Womankind and the Third World put together.
As the old anthem goes,
"Among all the nations of the Universe
Shines brightly that of Brazil
Among all the nations of the Universe
Among all the nations of the Universe
Shines brightly that of Brazil."

False, Shing-Tung Yau is Chinese from a period where China was very much third world, and Ngo Bao Chau is Vietnamese.

Seriously? The guy from Princeton and the guy from the University of Paris? I knew things had been though on the USA and Europe lately, but I had no idea...

If you're going to move the goalposts from "place of birth and education" to "where the person works", then Artur Avila did most of his relevant work in the University of Paris also. He left IMPA after his PhD and only very recently (when rumors of his future Fields medal were flying) did he get a position at IMPA again.

All the available data (mostly anecdotal because of the narrative) is that young muslim women do far better than the young men in school but then mostly don't enter the workplace for cultural reasons and/or fear of retalitory violence.

About the time the young men might want to enter the workforce they're just not qualified to do anything beyond menial work or selling ethnic food.

To be clear I'm talking about western europe.

Also young muslims males don't much like having women teachers.

Like the Cardassians in DS9.

How do they control for genetic differences across countries? (Or is it an implicit / explicit assumption that there are none?)

Under what model of cognitive achievement does genetic factors influence men and women differently?

Why shouldn't they? I think you can easily think of a model in which for example climate differences have meant that women and men have evolved different skills in different places in the world.

For several thousand years, women have done most of the farm work in sub-Saharan Africa due to light soil, climate, disease burden, etc.

Is it all that surprising that black schoolgirls tend to work harder than black schoolboys?

In evolutionary terms, women everywhere probably did most of the farm work, since it's a direct extension of women being the people finding and gathering the roots and berries. In a transitional period, it would make sense for women to tend the gardens while the men went out to hunt. The time period during which men worked the farm and women stayed home to sew is probably more the abberation than the norm.
Only when agriculture got intensive enough to involve plowing of large fields would it make sense for the men to do the work exclusively. I'm not sure that agriculture in sub-saharan africa ever got to that point. Many of these tribes were still basically in the stone age when European colonials arrived.

"The time period during which men worked the farm and women stayed home to sew is probably more the abberation than the norm."

I wonder if that time period even existed; at least in Portugal works like harvest are stereotypically female (google has more results for "ceifeira" than for "ceifeiro")

Isn't it kind of aberrant among mammals for humans to figure out how to harness male talents in...anything useful?

What about lions?

I wonder if that time period even existed; at least in Portugal works like harvest are stereotypically female

I wonder if it's dependent on some particular technological development, like the harnesses needed for animal-driven ploughing. Does ploughing with a team of oxen require more upper-body strength maybe? Or maybe some areas aren't suited for ploughing, so there's typically more use of hand tools?

It wouldn't surprise me too much that once you stop having to worry about the next tribe coming over and murdering you in your sleep that the need for men dropped precipitously.

Plowing is indeed an upper-body strength job.

I think you're confusing social evolution with genetic evolution.

I am not sure I understand your question. Men and women are different because of genes. Intelligence has a huge genetic component.

"Men and women are different because of genes. Intelligence has a huge genetic component."
Men and women are, on average, different in generic ways (men tend to be taller, stronger, etc.). Why would Afro-whatever women be more intelligent (or conscientious than Afro-whatever men--why the gap between than should be larger than between White men and White women)?

a) it's not about intelligence in general terms - it's about specific characteristics, in this case maths
b) because they have lived Afro-whatever women and men have lived in different environments compared to white men and women for thousands of years and there is this thing called evolution

Again, what does it have to do with the differences between men and women and, more to the point, with the alleged differences betwee Black men and Black women being bigger than the ones between white men and white women? Exactly which "environment" selected women who are more skilled (or at least more hard-working)mathematicians than their mates?

Men and women are the same species, and as a result, they have the same genes. Being mammals, the only difference is females have two X chromosomes, while males have one complete X chomosome and one cut down version called the Y chromosome. Male and female bodies are, on average at least, different environments and this can and does result in different expression of genes.

Emil, it's not possible to control for genetic differences across countries. First of all, we don't know what gene alleles contribute to maths test scores. Secondly, if we did know what gene alleles contributed to differences in maths test scores we'd have to be confident they either vary little in their contribution in different environments, or have a good idea of how much they contribute in different environments. And thirdly, we'd have to know the frequency of the these alleles in different countries. That last one would be the easiest to work out.

But fortunately, or unfortunately from the point of view of our being able to survive things like the Black Death, there isn't much genetic variation amoung humans. We had quite a genetic bottleneck not very long ago in evolutionary terms. So, unless there is some reason to susptect that our recent evolutionary history may have affected the incidence of gene alleles for maths test scores among some groups, there is unlikely to be a large genetic component to maths test scores difference between populations.

Maybe there was a strong eugenicist movement sometime in history which subjected people to maths tests and killed anyone who didn't do well, and then erased it from the historical record?

Just grasping at straws, trying to think up things that would cause strong differences in genetic components of maths test scores.

I'm pretty skeptical. Just about any level of maths skills is good enough to plant rice, take goats for a walk and make babies.

Maybe being bad at counting contributed to higher birth rates as people failed at using the rhythm method? Actually that would probably go the other way, as on average pre-industrial peoples used control over fertility to improve their chances of survival and the total number of descendants they left.

Anecdotal but I'm Singapore - where gender equality and meritocratic achievement are about as good as it gets - female students often top the class in my kids' schools and produce the highest so called PSLE scores in the country before entering secondary school.

Nanyang Girls High School is repeatedly the hardest school to enter every year as well. Jim Rogers sends his daughter there.

Boys don't mature as fast as girls (source needed) and they grow longer ( lazy link).

I wonder how much of our views of boys and girls, in a true meritocracy, would be informed by the genders' respective growth rates.

Politics means that I likely won't ever know the answer, sadly.

Is someone preventing you from conducting a study of it?

Practicality is preventing him from conducting a study. Politics is preventing academics from conducting a study.

ACademics may conduct whatever study they want. Those with tenure are particularly insulated from whatever politics might come into play.

No. You need IRB approval for such a study and you would not get it. The weasel word to look for is "group harm". From the standard textbook for IRB committees (Elizabeth A. Bankert, Robert J. Amdur, Institutional Review Board: Management and Function, 2006), page 135:

"Examples of research that caused group harm were the many studies comparing the average IQ of various racial groups, especially..."

I have tenure, do genetics studies, and I would likely not get permission for Mike's envisioned study, even if I funded it myself.

Women have no need to evolve problem-solving ability, they can just manipulate men into solving their problems.

The only problem with this superb technique is than manipulable men are idiots for problem solving.

Unless the solution is a bigger hammer, applied with brute force, followed by beer on the deck then sex with their women. Incentives do matter.

Technical intelligence (to solve problems) has little correlation of social intelligence (to avoid being manipulated). And even social inteligent men could want to be manipulated, if the reward is goog (see alan's comment)

Honey, when you guys hog all the power and resources, then manipulating you IS a problem-solving skill, the only one left to us.

How is that not problem solving?

It's a different kind of problem solving, no?

"Honey, can you take out the trash?"

"No you manipulative bitch!"

Men manipulate themselves to solve problems for women.

And when that fails they just manipulate themselves.

Hmm, looking at Figure 1 (where they got a correlation coefficient of .22 showing "more gender equality in the country of ancestry, the higher the math scores of second-generation immigrant girls relative to boys) and Tables A.1 and A.2, it does seem like all the countries with a large gender gap (including in a "girls get higher scores" direction) were obtained from countries with a much smaller sample size.

Figure 1's correlation coefficient was obtained by averaging across countries first, then producing the linear correlation. To some degree that means that the conventional conception of statistical confidence doesn't quite work. (By averaging first, the 46 respondents with Korean ancestry, who had a very large gender gap, exercise outsized influence on the correlation compared to the 1,762 respondents from Turkey, who had a small gender gap.)

The results in the other sections are based on an individual level and seem much more robust.

Very good.

My commenter "Simon in London" is a lecturer at a college with a highly international student body. He says that among his Middle Eastern, African, and white English students, the females tend to work much harder than the males.

Countries like the United States and northern Europe are unusual in having a certain percentage of males who like hard intellectual effort.

I was TA in a math dep in NL and I can tell you that some of the hardest working guys we had were Asians (also including south asians).

This cryptic comment by TC is a mystery to me: "I believe we will learn more yet when women stop improving, relative to men, at chess. But so far that has not yet happened." - improving, relative to men, meaning catching up with the men? Or getting better at chess faster than men? The latter is true only because fewer women took up chess. The former seems false to me, with the outlier being GM Judith Polgar.

I have noticed a trend however: women that are good in chess seem to be hot (attractive), with a couple of exceptions best left unsaid. The young Judith Polgar (and her two sisters) was an example of this, and there are numerous Eastern European examples. For a sample, Google Images "Irina Krush" and you'll get her (above average in looks) and her hot chess friends.

You seem to have not followed chess closely in the last 15 years or so. In Judith Polgar's era there were only a couple of female GMs, now there are more than 20. Polgsr herself no longer plays, and would not be the strongest female player if she did (though her peak rating is still the best ever by a female player). Female players are still far weaker than male, but they are catching up for sure.

Are they catching up, or are they improving from a low standard?

A long time ago people suggested maybe women would turn out to be faster marathoners because their times were improving so fast as more women got into running. They postulated all sorts of just so stories for why that would work (like higher body fat stores and pain tolerance designed for childbirth). But of course it didn't happen and no-one says it anymore.

They're still way behind. Now that Judith Polgar has retired the best female player is Hou Yifan. She is an exceptional female chess player , Note that she is ~ 100 point clear of the field of the rest of the women but she is still ~ 70th in the world rankings ( male and female). The second strongest woman ( Humpy Koneru) would probably rank ~ 200th in the world. The cultural component is small. There are simply more exceptional high IQ men due to the IQ distribution of women and men ( larger standard deviation for men).There are many countries where there are no special obstacles for women to play chess.
As for the GM title, there are many GM these days you can be at ELO 2500 and have one.
So perhaps the average female rating is moving up, but there are no more exceptional female players than 30 years ago ( just one)

> The cultural component is small.

This has to be a joke as the Polgar children were an experiment to see if environment could produce genius.

Actually, no, as both of their parents are exceptionally intelligent (I think they are both university professors). For influence of the environment, you have to look up Rahm Emanuel's (adopted) sister.

Someone finally mentioned the difference between male and female IQ std. deviation. This fact has been know for about as long as IQ test were in existence (about 100 years), and has a huge influence on the percentage of men/women that are on the top in various fields, including top chess players, Nobel prize winners etc., but is almost never mentioned in public discussions.

As a female in a STEM field I am pretty much certain that the math difference is almost entirely cultural.
Consider that in grade school in the US girls do at least as well as boys in math. The gap only appears in high-school years when girls suddenly become consumed by social status and dating. The latter is a biological phenomenon in part, but it is shaped by culture. In our culture, girls who are good at math generally are not popular or regarded as sexually desirable. Girls quickly learn that being a math "geek" is not cool, and will not get you dates. So (unless they are an uber-dork, like me) they stop focusing on getting good grades in math.

In addition, there really is no biological reason why girls would be less good at math. According the the usual story of evolution in a hunter gatherer environment, the men would hunt big game, while the women would gather berries. The women were also responsible for tasks like sewing and mending clothing. Neither of these tasks is less mathematical or less demanding of abstract reasoning skills. It's hard to relate anything in primitive society to abstractions like algebra or calculus. It's not like the men were explicitly calculating the flight trajectories of their spears. And remembering the best spots for gathering berries and roots requires good navigational and mapping skillls and a good long-term memory.

I don't agree with the last part. I think the mere fact that hunting men had to navigate larger distances whereas women were typically closer to their (possibly nomadic) home meant that men required better navigating skills than women. (Women of course developed other skills)

Navigation over long distances vs. detailed memory of the local terrain are different skills but one is no less "mathematical" than the other.
Personally, I have awesome navigation skills. I once found my way home independently from over four miles away when I was 6. I have sixth sense for which direction is North. I can navigate by car without a map or a GPS router just by heading in the right direction and looking for landmarks (provided that the road network is interconnected enough and I don't get trapped in a subdivision).

You are also a woman in STEM so perhaps this explanation does not apply to you.

"Navigation over long distances vs. detailed memory of the local terrain are different skills but one is no less “mathematical” than the other."

Err no. Long distance navigation requires abstraction, the capacity to find specific select landmarks while ignoring the rest and having a good sense of direction and distances (more or less what you yourself describe). Detailed memory of the local terrain requires, well detailed memory, and very very little mathematics.

And ADBG is correct, the fact that you are as better than the average man at mathematics and STEM says very little about the average woman.

What the heck does finding specific landmarks while ignoring the rest have to do with unstanding algebra or calculus?
It's an extreme stretch to try to relate this to a different in math ability. Also, as noted below the women would also need long-distance navigation skills in nomadic groups, because the whole tribe is moving around constantly, and the women could become separated, or need to make side trips, or just need to remember where on the annual trail the various food spots were located. They have to know the whole terrain the the group travels just as much as the men do.

Abstraction is a key feature to both mathematics and navigation

How is remembering landmarks "abstraction" ?

I didn't say that. they were two items I listed (together with others) as required in order to be able to navigate

The suggestion that only long distance navigation is mathematical seems to suggest that only spatial reasoning is mathematical. That suggestion is a joke.

Sincerely, a (male) combinatorialist who has the worst spatial skills imaginable.

If there are any non-cultural difference in overall math ability, then you can't use an exceptional case as a benchmark. So, HM, you need to look at the average female, not yourself.

Well, from the girls I knew in grade school, I can't attest that I was so much dramatically smarter than them. In the sixth grade there was a whole group of girls who were good at math (we were a year ahead of everyone else) and we were all competing to see who could get the best grades. The difference between me and them was that I was poorer and more nerdy and they were more rich/popular. I can't say they didn't keep up with it, because I moved shortly afterwards, but the sense I got was that most of the other girls my age simply became a lot more interested in fashion and dating and stopped being interested in math. It wasn't some cognitive barrier they hit where they couldn't keep up. They just lost interest.

Er Wasn't dramatically smarter ...

HM: it's not necessarily about being smart in general or working harder. It's about being good at the specific topic of mathematics. I can use myself as an example; I am a very numerical guy (engineer who works in an analytical job etc) and most women I know tend to be less numerical than me (my wife is one of them). That doesn't however mean that they are less smart than me. On the contrary they are often (not always) much better than me on other things which also require intelligence. As an example I believe (this is purely anecdotal) that women tend to be better at men at memorising details whereas men are better at abstraction. This tends to, on average, mean that:
- women are better at e.g. chemistry, history, languages and can be pretty good at law
- men are better at e.g. mathematics and physics

Also, if you are nomadic, then you move around a lot. So a woman would have to remember where the berry patch was near that spot they camped three years prior. I actually don't see any reason why the women wouldn't need long-distance navigation skills. The whole tribe has to move, repeatedly. People get lost and separated and have to catch up with the rest of the group.

Who knows what was important during evolution - many things happened, some didn't have any inherent reason. How do you KNOW that there is no biological reason for the difference? Perhaps there is. And same question for the others - how do you KNOW that the navigation problems etc. result in different average mathematical ability? They could. Or not. How do you know?

I don't know. I'm only saying that the biological story doesn't actually support a difference in math ability. Those arguing it does seem to me to be confabulating reasons to support a conclusion they are predisposed to believe. And I havn't personally observed anything that would support innate differences in math ability from my own experience.

Fully agreed (also on the critique on some of my posts) and it illustrates the original point I wanted to make (how can the authors of the study conclude that it is about culture and thus (implicitly) not about genetics / other factors)

The just-so story behind "men are better at math" reinforces the cultural myth. One may was well ask how the culture KNOWs this.

FTAOD: I was agreeinf with Andy

Algebra is different from earlier math instruction.

Carol S. Dweck thinks that girls develop motivational patterns that lead them to not enjoy challenging subjects that don't come relatively easy:

I think it is more likely that some students just find algebra easier than others and that may include more boys than girls.

Algebra was the hardest math I ever encountered. It was a paradigm shift for me. Before and after than point I found it easy, up until the point it became tedious. The 2nd semester of Differential Equations was just an annoying case of memorizing a bunch of very specific case formulas with few novel concepts and wasn't really anymore complex for someone at that level than an Accounting class would have been.

I learned algebra in the sixth grade, which was before puberty. Maybe that's the difference.
When girls (and boys too) hit puberty they become less interested in academics and more focused on socialization and dating. Girls hit puberty a bit earlier than boys, so if the concepts are introduced during that time period that would generate a gap.

This may well be true but (assuming it is) I am not sure that you can distinguish the genetic impact from the cultural one based on only this. In other words; is it some genetically developed trait that makes girls focus on certain things (e.g. mating) when they hit puberty and does this genetically developed trait differ between different origins or is it about culture? I don't think you can distinguish the two through the study the blog post refers to. Therefore I question how the authors can conclude that it is about culture, and not (also) about genetics (and possibly also factors that I cannot think of now).

I'm suggesting that in some cultures, math ability (or disability) is is considered a more "attractive" quality in a mate than others. Thus when girls hit puberty, in a culture that values math ability in mates, the girls would work harder at being good at math. In a culture in which math ability is not valued in a mate, the girls will not work as hard. Also, it's not just about dating, but also general social status. Does being good at math make you a high-status female or does being head cheerleader? Do the other girls admire math ability or ability to apply makeup effectively?

(Note that in some cultures being good at applying makeup would one you an appalling slut, so there is definitely a difference here. )

Even if all of the above is true, I am still not sure how you can come to the conclusion that there is not also a genetic impact

I'm sure there are biological genetic differences between men and women, including those that affect intellectual capacities.
I just don't think that math ability is really one of those differences.


I have a couple thoughts pertaining to your comment:
1. "Culture" is different from "Institutional Oppression." That's part of what the PDF points out. It's one thing if schools say girls cannot sign up for math classes, it's entirely another thing if girls themselves select out of math classes.
2. This paper suggest Culture is the major driver, NOT Institution.
3. It's not clear we can change culture as easily as we can change institutions.
4. It's not clear that we SHOULD change Culture, at least to the extent that every field is equally represent among all genders. Culture is "Way of Life." If I was talking about eradicating any other kind of "culture" in recent Immigrant communities, someone would ask if I am voting for Trump.
5. It's not clear who has "ownership" of changing cultures WRT STEM. Silicon Valley? Schools? The federal government? Churches?
6. We all know what this is really about: jobs @ Silicon Valley, or other cushy jobs where women are under-represented.
7. Given point 6, how predictive are grade school and high school tests of high performance LATER ON? It's one thing to pass a high school science test, it's another thing entirely to make Google: does greater male variance in intelligence exist and mean virtually all geniuses are male?
8. Are we even having the right conversation? Is this about STEM in general or women in STEM? If 99% of girls drop out of STEM and 98% of buys drop out of STEM, that creates an "uneven" gender pool of 2:1, but the big benefits is dropping the 90+% dropout rate regardless.
9. Are the women who refuse to pursue STEM in any way negatively affected by that decision or do they simply find remunerative employment and life satisfaction in other fields anyways?

Well that's gobbly-gook. Looks like the website killed my formatting. :(

It’s one thing if schools say girls cannot sign up for math classes, it’s entirely another thing if girls themselves select out of math classes.

Culture can be oppressive. If girls are self-selecting out of math classes because the culture is telling them that they will be undesirable mates if they are good at math, then they aren't self-selecting because they're just naturally less good at math. There is nothing inherently more beneficial about a culture that tells girls they are supposed to learn how to do their hair, apply makeup, and wear fashionable clothing over one whihc tells them to be good at math. I see no reason why THAT aspect of the culture ought not to change. Are beauty magazines and barbie dolls an important and valuable aspect of the culture that we don't want to get rid of?

As to "ownership" of the culture, I'm not advocating any particular policy. I think things are going in the right direction. Cultures change because people voluntarily adopt different norms. Lately there's been a whole "sexy geek girl" concept poping up in popular culture, and that sort of thing is a sign of some evolution on the subject. To some people, it IS "cool" for girls to be good at math.

"We all know what this is really about: jobs @ Silicon Valley, or other cushy jobs where women are under-represented (...) "it’s another thing entirely to make Google."
One thing at a time. Both the paper and Hazel are talking about girls trailing boys at High School Math. If and when this gap disappeares, one can argue their women (and most mathematicians) just lack the magic elusive quality that makes people "make Googles". As of now, the question remais, why do the gap exists at High School in the first place?
"how predictive are grade school and high school tests of high performance LATER ON?"
A lot, I hope. We use those things to decide who gets what kind of education.

Yes, culture can be oppressive. We're talking about American culture, where women make up the majority of post-secondary students. "Boo hoo, I wasn't popular in high school either" - is my response.

I'm not whining about not being popular. I'm pointing out that girls are subject to different social pressures than boys.
I'd also argue that the reason American kids in general are worse at math is because BOTH boys AND girls in America receive the "math isn't cool" message more than they do in other countries, especially in Asia. Both phenomenon are due to cultural messages rather than innate ability.

The "greater male variability" hypothesis is standing on much firmer ground than the idea that males, on average, are innately (much) better at mathematics imo.

Boys become consumed by social status and dating around high school too.

In our culture, girls who are good at math generally are not popular or regarded as sexually desirable. Girls quickly learn that being a math “geek” is not cool, and will not get you dates.

That wasn't my experience in high school. There, boys could have cared less, they just want girls to look good. About the teenage girl social structure I would have been surprised if that were true. It seemed to me that the popular girls were smart and unafraid to show it. It's probably different in other places, my high school was majority White and mostly middle to upper class. But I don't think you can say that that's how the culture in general works.

Girls have higher grades in all subjects, math included. This reflects not greater math ability,(they have lower ACT math scores) but greater effort.

I have no doubt that women can perform as well as men at elementary math or high school mathematics. However for logico-mathematical ability there are more exceptional men than exceptional women. That's a consequence of the IQ distribution for men and women: same mean but higher standard deviation of IQ for men vs women ( more dumb men , more highly intelligent men).
It's not cultural. It;'s obvious when you look at fields that require high intelligence. Top mathematicians are males, top physicists are male. The few women that have a Nobel prize in physics ( Marie Curie) or are exceptional in Mathematics ( Emmy Noether, Sophie Germain earlier ) stand out because they are exceptions. There will be some but as expected much fewer. Similarly in Chess it's obvious, very few exceptions.
The cultural meme is political correctness

Well, for most of human history women did not get as good education as men did, so that's hardly a surprise. Only recently have women been as well-educated as men and continuine into college years. Also, only recently have women been in any way encouraged to pursue careers outside of traditional teaching and nursing type occupations. Which brings us right up to the fact that the culture still tends to direct women more towards non-mathematical careers. Now some of that might be because women become less *interested* in math for various reasons , some of which are rooted in biology, but that doesn't mean that women are innately less good at math. After all, becoming exceptional at something requires sustained interest and practice. It could be that those women who DO maintain an interest in mathematical subjects beyond grade school are just as likely to become exceptional at it.

Larger brain size in males should be expected to be a very important biological reason for greater math ability in males. In terms of caloric demand, brain matter is very expensive and we would not expect males to have larger brains without an intelligence payoff.

@HM - you go girl! I personally think women are smarter than men. But the men, being physically stronger, asserted themselves in positions of power. It's like the mafia taking over an Italian town: once they resort to violence, who's going to stop them? As for abstract reasoning, it's just a male cultural thing: by analogy, notice the best chefs were women until men started getting into the field.

Also a society run by women--pace the Amazons of Greek mythology--are less likely IMO to start wars of aggression. Most women don't care about war (pace the Greek Revolutionary hero "Laskarina Bouboulina ...heroine of the Greek War of Independence in 1821, ... a captain from Hydra island")

If interest in chess also has cultural components, then I think changes in the field will not be particularly telling.

Girls don't go into STEM fields for the same reason they don't go into Alaskan crab fishing: Because they don't have to.

Women may earn less than men, but they control the overwhelming majority of household spending. This makes their decision to work less hours in less difficult fields look quite rational.

Men go into hard (STEM) and dangerous (crab fishing) jobs because they have to. Women from repressive societies go into STEM because it's their only way out of that society.

@sam -good points, though as an aside I suspect that Alaskan crab fishing is dangerous because: (1) the Bering Sea is shallow, 100m or so depth, and big waves form from shallow waters as any mariner can tell you, (2) the industry is 'informal' and lots of 'mom-and-pop' ships with shoddy equipment compete dangerously with one another for a limited catch. Here in the Philippines, artisan gold mining is dangerous (like in Africa) since the miners are informal, lack safety equipment, and compete with one another rather than cooperate.

There is a huge difference between being "good at math" in the sense of getting A's in school and good scores on your SATs and having the chops to contribute original research (or be a chess grandmaster). It's quite possible that cultural norms may influence the accomplishment level for the first few standard deviations but I doubt that cultural changes will fatten up the Fields medal tails much.

Your conclusion is the opposite of what common sense dictates. Just getting a tenured research job at a top mathematics department is an INSANELY competitive proposition. So, so much has to go just right for it to happen. It's much more likely that small fluctuations (a little more prejudice here and there) will change a very sensitive result (getting a research job at MIT) than that they will change a less sensitive one (getting As in school).

Getting a Fields medal is a level of achievement completely outside the scope of most people's experience. Not only does your entire life have to go right, but research-wise you have to be at the right place at the right time and know the right people and be working in the right questions in the right field. Literally a butterfly flapping its wings could take away your Fields medal.

As a professional mathematician, there is no doubt in my mind that cultural shifts will have a DRAMATIC impact on the number of female Fields medalists.

Nonsense and more non-sensical as it proceeds.
We need to stop evaluating people in variable terms, 'this better than that', 'gap', etc. It is lazy. Find a 'good enough' baseline value, provide underlying assumptions, and proceed.
We need to stop categorizing people into essentially arbitrary and self-reinforcing 'niches', despite deep cultural entrenchments. Why not the blondes vs brunettes or short vs tall, etc. As with advertisements, stereotypes go away when not noticed, discussed, or debated.
MR needs to be a bastion of forward thinking not a refuge of the sensational and populist.

"Forward thinking" sounds very un-thinking.

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