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Cathy O’Neil: Women in Math

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By Cathy O’Neil, a data scientist who lives in New York City and writes at mathbabe.org

A study recently came out which was entitled “Can stereotype threat explain the gender gap in mathematics performance and achievement?”. One of the authors created and posted a video describing the paper, which you can view here.

As a preview, there seem to be four main points of the paper and the video:

1. The papers on stereotype threat normalize with respect to SAT scores which is bad.
2. Evidence for stereotype threat is therefore weak.
3. We should therefore stop putting all of our resources into combating stereotype threat.
4. We should instead do something easy like combating stereotypes themselves.

Before we go into the details of the paper, though, we need a bit of context. For that reason, this post is split into three parts. The first addresses a meta-issue, namely that of the “null hypothesis” in this discussion. A frustration that I have, and that I think is shared by many of the women I know in math, is that the (often unspoken) working hypothesis is that in fact women are just not as talented, and it is somehow up to us women to prove this otherwise, presumably by convincing men that we’re geniuses.

The authors of the above paper fall prey to this disingenuous line of thought, by proclaiming stereotype threat is an insufficient explanation but not offering any alternative explanations. This sets up an implied false dichotomy: if it isn’t explained by such and such, it must mean girls are dumb.

Not only does this undermine serious intellectual debate, but it often turns people off from entering the debate in the first place, because they sense the manipulative nature of the discussion. But that’s a pity, since, with the correct assumption, namely that women and men have equal talents but things are holding back women, we could probably make lots of progress on what those things are.

The second part is directly related not to the paper but to the blog post which referenced the paper, which changed the conversation from “math performance gap” to the question of “why there are no women math geniuses”. This is an interesting twist, and in my opinion warrants addressing separately.

In the third part I argue directly against the paper and its conclusions.

1. The Null Hypothesis

Needless to say, I think the onus is on the scientific community to prove that women aren’t as mathematically talented as men. In other words, I do not accept the defensive position that I need to prove we are as smart: the null hypothesis is that a series of effects, one of them stereotype threat, explains any perceived difference in talent.

In his now famous lecture at NBER in 2005, Larry Summers putatively discusses the issue of why there are fewer tenured women in science and math departments at top universities. However, if you read the transcript, you will note that, when he gets to the “different availability of aptitude at the high end” part, he does us a favor of sorts by admitting what his underlying working hypothesis is: that girls aren’t as good at math. His argument using standard deviations of test scores is ridiculous, especially if you consider 1) how differently women do versus men on the same test in different conditions, 2) how much that difference has itself changed over time, and of course 3) the question of what the tests themselves are measuring.

To test why this null hypothesis is so damaging, my friend Catherine Good suggested the following thought experiment: imagine if he’d gone up to the podium and, instead of saying that women aren’t all that good at math and it was partly explained by when he’d given boyish toys to his twin girls that they took care of them instead of constructed things, he had instead substituted gender with race. Here’s the passage:

There may also be elements, by the way, of differing, there is some, particularly in some attributes, that bear on engineering, there is reasonably strong evidence of taste differences between little girls and little boys that are not easy to attribute to socialization. I just returned from Israel, where we had the opportunity to visit a kibbutz, and to spend some time talking about the history of the kibbutz movement, and it is really very striking to hear how the movement started with an absolute commitment, of a kind one doesn’t encounter in other places, that everybody was going to do the same jobs. Sometimes the women were going to fix the tractors, and the men were going to work in the nurseries, sometimes the men were going to fix the tractors and the women were going to work in the nurseries, and just under the pressure of what everyone wanted, in a hundred different kibbutzes, each one of which evolved, it all moved in the same direction. So, I think, while I would prefer to believe otherwise, I guess my experience with my two and a half year old twin daughters who were not given dolls and who were given trucks, and found themselves saying to each other, look, daddy truck is carrying the baby truck, tells me something. And I think it’s just something that you probably have to recognize.

It begs the question, why did the women in kibbutz quit working on tractors? The way Larry tells his story, he makes it clear he thinks that it’s because the women wanted it that way (thus his story about the twins). But surely it is as plausible that: 1) Men, having a vested interest in proving their manhood (which they do and in cultures around the world leads to certain types of work being seen as “manly”) weren’t keen about day care duty and/or 2) women were hesitant to cross the lines of gender stereotype (it might lead them to be perceived as being masculine, or even worse, emasculating). And it also isn’t hard to imagine that parents ooh and ahh more when small children play with what are perceived to be gender-appropriate toys and are quietly or even vocally uncomfortable when boys play with dolls and girls play with trucks.

One last word about the null hypothesis and why I’m so devoted to this issue: when I and two other girls (and, as it happens, no boys) in the 6th grade did well enough to go into a special, advanced 7th grade algebra class, my (female) teacher brought us up to the front of the room and told the three of us “I don’t see why you would challenge yourselves like this anyway since you are girls, and you won’t be needing math when you grow up.” I was the only one of the three of us to actually choose that class, and I was the only girl in the algebra class. One of my friends was one of two women in a class of 45 students studying artificial intelligence at Yale. She was expecting praise for being one of only two students to get a program to work on a particularly tough assignment. Instead, she was accused by the professor of stealing the code from her male classmate. She left the major. Until stories like this become rare, or even uncommon, I will assume that there’s too much cultural influence to figure out the real story.

Going back to Larry Summers, his lecture did two things: 1) it breathed new life into the age-old stereotype that women aren’t as good at math as men, and 2) it attributed that difference to an underlying innate ability difference- that is, he conveyed a “fixed ability mindset” regarding math (more on mindsets below). As the leader of an educational institution he introduced the two ideas that together are like a powder keg: they can undermine women’s feelings of belonging in math, which in turn informs their mathematics achievement and intrinsic motivation to remain in math.

Now more about Catherine Good. She talked at that same conference where Larry Summers put his foot in his mouth; in fact she was the speaker after Larry at that conference, and she was talking about her paper that gives evidence that the above “powder keg” message tends to push women out of math (but Larry didn’t stick around long enough to hear her talk, unfortunately). She is also an expert on stereotype threat and helped me look at the study. More on her thoughts below, but I still want to talk about the concept of “genius.”

2. Women and the Concept of Genius

Let’s define, as one of the commenters does from a post, a “genius woman in math” to be any woman who has won a Fields Medal. Since there are no women who have won Fields Medals (versus 52 men), this is a pretty tight definition. I would argue, and I might expand on it in another post, that even without the above definition, the concept of “genius” is a social construct which is rarely if ever applied to women, except perhaps after they’re dead. Please comment with counterexamples if you know of any.

So here’s what I think. There are lots of reasons that women don’t win Fields Medals. I will name a few.

• Fields Medals are awarded to mathematicians under the age of 40, for some reason, and women mathematicians typically do good work into their retirement age, whereas men usually do their best work young (this also explains why Harvard has so much trouble hiring women- by the time they are convinced the woman is a genius, she’s 55 and has grandchildren and frankly probably sees the offer as tokenism).

• The commenter who defined a “math genius” as a Fields Medalist said that it would be an objective measure. But Fields Medals are awarded by a bunch of guys who decide what’s important and who’s responsible for the important results. In other words it’s a political process.

• Women don’t care as much about winning Fields Medals. This matters, because I know of men who explicitly worked on problems in order to win the Fields Medal (you know who you are).

• It’s a serious and bizarre case of narrow focus.

• Why is math genius defined so narrowly? I would personally define it more broadly (a topic for another post), and there’d be plenty of women geniuses. With my definition, though, I’d guess that women who are geniuses have lots of options and they often choose something they consider more personally rewarding than an academic job.

• Women’s intelligence may also manifest in different ways: note that most of the assholes on Wall Street are men. This kind of makes sense since women are typically not as driven by testosterone and competitiveness. This doesn’t mean they aren’t geniuses or that they couldn’t have done the work the men on Wall Street did (my experience proves that).

• The Fields Medal distorts the mathematical process itself, by implying that there’s a single superstar who swoops in and solves the problem that all the other people were incapable of doing. In fact mathematics as a field is an enormous collaboration, a scientific project, where everyone depends on the community around them for coming up with questions, defining the “interestingness” of questions, and giving context to results. The idea that there’s one winner out of all of this, or even one metric by which we could measure such a winner, is silly. See this post from Quomodocumque.

• Another point about genius (in any domain): research is showing that to truly express one’s genius takes thousands of hours of practice. So genius may be a latent trait but will never be expressed without many hours of hard work. This point is very often lost and is related to women in that their apparent geniusness depends to a large extent on how supportive their environment is for all that investment of time.

3. The Paper Against Stereotype Threat

I am finally ready to address (with Catherine’s help) the issues of the paper in question, which I will repeat:

1. The papers on stereotype threat normalize with respect to SAT scores which is bad

In fact the author “discards” a bunch of stereotype threat studies on these grounds. However, it is totally standard to normalize with respect to some other metric (would you rather we didn’t normalize to anything?), and in fact it essentially penalizes the studies, since it has been shown that stereotype threat is in play even for the SATs. On the other hand, the standard for normalizing (this is called “including a covariate”) is that the groups being compared should not differ significantly in the covariate, presumably because it’s harder to argue that your are in fact correcting for that aspect. Because men and women sometimes do differ significantly in SAT scores, including them as covariates could be a technical violation of the rules of conducting a so-called ANCOVA.

Is this what the author is complaining about specifically? Did he, for example, check to see if the samples in the “discarded” studies actually differ in the covariate? It seems he’s making the assumption that they did, but it’s not clearly stated that they did. It’s certainly not a given that the men and women in these studies did differ in the covariate, and he needs to make that precise. If they did not, then there’s no valid argument against using SAT scores.

2. Evidence for stereotype threat is therefore weak.

There is ample evidence that stereotype threat is very real. Keep in mind that the authors of this study have not shown evidence against stereotype threat, but have simply complained that they don’t like the existing studies for it. And their standard for what “replicates” the original study is overly stringent- they only wanted to include studies that found significant interactions between gender and condition. Interactions are easiest to find when you have a “crossover effect” (e.g. males are higher in condition A but lower in condition B), but often we find “span effects” in which the males and females may be equal in condition A but differ in condition B. This can also be an example of stereotype threat. For example, in a paper written by Catherine, she didn’t find a significant interaction (males and females performed equally in condition A) but when the stereotype threat was reduced, women outperformed men. To discount this and other studies as not providing evidence of stereotype threat simply because an “interaction” wasn’t found is playing games with statistics.

3. We should therefore stop putting all of our resources into combating stereotype threat.

Nobody who studies stereotype threat claims it explains everything. It is part of a larger picture. The good news is that there are interventions for it (described below).

4. We should instead do something easy like combating stereotypes themselves.

The idea that it’s “easy” to combat stereotypes is completely naive. There are tons of ways that stereotyping is understood to be very difficult, if not impossible, to get rid of. Some of them have to do with an evolutionary need to simplify first impressions of people (i.e. categorize) so that we can tell if they are an immediate threat to our safety. This may be the most baffling part of the whole thing, because the authors should really know better.

I want to end on a positive note, because the news is actually pretty good. There is a way to combat stereotype threat, and I’ve tried it and it works. To understand it, it helps to think about the way people think about intelligence itself. As a simplification, people either think that intelligence is fixed and rigid (you’re either born with it or you’re not) or they think that intelligence is malleable and can be learned and practiced.

It turns out that if someone believes the latter “malleable intelligence” view, then they work hard and are hopeful and stereotype threat is to a large extent alleviated. Whereas if they’re convinced of the former mindset for intelligence, the effect of stereotype threat is more pronounced. In situations where the stereotype is salient (“girls are bad at math” is salient when taking a math test), the situation itself can convey a mindset of fixed ability and all the hallmark responses that go along with that mindset then follow. To encourage a malleable view of intelligence can help combat that fixed view and thus the threat of the stereotype.

The way I used this information was as follows. I started a class in teaching proof techniques at Barnard College (there were both Barnard students and Columbia students in the class). At the beginning of every class for the first two weeks I described how mathematicians aren’t born knowing how to prove things, but rather they learn techniques, and practice them until they are proficient. Note I wasn’t directly confronting or addressing stereotypes, but rather setting up the mindset where the studies have shown stereotypes have less negative power.

The class went great, and is still going on. I will post soon about my experiences starting that class and others like it.

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118 comments

  1. pegnu

    “note that most of the assholes on Wall Street are men. This kind of makes sense since women are typically not as driven by testosterone and competitiveness.”

    While I agree that there exists many woman who are as good as men at math, and that Summers is an idiot, it is rather peculiar to bring in ridiculous stereotypes about men in piece about how stereotypes hold down women.

    1. LeonovaBalletRusse

      pegnu, but this is the ATTITUDE toward women in math by men in math; because the men compete so much against each other, the must (and do) dismiss women and their ideas in math, and they do a lot of Male Bonding vs. the women in math, especially if they are really good. They just cannot abide the thought that a woman might win a fair competition against them, so they join together in eliminating women/girls at the pass. I mean, it’s bad enough to be upstaged by a guy when you’re a guy! to be upstaged by a woman is just an insufferable failure and insulting.

      It is so painful for women to excel in one of these *High Testosterone* fields, that only the most determined survive. When I was in retail brokerage, I had to listen to sexist filth all day long, as *the guys* carried on with their Macho banter to cover their anxiety and dream of being/remaining Top Dog. My defense mechanisms nearly ruined me, even though their hostility was not directed at me. It is the *locker-room* environment that makes it so difficult to excel in these fields, especially in math at an Ivy or at MIT, which must be the most misogynistic place on earth, even considering Larry Summers.

      Let’s face it: These men don’t want women to rise to high places in Their Club. I mean, what would it mean if a Dame became a “Big Swinging Dick”? Aren’t they all on Viagra from adolescence? What does this imply for women who are good at math?

      1. mjay

        I’m so tired of moron American feminists playing victim Olympics everywhere they stick their noses. The Israeli and Chinese women in my topology courses in college did extremely well and didn’t piss and moan like every freeloading American feminist liberal arts major.

        You want to see real sexism and bigotry? Go to divorce court where men are subject to legislation the same women’s rights bigots lobbied for and built on for years, the same legal codes that denies men their children and livelihood at the drop of a hat.

        1. LeonovaBalletRusse

          I agree with your second paragraph. Your first tells me you need to work on your hostility, due to heaven knows what traumatic experience from American women, because it can’t be good for you to live with such hatred in your head.

  2. craazyman

    well I was an advanced program math geek in high school before I encountered mental problems, and the best math teacher I ever had was a woman. No question about it.

    However, she was a lesbian, which I’m not sure proves anything.

    I think everyone can count and all math (mostly) is just forms of complicated counting. Sometimes counting backwards like division. Sometimes forwards like multiplication. Or sometimes thinking of shapes like geometry. and then converting them to things you can count and draw — that was the most fun I ever had in school, geometry that is.

    It may be some woman shy away from math because they see all these geeky introverted guys with greasy hair and think “Sh–t, get me away from that stuff!” haha.

    Or the math teachers. Most are not-very-articulate geeky guys who have no fashion sense at all. Lets’ face it, the the normal female would prefer not to have to deal with these personalities. That seems reasonable to me. Not everyone is borne to adore the wordless glory of imaginary numbers, dandruff, mismatched jackets and ties, and ugly shoes. It makes you want to become an art history major. hahaha. or maybe something like “communications”. Oy vey. what a circus humanity is.

    1. F. Beard

      As usual, I posted my own remarks before reading others yet we have come to more or less the same conclusion!

      1. craazyman

        serioulsy Beard, your right.

        the average math geek is like the dude who speaks chinese. if you let yourself be impressed by the strangeness of the form of expression, you’d think the guy (or girl) was an Einstein.

        but if you know the language it’s like “Whoa man I gotta pee, where’s the bathroom?”

        yeah a genius for micturation. hahaha.

        that’s not to sayy there aren’t titanic geniuses in math. there are. and i see no reason why a female can’t become one any more than the next guy. everybody can pee. haha

    2. pegnu

      I disagree. Being good at math is completely different from being good at mental arithmetic. These are quite different skills.

    3. LeonovaBalletRusse

      My Trig teacher in high school (I was a math major) was a brilliant, straight-talking elderly woman who had graduated from Mt. Holyoke. She made everything so easy, while very interesting, that she performed magic: her lessons opened minds with wonder, like the yellow rose in Dante’s “Paradiso.” All other math teachers in the school were males, and they were excellent also.

  3. F. Beard

    I, for one, think mathematical ability is overrated. Look at what the “geniuses” on Wall Street and the banking system have done to us. And look at double entry accounting which is used to justify what is essentially counterfeiting. And look at the insane calls for a balanced budget for money ISSUERS!

    So even if it were proved that women are less capable on average than men wrt math, I’d say “So what? Thank God we are not all limited to a form of thinking that has led to disaster.”

    1. Nick

      Math also brought you: everything that NASA has done, from moon missions to satellites in space, weather forecasting, engineering of all disciplines that has built your infrastructure, car, and house…and the computer on which and the internet through which you are ranting about the overvaluation of mathematics.

      Absolutely terrible.

      1. F. Beard

        Strawman. I am not attacking math. I am attacking the whole ideal that economics can be amoral at least to the extent of ignoring “Thou shalt not steal.”

    2. LucyLulu

      I don’t believe it takes much in the way of math skills to work on Wall Street. Accounting and such takes no more than simple algebra.

  4. Conscience of a conservative

    We constantly hear that men and women have brains that are wired differently. And while this does not and should not mean a man has to be better than a woman at math, it does suggest that gender biases are not out of the question when looking at aptitutde or ability to excel on average in one area versus another. And it could very well mean that females excel in one branch of math, and men in another or that they solve problems differently. Why not embrace the differences.

        1. lowfiron

          wiring would not mean you could not successfully solve a problem but you might have a different approach. even if the wiring could be perceived as a ‘shortcoming’ it would be hard to define that ‘shortcoming.’ then there is collaboration and corroboration. then to as stated, a web of support which is a cultural condition or personality effect. women have the ability, no doubt.

          1. F. Beard

            Agreed. I am not knocking anyone’s inborn abilities.

            Yet wisdom is vindicated by all her children.” Luke 7:35 New American Standard Bible (NASB)

  5. santcugat

    I don’t think “girls are dumb” is a fair characterization of anyone’s position here. For normal men and women, almost everyone agrees that there isn’t a biological basis for any claims of superiority.

    The question is about what happens at the extreme end of the distribution. My feeling is that sample size is so small that no matter what theory anyone comes up with, it’s likely to be unprovable.

  6. skippy

    For the first time in my life, I believed it possible, to witness two individuals out of time phase and some how… accomplish to insert foot[s into mouth[s, chew on it and like a cherry on top, put an aperture through the hole mess.

    Congratulations beard and craazyman!

    Math had no intention, it was men and some women that did this.

    Skippy… amends mathbabe. I for one, hope your work goes well and look forward to more posts.

    1. F. Beard

      Math had no intention, it was men and some women that did this. skippy

      I intended to be very good at tennis but it made no difference; my younger brother was born with TALENT and I wasn’t.

      Anyway, I said “on average”. And “on average” men are inferior to women in some ways.

      1. skippy

        “Thank God we are not all limited to a form of thinking that has led to disaster.”… beard

        Skippy… you can never keep your augments straight.

        BTW the overwhelming majority of people involved – perpetrated this finance mess would claim, to be Christians or sect of it. Math encourages thinking, you don’t.

        1. F. Beard

          you can never keep your augments straight. skippy

          You remind me of the British in the American Revolutionary War who complained the Americans were not fighting “according to the rules”.

        2. F. Beard

          BTW the overwhelming majority of people involved – perpetrated this finance mess would claim, to be Christians or sect of it. skippy

          Don’t forget Jews. But at least Jews have an excuse for usury since it is permitted for them to collect it from “foreigners” in Deuteronomy 23:19-20. As for Christian bankers, they appear to have no excuse.

          1. skippy

            Thousands of years, repetitive behavior and you make delineations, off setting the blame[?], the jews?

            “Don’t forget Jews. But at least Jews have an excuse for usury since it is permitted for them to collect it from “foreigners””… beard.

            To reiterate… “Thank God we are not all limited to a form of thinking that has led to disaster.”… beard

            Mathematics was not the culprit as you assert (form of thinking), it was people, people that were *limited* in their thought… by profit and only profit, their profit.

            Skippy… whither you like it or not, their part of your religious sect. Have fun cleaning house.

          2. F. Beard

            Mathematics was not the culprit as you assert (form of thinking), skippy

            I did not assert that math was the culprit except insofar as people have limited themselves to that mode of thinking.

            A little moral thinking such as acknowledging that theft of purchasing power (so-called “credit”) is not a sound basis for a money system would have prevented this mess.

          3. F. Beard

            Have fun cleaning house. skippy

            Not my call since I don’t belong to a church but I imagine that bankers are going to be far less popular in churches soon.

          4. skippy

            Credit?

            Try raw power, power over others, power to do what you want, when you want, to whom you want. To tell people what to think, when to think it and for YOUR own reasons.

            Skippy… Money in any form, just sucks you into their game. Honest and ethical money hahahahahahaha! But live it we must…sigh.

          5. Mansoor H. Khan

            Skippy,

            “whither you like it or not, their part of your religious sect. Have fun cleaning house.”

            Everybody walks around with some kind of a mental model to navigate the world day to day whether their mental model has a label or not.

            Though, you are correct about cleaning house. The whole point of this life (on earth) is to do our part in “cleaning house” while realizing that anywhere near perfect clean house cannot be achieved here (our left brains cannot deliver on the vision of the right brain).

            But our right brain does help us see beyond the finite to the infinite to some degree and by extrapolation (faith) we can work toward perfection (possible after death as in heaven).

            mansoor h. khan

          6. F. Beard

            Try raw power, power over others, power to do what you want, when you want, to whom you want. skippy

            Human power is administered through other humans. Caligula thought he was a god till he was assassinated. Stalin was supposedly smothered to death by Khrushchev with a pillow. Officers have been fragged for incompetence by their own men.

          7. skippy

            I have had my ears receive, in many forms, profit comes before people… in my life, credit played no part in their thought[s.

            No one sitting at the big table would even consider your solution… period, and first of all you don’t *have* a seat at said table.

            Skippy… from some very big players, T1 stuff. BTW nice job you have as religious singularity (caves have broadband?), all the up side and zero down side exposure.

            PS truly unsurprising of you and cazzy to be first to carry out your women[s agenda. Try http://www.youtube.com/watch?v=Bf2LB0IG1xo

          8. F. Beard

            profit comes before people… skippy

            The purpose of profit is to benefit people. I advocate common stock as a means to share wealth and power.

            No one sitting at the big table would even consider your solution… period, skippy

            That’s their problem, not mine. I did not cause this mess.

            and first of all you don’t *have* a seat at said table. skippy

            Don’t want one.

          9. skippy

            “The purpose of profit is to benefit people. I advocate common stock as a means to share wealth and power.”… beard

            Skippy… data please, observable and repeatable observations, from more than one source. Your vapors don’t count.

        3. LeonovaBalletRusse

          skippy, why do you get into these quarrels? Don’t you know *a priori* how they are going to end? Resist the temptation. Your free-standing comments are much more interesting. Don’t feed the …Oh, well.

          1. F. Beard

            Haha! One would think we could agree that the counterfeiting usurers are the common enemy and agree to fight among ourselves later (except I have no plans to do any other fighting later).

      2. craazyman

        I too wanted to be better in tennis than I was. In my case I had no coaching, which doesn’t mean I would have ever been good enough to be a collegiate or pro competitor (probably not) but I will never know.

        I suspect females are often unconsciously socialized to avoid math because it’s perceived as being “masculine”.

        A former girlfriend of mine, the love of my life actually, was in this category. She was (presumably “is” wherever she is) highly intelligent and immensely creative — but she could not do math to save her life.

        It was not a matter of intelligence or aptitude, IMO. It became clear to me that it was because she felt at some unconscious level, that it assaulted her femininity. She was from a nation where women have very strict social roles, even though she grew up as an American. I suspect there was a heavily unconscious socialization thing going on there, but I’m not sure one can ever “prove” this.

        1. ajax

          I’d suggest adding a game theory perspective. Everybody
          is trying to “optimize their life”, roughly speaking.

          If in one age, men seek outwardly “less successful” women,
          then a single heterosexual woman wants to optimize on two
          axes: a) finding a good mate in mariage and b) finding
          success and/or fulfillment in geeky pursuits.
          If positioning to improve on a) involves positioning to
          accomplish less on axis b), and vice versa, there will be
          a trade-off.

          So there are all these axes of desirables, but stereotypes
          mean that there are trade-offs. How much of a trade-off
          will a given person accept?

          In math., I have very high regard for Emmy Noether and
          Sophie Germain. I wonder if they ever wrote
          autobiographies …

          1. MyLessThanPrimeBeef

            Ajax, you beat me to it. Here is what NOVA said about Germain:

            Math’s Hidden Woman
            By Simon Singh Posted 10.28.97 NOVA In this excerpt from Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem, Simon Singh recounts the true story of Sophie Germain, an 18th-century woman who assumed a man’s identity in order to pursue her passion—attempting to prove Fermat’s Last Theorem.

            Let’s hope we stop propagating this ‘women can’t do math’ sterotype.

            Another one we can do without is, ‘Men, lacking intution, can not be powerful goddesses.’

          2. MyLessThanPrimeBeef

            By the way, the Sophie Germain prime numbers are quite elegant, none of that brute strength of men-discovered prime numbers.

            Is it stereotyping to say women are better with odd numbers and men with even numbers?

            I guess it is. We should avoid that.

          3. LeonovaBalletRusse

            ajax, it’s smart to master game theory and use it in daily life. BUT our reactionary society does not encourage it, preferring *life according to myth* instead.

        2. LeonovaBalletRusse

          craazyman, the most telling studies are those that demonstrate what happens to girls at puberty: they do an about-face and *play dumb* so they won’t suffer ridicule and rejection from boys. What kid wants to invite that?

    2. F. Beard

      And your “flattery” of women is ironic too in that many are quite happy with “womanly stuff” even when they are capable of much “more”. Example: A co-worker I knew, a beautiful red-headed physics major, would not use a George Foreman grill (the obvious way to cook steaks since it does both side at once) because she liked to stand at the stove and flip the meat herself!

      Anyway, vive le difference!

        1. ambrit

          Dear Bagbalm;
          Now just hold it there Sweetcheeks! There certainly are Coloureds at our countryclub! And they all wear nifty uniforms too!

        2. F. Beard

          Hah! I am “white” but I doubt I could stand a country club for long if they are anything like a meeting of Republicans.

  7. Jack Straw

    Two of the most decent academics I ever met were Institute for Advanced Study guys. They are also two of the most powerful intellects I ever met, and exceptional in not being terribly maladjusted. But, they never won Field Prizes, either.

    It’s oddly coincidental that this discussion is taking place right after the Super Bowl, because sports is an area where a very similar discussion takes place all the time, in the open.

    Generally I hate using analogies, but here it seems right: in two head-to-head Super Bowl appearances, Eli Manning has PROVEN than he’s a BETTER quarterback than Tom Brady. This argument is being made as I type on a thousand call-in shows, and EVERYBODY everywhere KNOWS it is … what? And, is he really better than his brother, the all-time grind?

    Here, the analogy works because it shows an alternate area of extremely high achievement and the differences in ability at the top. Eli Manning shows, to me, that it’s better to be lucky than great, and I suppose to the extent he himself understands that – and I think he more-or-less does – he really is great. I think.

    1. craazyman

      so true. that N England defense is just a hair too weak, even for Brady to overcome. I am sure Eli knows it and knows he would have lost if he’d been on the other side.

      Not to say he isn’t great though. he is.

      1. NotTimothyGeithner

        Brady looked off except in the hurry up drive at the end of the half (and even the game; there just wasn’t enough time) and the next drive out of the half. I think the offensive coordinator shake up may have hurt the Pats from week to week. His Welker throw was high. He was late on throws to Branch or Branch was off. I think McDaniels may not have had a feel for the plays he was calling because Brady had time to throw.

    2. ambrit

      Mr. Straw;
      I believe it was Napoleon who remarked that he’d rather have a general who was lucky rather then smart.

    3. LeonovaBalletRusse

      I guess he was *lucky* to have Archie Manning for his father. He went into the family business in turn, and has made the most of it.

  8. Roger Bigod

    I’m pretty sure I agree with the goals, but I found the posting frustrating because I’ve never heard the term “stereotype threat”. And the linked paper didn’t explain it. Reading it was like signing up for an advance calculus class without having encountered any trig. I was like “what are these sine and cosine of which you speak?”

    1. M

      I thought exactly the same thing re ‘stereotype threat’ (say what?), and came to comments specifically to see if anyone else mentioned it.

      My personal experience re science and math: as an adult I discovered a talent for those things, but as a kid – even through college – there were so many ‘GIRLZ KEEP OUT!!!’ signs I just didn’t bother, because the world is full of lots of interesting things and I just went to play elsewhere.

      However, one of my nieces is currently majoring in math at a pretty good school. She is a very girly girl, too.

      1. LeonovaBalletRusse

        M, a girl today faces a different path: she CAN be brilliant, ballzy, and beautiful, and get paid well for her personality/talent/skill/work ethic. BUT have you read about these *winners* at Princeton, playing the whore to the troops and proud of it? What’s with that? Are they training for positions at The World Bank/IMF?

      2. ScottS

        Software engineering is one of the most intrinsically female-friendly fields ever if we’re talking stereotypes. It is, unfortunately, full of “NO GURLZ ALOUD!” signs.

        Where I think the lack of women in Computer Science is most glaring is usability and requirements. The user experience is under-rated. It’s assumed to simply fall out of a good implementation. I’ve never even experienced an interview that asked usability questions — just hairy-chested programmer questions, and the occasional software lifecycle question.

        So there’s no emphasis on usability, an area where women (stereotypically) could excel — to the extent that it’s not even tested for. There really isn’t even a word for it outside of academia, and it’s looked-down upon, I’m sure, since it doesn’t rake in the defense dollars.

        And start-to-finish, software is, or at least should be, a very social endeavor. It really suffers from the lack of female participation.

      3. spooz

        My girly daughter was embarrassed when she had her picture posted outside the math office as “math student of the month” sophomore year. Later, after she transformed herself into platinum blond pompom girl, she experienced a loss of self esteem; kids who didn’t know her assumed she was an airhead because of her appearance. She is now going through yet another transformation, and is talking about embracing her inner geek. Whether she changes majors from psychology to engineering remains to be seen.

    2. Mel

      Wikipedia. It’s the brain freeze that can be caused by fear that one is going to screw-up and make one’s entire group look bad.

  9. KelvarOlvar

    I for one found the whole basis for the argument flawed. The person writing this story sets out with preformed conclusion that men and women are the same down to the last micron the only difference possible being cultural. Our anatomies being male and female are very different. We have so many differences biologically on so many levels not just brain that are normal. Why can we not accept that possibly there are differences when it comes to extreme degrees of functionality as being at least partially innate to the sex of the person? For example it is a well accepted fact by doctors that males can stand to have way less fat as a percentage of body weight on their body then women and still be healthy in order for a woman to get down to the same fat percentage as a healthy athletic male would put in jeopardy there reproductive systems. It would also interfere with there ability to reproduce. Why is it we are so ready to concede to innate biological differences as being possible in this case but not in brain functions.

    1. craazyman

      I’m no brain scientist but I think the processes of creative and analytical thinking that underlie high-level mathematical reasoning are not all that different from other forms of thinking.

      these would be pattern recognition from observation of reality, creation of metaphors and analogies, expressing of meaning through sytactical structures, the perception of self-consistent descriptive systems, etc.

      Much of these qualities are evident in other forms of expression, such as the visual arts, music and literature. I do not believe there is an inherently mathematical process of thinking that could be derived from the sexual orientation of a brain. However, this is just my own perception of reality, and not based on any “study”. I am way to lazy for that. hahah.

      1. Valissa

        I’m no brain scientist but I think the processes of creative and analytical thinking that underlie high-level mathematical reasoning are not all that different from other forms of thinking.

        While that sounds nice, I don’t think it’s true. Not all types of math thinking are the same. I learned this from my own experiences, but it took me a long time to come to that conclusion because I was predisposed to think all math was the same and relied on the same type of mental skills.

        I have a BS in Math (1980), however I did not decide on this until my senior year. My first 3+ years I had majored in chemical engineering followed by geological engineering. I changed both majors based on realizing what types of companies & industries I would be working for and where those were located. Since I had to take plenty of math classes (getting all A’s) for my engineering majors I thought it would be easy to switch over. For the most part it was, but not completely… as this story shows.

        The math class I had problems with was Real Analysis, which is basically organized Point-Set topology and related proofs. I was terrible at it. I had never had problems doing proofs before, so I was quite puzzled about this. So I asked one of my fellow students to coach me in this type of analytical proof. He was very charming in the way he laughed at my attempts at proofs so we started dating. Despite my best efforts I only managed a “C” in the class (my only C ever). Then the following semester we both took Graph Theory. I was amazed to find that I blew the curve on every exam typically getting 105 or 110 (>100 due to extra credits given on the exam) while the rest of the class members felt very fortunate to receive an 80. Needless to say my boyfriend was quite annoyed with me (fortunately keeping his good humor about it), which triggered converstaions to try and figure out why I was so terrible at Real Analysis and so naturally good at Graph Theory. We never came up with anything.

        Then some years after my BS I decided to go to graduate school for an MS in Applied Math (to go witht he computer skills I had acquired along with the Math degree). I was fortunate to arrange independent study in Topology with one of the Math Profs. The first part of the course was the same sort of Point-Set topology that I was so miserable at as an undergrad. I thought having the private tutor would make a difference. It didn’t. I studied harder than I ever had before, had the freedom to ask any question I wanted and could not GET IT. The first time in my life that I was not able to learn something and it was a very humbling experience. In the end my Prof thought that the best way for me to learn topology would be via math history of ideas, as all the great math insights came first and the hiighly detailed system of analytical proofs to back those ideas up came second. However that would not be a practical way for me to learn so that was a major reason I gave up on the Applied Math MS path.

        Later on when studying some neuroscience I was able to reflect back and figure it out. There are different types of intelligence and brains work differently. Perhaps some of that is due to gender influence, in a biochemical or structural sense, but I don;t think difference maens better or worse or capable versus less capable. I have no gender based opinion on why I was great at the type of thinking required to be successful in Graph Theory and horrid at the other type (which was kind of required to go further in the field at the time). The only thing I have realized is that Grpah Theory requires associative thinking, seeing connections between things (which I do well), while point-set topology is very detailed drilling down kind of definitions and mental constructs (which I do poorly adn very much dislike doing)… quite opposite ways of thinking.

        1. craazyman

          interesting story. so you’re a math chick! I might have guessed, given the clarity of your thinking, which I think propelled you toward math as much as resulted from the study of it.

          Oddly, despite your perseverance, I retain my belief that you could have “gotten it” with the right combination of words and ruminations, which can suddenly erupt in clarity after lenghty periods of total confusion, as you know, no doubt. This may sound improbable to you, and I have no doubt folks have aptitudes for different things, but it’s an illusion I will keep anyway. :)

          1. Valissa

            No, I think you are correct that I could have gotten it eventually. Especially if I had been willing to take the time to learn the history of math first, as my prof suggested… like from the book FB recommended below. If I had been driven to be a mathematician I might have stuck with it, but it was mostly a career move.

            At the time I was ~25 yo, had a full time day job (software engineer writing math apps for researchers) and active social life so it wasn’t worth it to me to spend huge amounts of time on this grad program. About the same time frame as I dropped out of the Applied Math program I took my first meditation class. That was much more interesting and sent me off in the direction of consciousness studies and “applied spiritual philosophy” instead. Life paths are unpredictable strange creatures ;)

        2. F. Beard

          In the end my Prof thought that the best way for me to learn topology would be via math history of ideas, as all the great math insights came first Valissa

          Excellent point. I had a math block myself till I read The Loss of Certainty by Morris Kline. That’s when it dawned on me that many mathematicians, in their desire to obtain greater rigor, be more abstract, and show off (?) have taken simple concepts and made them unintelligible to many. Also, it helps to see the flaws in thinking of great men since it gives one permission to be human one’s self.

          and the hiighly detailed system of analytical proofs to back those ideas up came second. Valissa

          And (according to Morris Kline) to have reached a dead-end anyway?

          1. Valissa

            I wish I had known about this book back then. The book was first published in 1982 and I think it was 1984 when I was trying to learn point-set topology from the prof, so it was in print at the time.

            Thanks for the recommendation… it looks fabulous! I just ordered a used copy from Amazon (after reading an excerpt) for my library :)

          2. LeonovaBalletRusse

            F. Beard, re Loss of Certainty: so it kind of turned into a pissing contest? That sounds like Wall Street, all right.

            Also, Nikola Tesla had something to say about those who get farther and farther from reality because they use mathematics alone to “prove” their theories. Tesla predicted that his way of comprehending reality, as a scientist studying empirical evidence, and going through the process continual of *trial and error*, history would vindicate his theories of the universe above the theories of mathematicians far from observed reality.

            Karl Popper (clip on YouTube) embraces the value of *trial and learning from error* in the study of reality throughout history, as those of more *scientific* than *mathetical* attitude stand on the shoulders of giants and carry on, in the time-honored *scientific* practice that has endured for centuries.

        3. Roger Bigod

          There’s a lot of “wooh” associated with the concept of hemispheric specialization, but one possibility that may be on point is visualization (non-dominant hemisphere) versus logical deduction (dominant). There was a study mentioned in the Notices of the AMS to the effect that professional mathematicians tend to be visualizers. Males tend to segregate lateralized abilities to one hemisphere or the other, while females tend to use both. As we all know, language goes in the dominant hemisphere, but Japanese use the non-dom for side the ideographic kanji. Males are supposed to have an edge on 3D visualization though, supposedly so the hunters could anticipate the paths of rocks and spears for bringing down prey.

          The French mathematician Bourbaki (actually a communal effort) based “his” whole compilation of modern math on point set topology. And in all his heavy volumes, there’s not a single graph or diagram. If you notice a copy in the library, don’t touch it. You’ll break out in hives.

          1. LeonovaBalletRusse

            RB, these are generalities, but studies have shown, that *by inclination*:

            Boys tend to want to see rather than hear, and to manipulate others and their environment, rather than to work out a satisfactory compromise with the same. For them *mastery* tends to be mastery of the not-them. They are driven to dominate or bend the not-them to their *Will*.

            As my observation of activity in Montessori “Children’s Houses” revealed, girls acted quite differently. The were attentive to others, and like to listen and share; they were spontaneous *hostesses* with the snacks; they were more cooperative with others. They competed only with themselves, doing the exercises with regard to their past performance.

            But America has *fixed* that. Computer games are turning all kids into boys. No problem.

            It is known that *Word* was invented for males, who could not compete with females in *Word-Perfect* functions, where sustained memory, rapid touch-typing, and mastery of abstract concepts and complex suites of activity on the fly were necessary for success. With Microsoft domination (male dominance), hunt-and-peck typing prevailed, processing a document moved from the abstract to the concrete manipulation of *windows* before one’s eyes.

            Microsoft *fixed* the problem. Windows and Word gives us all the limitations of males.

            America as a whole has become a world of force, of crude male dominance. Women are EXPECTED to find their place within this world. No subtlety at all.

        4. ScottS

          @Valissa,

          I flat-F failed my Non-Linear Optimization class twice before passing it with an A on my third try. I had an amazing professor the third time who simply explained it better (better for me, anyway) plus two sincere attempts at “getting it” behind me.

          Anyone can learn anything if they persevere. It may require a “lateral drift” as Robert Pirsig termed it.

        5. ChrisPacific

          Real analysis has been the bane of many otherwise smart and capable people, especially ones with an engineering background. Engineers are generally advised to avoid it like the plague, unless they plan on becoming mathematicians.

          I think a big determinant of successful learning in mathematics is how it’s taught, and whether the teacher is fortunate enough or skilled enough to hit on an approach that works for the student’s learning style. Concepts can literally go from impossible to trivial in an instant when the student has found an appropriate mental framework for them. I remember on one occasion a friend, despairing of ever being able to explain double integrals to a particular student, tried comparing them to a nested loop. The student happened to be a computer science major, and all of a sudden everything fell into place and it was obvious.

          So while I would agree with your “brains work differently” conclusion, I’d be careful about attributing too much of it to gender differences. (For example, the female friend that I described in my earlier comment aced real analysis).

    2. LeonovaBalletRusse

      You’re right, it’s the individual that counts. But the *bonding* in competition with the *Other* makes this almost impossible. Of course it is best NOT to talk in these generalities; but maybe that’s the only way to address wholesale prejudice.

    3. JTFaraday

      “would put in jeopardy there reproductive systems. It would also interfere with there ability to reproduce.”

      Their reproductive systems, not there reproductive systems.

      Their ability to reproduce, not there ability to reproduce.

      Sorry to be pedantic.

    4. LeonovaBalletRusse

      When it comes to suffering, Freud was right: Biology is destiny. For sure, women who elect not to reproduce must conquer biological destiny as breeders, and PMS is a trial from hell, but perseverance is the key to success for everyone.

  10. Susan the other

    I liked this post and hope there is a followup. It was fun to observe that the comments went from math, to sex, to football. Here’s what I wish: that math had more than one vocabulary. That it had equally precise but different sets of words to convey the logic of the problems. And I would love to see a different kind of study about aptitude in math, or any field: instead of studying the smart kids, study the dunderheads. Where do they tune out? I think they tune out most frequently when they get bored or they sense a disconnect in logic. And, I would just like to point out that there are lots more guys who are bad at math than good at it – but guys are never stereotyped as too dumb to learn it.

    1. LeonovaBalletRusse

      Excellent observation, Susan. Yet, how many men are in love with mathematics because math is *pure*, free of the *complications* of language? That’s why many *on the autistic scale* choose math as a study, as has been shown. This is the fly in the ointment, which may have less to do with *aptitude* than with natural propensity, because of the *forgiveness* it affords to the practitioner who fails to fully communicate via the spoken/written word.

      1. LeonovaBalletRusse

        Also, because of this, the rule of quants in Finance proved disastrous, because Economics and Finance is NOT comprehended by mathematics alone, as has been shown. These fields involve relationships and emotional states, but the quants in HFT still are trying to make Finance and Economics *pure*–as pure as their dream of The World According to Kurzweil and the Self-Correcting Algorithmic World of *Trade* free of *human complications*.

        Some might call such ambition *insane*.

  11. Hard Head

    Thanks for this article. I was always an excellent student, except for math. I have a working knowlege of arithmatic only because my Mom spent hours each weekend reviewing the material with me. Ratios and percentages made sense because I could see them being used in real life. I loved geometry for the same reason, it had immediate and concrete applications.

    Algebra confused me and I used every trick in the book to avoid calculus, trigonometry and every other form of higher math in high school and college.

    My lack of math proficiency kept me from pursuing a major and a career in microbiology, which was my passion. I wasn’t until I married a math major that I realized that math was at the base of every science and engineering discipline. Through him I learned the uses of various forms of math for everything from building bridges and roads to how much compost to use in my garden.

    I felt cheated. I feel that if teachers and other adults had shown me how math is used in practical, concrete ways (perhaps teaching math as a part of a project as opposed to theoretical marks of chalk on a board) I would have appreciated math and tried harder to master it.

    1. LeonovaBalletRusse

      HH, clearly you had bad teachers, which often occurs in mathematics. I was fortunate at the high-school level to have great teachers in algebra, plane geometry, trigonometry, *advanced math* (set theory and the like).

      At the University level I was not so fortunate. After Calculus, I quit math.

  12. Ed Bradford

    My microscopic experience with two women (1. A Women’s Studies professor, 2. My daughter) is that women are simply not as interested in math. I don’t and never have thought there were differences in abilities in solving math problems – at least I have never noticed any. Even from my Advanced Math classes in High School, where the number of boys and girls was about equal, I noticed the grades were pretty evenly distributed (they were posted so we all knew each other’s grades).

    Does ‘interest of the individual’ factor into the explanations for the smaller number of women in math and engineering?

    1. xenadu

      You miss the point – that children pick up social cues that we are completely unaware of and those cues reinforce some desires and squash others. Perhaps your daughter has simply picked up the cues (from TV, other kids at school, teachers, etc) and dutifuly followed them.

      No one has to teach little boys not to wear dresses, even though men’s clothing was essentially a dress at various points in history (and some cultures like Scots associate skirts with men, not women).
      There is nothing about dresses that inherantly make the form feminine… we just pickup the social cues as we grow up. We see women wearing dresses but men never do. We see women reading fashion magazines with pictures of dresses on the front. In the store we see women wandering around the dresses but usually not men. Our parents don’t put us in dresses, but they do with our sisters. No one has to tell us “don’t wear a dress”, we just learn it as part of our culture. Industry only makes dresses for women’s body shapes because those are their only customers, which just helps re-inforce the idea that men don’t wear dresses. And just like anything else there are a few outliers for various reasons (kilts:tradition, crossdressers:mental, actors:disguise) – some more culturally acceptable than others.

      So ask yourself: is it possible that “women don’t do math” is another one of those cultural rules that we unconciously teach? And given that assumption, is it any wonder that women get crap when they try to enter math/engineering disciplines? How would you react to your co-worker showing up to work in a dress? Ridicule I’d imagine, because he’s violating the unspoken cultural rule that men don’t wear dresses. It doesn’t matter that he’s still smart, still does his job, still acts like he did before. He will likely be shown the door OR he will simply be ostracized and not allowed to participate in group functions (leading to denied projects, promotions, etc). Do you think he would still want to wear a dress under those circumstances? I doubt it… not worth the trouble.

    2. LeonovaBalletRusse

      EB, it is a fact that if you are really interested in effective human relationships, especially attentive to the life of the *Other*, you will find fields of study more interesting, and enjoyable, than math. If you have many talents and skills, as your daughter seems to, there’s not enough *humanity* in math. Such a person is not likely to pursue math in competition with a trove of Math Geeks, if she has other options that are more fulfilling.

  13. alimentary my dear Watsoned

    “Women’s intelligence may also manifest in different ways: note that most of the assholes on Wall Street are men. This kind of makes sense since women are typically not as driven by testosterone and competitiveness.”

    Stereotype threat indeed, self parody hallowed be thy name.

    “…there is a greater “packing density” of the neurons in the female brain.

    The male brains were about 12.5 percent heavier than female brains. Hence the greater neuronal packing density in the female brain nearly balances the larger size of the male brain. The g Factor; Jensen pg. 149

    http://www.amazon.com/Factor-Science-Evolution-Behavior-Intelligence/dp/0275961036#_

    See. Women are denser.

  14. steelhead23

    In high school, I was an excellent math student. Took em all. But, I was routinely bested by Roxanne, an Asian-American girl. Roxanne shared with me that every night, since grade school, after dinner her mom sat down with her and went through her homework. Every night. My memories lead me to a different stereotype – not that Asian-Americans are better at math than Cajuns (true, but hardly relevant) – but that girls tend to believe that if they excel in school, particularly math and science, they won’t get dates. After all, no high school boy wants to date chicks who are smarter than they are. For girls, appearing dumb, but cute is broadly considered an attribute.

    1. ajax

      As an aside, in recent years young women from China
      (the People’s Republic of China) have been getting
      an “interesting” number of gold medals at
      the International Math. Olympiads, which occur yearly.

      I don’t know much about dating in China though …

      1. LeonovaBalletRusse

        Chinese girls/women with brains/talent are EXPECTED to excel and to compete, and to be active rather than passive. They are not expected to *Pleez U*. They work like hell, and they expect to compete on the world stage. Their sense of personal dignity is enmeshed with their ambition for success as individuals.

        Maybe *expectation* has a lot to do with what happens in America. We can see that we’re going to get creamed.

    2. LucyLulu

      In high school, I was the best math student in my class, and it was a very large school. I had no dates, except for maybe a couple with some really geeky guys. It influenced my decision to go into nursing. I’m 54. Later on in life, in the late 90′s, I got a degree in software engineering and thus took some more math courses as well as programming courses (and I believe they use the same type thinking, symbolic and problem-solving) and was again the top of my class, but no longer minded. However, like Yves, I was the only female in my compilers class of 45 people. I think the math and science taboo for women has improved but its still there. There is still a belief that men don’t like brainy women (though I’ve found quite a few exceptions). I think that men DO like to feel needed and as if they are more competent, at least in some areas, and perhaps that gets misconstrued by women as being a requirement that they be less intelligent. Though if I could find a man who is just handier around the house than I am, that would work just fine for me. Or even has more common sense (which isn’t difficult). Or for that matter, would put up with me.

    3. LeonovaBalletRusse

      Many Asian girls don’t have the same hang-ups with being perceived as a Math Geek as many American girls do, and their parents make sure of that. And, of course, ever since the social leveling of Mao, girls go for the gold in China, in full competition with boys.

  15. minty

    Why is anyone paying attention to Larry Summers? Its obvious by how he flubbed the mortgage crisis he can’t do basic math. Ok Larry. If you overprice and sell mortgage backed securities for far more than they are worth and the market crashes and burns does that mean you have a positive or a negative balance on your books?

    1. LeonovaBalletRusse

      Right, minty, Larry Summers has proven himself to be a World Class Jerk, so why do so many defer to him? Who the hell IS Larry Summers, and who sent him?

  16. Geof

    Sigh. I am disturbed by the comments. These critics do not seem to understand Ms O’Neil’s point about the null hypothesis. Would anyone seriously suggest that the apparently disproportionate number of Chinese women studying computer science (in my experience) has a genetic basis? If not, why make genetic difference the null hypothesis here for women of all races? Particularly when there is so much evidence of persistent and widespread social and cultural bais against women in a range of fields (over and above that exhibited in the responses here):

    http://www.theatlanticcities.com/jobs-and-economy/2011/11/income-disparity-women-creative-class/359/

    Some of the comments here read like lay critiques of climate change. “The climate is always changing!” “Men and women are just different!” Where does this determination to reject social factors come from? In the case of climate change, many advocates of laissez fair economics correctly recognize the threat to their world view respond and respond by denying the problems’ existence, reiterating “common sense” (“what about the sun?!”) when confronted with expert analysis (this tendency is indicated by several scholarly studies). What world view is so threatened by an acknowledgement that inequality between sexes is socially produced? How do people who understand the scientific method suddenly forget all about it?

    I can’t think of many women recognized as geniuses in their lifetimes. I do want to give credit to one who was: Jane Jacobs. As a smiling grandmother she doesn’t fit the stereotype. When she died, the Internet was awash with tributes to her brilliance. Maybe she’s the exception that proves the rule.

    1. steelhead23

      Golly Mam, I figured my hypothesis that girls, more often than boys, studiously attempt to avoid being labeled as nerds, suggested that the gender bias was self-imposed. That is, just a 2 year olds “want” to be bad, many high school girls “want” to be dumb. There could be no clearer bias to such a study of gender-based ability – and until all sexual stereotypes die (such as “smart girls don’t get dates”) there will be insurmountable biases in measuring ability by measuring performance.

      Smart girls rock!

      1. LeonovaBalletRusse

        Alas, many girls and women *duck* in a world of weak/insecure men, so that they are not entirely eliminated from the circle. Some learn that solitude is better than self-deformation so as not to be *a threat* to boys/men who already are overwhelmed trying to compete with other boys/men.

        What is American footfall for?

  17. Andrew Foland

    This not in math, but addressing highy-related issues science and engineering: I think Kathryn Johnston’s CFA talk was very eye-opening for me, a male physicist who had always considered himself very even-handed when it came to women’s ability to do science (my Ph.D. advisor was a woman, for instance.) . Pages 10 to 15, in particular, made me doubt I was as even-handed as I thought. I think there’s a lot of great education in this talk.

    Also, since you asked for counterexamples, I think Lisa Randall (very much alive) would be popularly considered a genius.

      1. LeonovaBalletRusse

        Aw, let’s get to the NUT, shall we? In our culture, girls/women are expected to be passive and accommodating, and to NOT compete with boys/man.

        I can’t tell you how often I have been berated by women for not being “sweet and feminine” enough in a corporate environment. Meanwhile, they backstab women who don’t fit the mold, hoping to eliminate them, because secure, assertive women good at their jobs impress secure, successful Bosses. Strong, secure, intelligent men appreciate the these traits in women.

        It is with weak, insecure men and women that the trouble starts.

  18. minty

    Okay, I am white, blonde and have an engineering degree and was always good in math. Really good. The genetic reason is that I am scottish who as well all know have an inherited ability to do engineering as evidenced by Scotty in Star Trek who could land the Starship entreprise drunk. Something evidently that Larry Summers could not do.

        1. LeonovaBalletRusse

          AND, since ancient times of male and female leaders among Highland Scots, women are expected to be as ACTIVE as men, in making progress for everyone. As a rule, Scottish women are expected to use their brains.

          1. Kaleberg

            It may be because Scots were highly literate even way back when they were dirt poor and considered savages by the English. Boys and girls were both taught to read, write and reckon. It’s hard to underestimate how important this is.

  19. ChrisPacific

    The top student in my final year honors class at university (equivalent to master’s year in US institutions) was female. This was a novel experience for me – not being outscored by a female but being outscored by anyone, as I had become accustomed to being top student in any environment.

    She also happened to be 16 years old. While I’m sure a lot of this was natural ability, it helped that her parents were educators who were extremely good at teaching mathematics to children – her siblings also attended university at very young ages.

    She was remarkably well adjusted socially (arguably more so than the rest of us, even) but I did get the sense that she faced some difficulties resulting from her situation, and that she felt pressure to perform. I once speculated in her hearing on why there were no female faculty in the department. She looked at me as though I was crazy and asked: “If you were a woman, would you want to work here?”

  20. davidgmills

    Ah, the old testosterone slam. If I had not found out at the age of 60 I had a testosterone deficiency, I might have dismissed this comment. But since I am now on testosterone replacement therapy after finding out I have a pitutitary gland that fails to pruduce leutinizing hormone, which in turn prompts the testicles to produce testosterone, I am very aware now of how hormonal difficiencies can make huge differences in the way we feel and act. My ears now perk up anytime I hear the word testosterone.

    My father was a professor of biochemistry and he hated these kinds of arguments because he felt that each one of us is so vastly different it makes little sense to group us either by gender or race. Individuals of either gender can be very good at certain things and very bad at others. Same goes for race. And as someone pointed out above, when you are talking about true genuis you are talking about the far extreme of the bell curve.

    But what now piques my curiousity, given my own hormonal difficiency, is how much sexual hormones contribute to the apparent difference in the abilities between men and women. My own difficiency has caused me to study sex hormones, not so much for the sake of intellect, but for the sake of how badly hormonal deficiencies or imbalances make you feel.

    What is truly interesting to me about this article, at least from a hormonal point of view, is the author’s observation that women seem to “get” math much later in life, at the age of 50 or so, when also in her observation, men’s math abilities seem to decline.

    In the case of women of this age, their estrogen levels have usually dropped by 40 to 60 per cent due to menopause. In the case of men, their estrogen levels have risen to where their blood levels of estrogen are the same as women, often more. Men’s testosterone takes a precipitous dive around the age of 50 — creating andropause. And both sexes suffer serious declines in progesterone, causing “estrogen dominance,” a term coined by Dr. John R. Lee, which refers to the ratio of estrogen to progesterone.

    So maybe, just maybe, sexual hormones do have something to do with this. Perhaps it has more to do with interests than ability, because if math proficiency does take thousands of hours of practice, that it something that is quite hard to do if you don’t like a subject.

    I remember studies that show girls do about as well as boys in math and science until they reach puberty and then boys take the lead. Well what kicks in at puberty? Estrogen and testosterone.

    But I would certainly not draw any conclusions one way or the other until we know much more about the role of sexual hormones than we do now. Maybe some pubescent girls should take some testosterone injections or some boys do the reverse before they take the SAT’s just to see what happens, that is if you want to use SAT’s as a benchmark for math genius.

    With the abundance of xenoestrogens and phytoestrogens in our environment now, the second may be happening anyway, as boys’ testosterone levels “ain’t what they used to be.” Not by a long shot. Of course, high levels of testosterone don’t actually fit the sterotype of the geeky math guy. So this could all be nonsense. Then again, it just may not be.

    1. LeonovaBalletRusse

      davidgmills, thanks. The topic of sex hormones is the Elephant in the room. I’ve been saying lately that *sex hormone management* at puberty ought to be considered in a world driven by lust for advantage and gain, compounded by the relentless hard-driving propaganda of *digital media* that must bring a Tsunami of anxiety into adolescent heads.

      “ADAM’S CURSE” shows us what sex hormones are good for, fundamentally. We need to get out of the *primitive* stage, have people tested for balance of the endocrine system, and begin to address the excess or deficiency of sex hormones seriously. This is a public health issue. Who will touch it?

  21. al-kasser forum

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  22. travizm

    hahaha look at all the blogg’ees eating up the worms coming from this post!

    Firstly I think political correctness really screws the potential to discuss comparative abilities between men and women…..which is a shame.

    Secondly I also think that maths doesn’t cause the problem. Its a limited and/or gamed derivation which leans maths that causes problems.

    This article was a nice play on this blog. Brain-food for the Raven’s.

  23. JTFaraday

    Why are there no female math geniuses? Same reason there are no female philosophers, except for Aspasia, the original “public woman,” and Hypatia.

    Doofus that I am, I’m more inclined to wonder why there are no female metalsmiths. Granted, this is not an easy genre. You basically improvise it into being and then “teach” it to yourself. And how do they get it moving so fast and still have it all come together like that?

    http://www.youtube.com/watch?v=J4SOoWbEJ58

    Anyway, with young people of both genders coming up so domesticated these days, not to mention over-scheduled, I’m not too optimistic about the future of American popular music.

    Who was that guy my extended family was picking on at thanksgiving dinner?–oh, right. Pitbull. Here he is posing with j-lo:

    http://www.youtube.com/watch?v=t4H_Zoh7G5A

    Soon all music will be synchronized into existence by Apple. Then it will code, and fade into the void like high frequency trading.

    1. LeonovaBalletRusse

      JTF, have you known many male philosophers? So many dismiss women utterly, and many treat women philosophers with contempt, believing them disqualified for the classification from the get-go. Even Hannah Arendt was somewhat cowed by Heidegger. Of course she was in love with him, and made excuses for him forever. She met the right people at the right time, and was able to prove herself splendidly. But such examples are rare.

      I think it has to do with a particular vanity to which male philosophers are prey. Maybe women don’t want to be in the same company with them.

      1. Schizo Stroller

        Re: women in philosophy there was a big debate at this site

        http://www.newappsblog.com/2011/12/women-in-tenure-track-philosophy-jobs.html

        It seems that a gender bias isn’t just Maths, of course there is the problem that Philosophy deals often with the concept of gender where Maths doesn’t, so less of an excuse there for the philosophers.

        (although the debate in philosophy was about the system and whether or not there was a need for positive discrimination rather than any crap about gender stereotypes, the problem in philosophy seems to be men aware of the reality of the social, class and other reasons for the gender gap but reluctant to relinquish their dominant hold on the academic reigns – the debate on who is actually better at philosophy was settled a long time ago – it was a draw – the result was called ‘equality’)

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