A Mathematician's Manifesto for Rethinking Gender

September 8, 2020 12:21 AM

How to Undo Gender Stereotypes in Math—With Math! - "A mathematician uses her craft to unravel arguments about differences between men and women."

I worked hard to be successful, but that “success” was one that was defined by society. It was about grades, prestigious universities, tenure. I tried to be successful according to existing structures and a blueprint handed down to me by previous generations of academics.

I was, in a sense, successful: I looked successful. I was, in another sense, not successful: I didn’t feel successful. I realized that the values marking my apparent “success” as defined by others were not really my values. So I shifted to finding a way to achieve the things I wanted to achieve according to my values of helping others and contributing to society, rather than according to externally imposed markers of excellence...

Why do we persist in thinking about gender differences? I think it’s telling to think about who benefits, when we think about why this research is even being done. Why is anyone trying to prove that there are innate differences between men and women in intelligence, scientific ability, competitiveness, or any other traits that seem to confer high status in society?

What the Numbers Say About Gender Differences: Data on abilities reveal a great deal of overlap for men and women - "The differences within each gender are greater than the differences between genders, so gender is not a good predictor of these behaviors."

x + y by Eugenia Cheng review – an end to the gender wars? - "A bold and optimistic theory of gender and cooperation, based on the insights of maths."

Cheng begins by addressing why it is unhelpful to associate characteristics with gender, and explains why “leaning in” and “positive discrimination” both fail to fix inequality. She proposes a solution based on her specialist subject of category theory, which is more interested “in describing things by the role they play in a context, rather than by their intrinsic characteristics”. Mathematically, she says, “if we have two things that are not equal, we could make them equal by making the lesser one greater or by making the greater one less ... However, there is a completely different way we could do it, which is by evaluating the two things on a new dimension entirely.” Cheng insists that proper maths, the fun kind, is not about being right, but is a way of thinking differently, and that includes exploring ideas that are impossible according to existing rules. It’s a way of seeing this exhausting debate from a completely new angle.

What she asks us to do is forget ideas of masculine or feminine characteristics, and instead think about types of behaviour that are either “ingressive” or “congressive”. Ingressive behaviours are competitive, adversarial and focused on the self over the community; congressive behaviours are collaborative, cooperative and focus on society over the self. It is a frustrating fact, she argues, “that although congressive behaviour is better for society, our society is set up to reward ingressive behaviour”. This book is a manifesto for switching that setup, beginning on a personal level and working all the way up to large-scale, structural change.

To the Mathematician Eugenia Cheng, There's No Gap Between Art and Science - "The boundaries between subjects are really artificial constructs by humans, like the boundaries between colors in a rainbow."

This is what I call congressive strength, which is not about being physically strong and aggressive, or daring and heroic, or rich and powerful, but more about bringing people together, and transforming oneself and society through deep understanding, insight and unity.

Want a Better Way to Think About Gender? Use Math - "In 'X+Y', the mathematician Eugenia Cheng proposes using category theory to end the gender wars."[1]

Her argument is that doing this will strip away unnecessary and confusing details, “a bit like the fact that it would be hard to carry a concealed weapon on a nude beach.” So, even as she adds what she calls a mathematical abstraction to the discussion, she claims it will allow us to remove confusing and unnecessary scaffolding...

Cheng explains how, when we rely on simplistic concepts like female and male, and the crusty logic that accompanies those concepts, we cannot have good conversations. As Cheng puts it: “If we object to the idea that ‘men are better,’ it’s not that helpful to declare instead that ‘women are better.’ It pits men and women against each other and sets up a prescriptive framework rather than a descriptive one.” She motivates us to strip away consistent triggers for dumb fights that lead nowhere.

What would she have us strip away? This is where Cheng becomes a logician. She wants to carefully think through our associations with the word “success” as they relate to gender. For example, she argues, it’s common enough to question why men are considered deeply different from women when the actual distributions overlap in most ways you can measure them, besides exceptions like the ability to bear children (yes, she mentions transgender men who can bear children). It’s also common to point out that “men’s attributes” such as competitiveness are more associated with success and are thus more rewarded, leading to all kinds of bad causal arguments that justify misogyny. What Cheng does now, though, is root out the underlying assumption that competitiveness is actually a good thing. What if it isn’t? That’s a question we often don’t get to, but when we refuse explicit mention of gender in behavior, we can discuss competitiveness’s flaws and benefits without specifically pointing fingers or assigning blame.

Finding the right formula for feminism - "Eugenia Cheng defies convention with her approach to teaching. The Chicago-based British mathematician tells Matthew Reisz why similar out-of-the-box thinking is required to improve gender equality."

A more productive approach, she suggests, relies on “building safety nets, having a network of supporters around you and defining failure out of existence by saying everything is a learning process. It is just a shift in psychology.”

Similarly, x + y cites a study from the 1990s into why men did better than women in Oxbridge exams. In subjects such as history, it turned out, one important factor was that “men tended to write essays that took a strong position and argued it fiercely, and that this was highly valued. A balanced position argued from all points of view was valued less.”

One possible response, of course, is to “train women to make more one-sided arguments”. But this is an example of what x + y describes as “pseudo-feminism…in which women are exhorted to become more like men in order to be successful”.

A central problem, Cheng writes, is that debates about gender often turn into “an argument about what we should be arguing about”. It is easy to get lost in endless, dizzying disputes about whether a particular piece of research really demonstrates that men are statistically “better at systematising than empathising” and, if so, whether this is innate and whether it is a reliable proxy for “better at maths”.

What this fails to address is that certain characteristics – such as taking a strong but perhaps simplistic position in an essay – may be associated with men (for whatever reason) and favoured by society, which then leads to men being more successful. Yet we also need to ask whether such attributes are actually desirable. In the case of the Oxbridge exams, as Cheng points out, we might consider the impact on our political culture: should “politicians be judged by how well they make a speech” or “how well they listen to other people’s concerns and respond to them”?

If we decide such characteristics are not desirable and we therefore work to promote other values, that will not only benefit society in itself but also help alter the gender balance of power without the need for quotas, “leaning in”, assertiveness training for women or many other familiar forms of intervention.

Equity: a mathematician shares her solution - "Look beyond gender — if research thrives on collaboration, a book asks, why do we reward individualism?"

Much has been written about the female premiers of Germany, Finland, New Zealand and Taiwan, and their remarkable success at dealing with COVID-19. But, as many pundits have noted, to focus on their gender is to miss much more important issues: the personal characteristics that define how these leaders operate, and the social climate that rewards communitarian behaviour.

These issues — relational abilities and enabling contexts — are central to mathematician Eugenia Cheng’s constructive argument in x+y. Whether one plus one is two, she shows, depends on how you define your variables and their relationship. One violinist and one pianist (Cheng plays the piano) might make two musicians, cacophony or sweet music, depending on how they interact. Considering such scenarios is the beauty of category theory, Cheng’s branch of pure mathematics...

Cheng argues that expecting individuals to conform with gendered averages has a high chance of being incorrect, and paves the way for undue criticism of outliers. “If a female mathematician is considered an anomaly,” she quips, “does that tell us something about women, about mathematicians, or about our preconceived expectations?” ... Clearly, we should stop trying solely to recruit women into hostile STEMM environments; instead, we should train researchers to be inclusive.

also btw :P
Conducting the Mathematical Orchestra From the Middle - "Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive."[2]

One of the things that give me the greatest satisfaction when I think about my career is, it’s not so much about the theorems that I’ve proven, but I think I am playing a supporting role in the mathematical community that is valuable to people.

Bill Thurston had this famous MathOverflow post where he responds to, I think it was an undergraduate, who was concerned that they might not be able to contribute to mathematics, because they weren’t sure how they stacked up to Gauss and Euler and Grothendieck. Thurston reminded this person that mathematics really is a community endeavor and there’s a part to be played by everyone.

posted by kliuless (12 comments total)

I just bought this book; so far, I've read the first chapter, which unpacks the list of bait-and-switches in arguments like “studies on babies staring at pictures of objects show that men are innately better at systemising; systemising is a key mathematical skill; therefore men are innately better at mathematics than women” (and there's at least four flaws in that sequence). I'm looking forward to reading the rest of it.
posted by acb at 2:35 AM on September 8, 2020 [3 favorites]

Sorta previously: How does pure mathematics apply to our daily lives?
posted by zengargoyle at 3:29 AM on September 8, 2020

Bill Thurston had this famous MathOverflow post where he reminded... [someone] that mathematics really is a community endeavor and there’s a part to be played by everyone.

I read that ages ago and then forgot how to find it and have been looking for it for years. Thank you!
posted by wildblueyonder at 12:58 PM on September 8, 2020

When I finally did start thinking about being a woman, the aspect that struck me was: Why had I not felt any need to think about it before? And how can we get to a place where nobody else needs to think about it either?

*sighs tiredly in trans woman*
posted by the tulips are too red in the first place at 1:49 PM on September 8, 2020 [3 favorites]

I read that ages ago and then forgot how to find it and have been looking for it for years.

previously :P

Even if one person could prove all the theorems in the path single-handedly,[*] they are wasted if nobody else learns them... What we are producing is human understanding. We have many different ways to understand and many different processes that contribute to our understanding. We will be more satisfied, more productive and happier if we recognize and focus on this.

cheers!
posted by kliuless at 7:49 PM on September 8, 2020 [1 favorite]

I read that ages ago and then forgot how to find it and have been looking for it for years.

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.

Closed 8 years ago.

Story of life.
posted by away for regrooving at 12:06 AM on September 9, 2020

(Placed a hold for x+y. Until I get to read that, to follow on the @ericmjohnson thread, I recommend Cordelia Fine, Delusions of Gender -- a detailed assessment of this area of research. I'll quote one bit of notes:

142 -
A cautionary tale about looking at brains. The prairie vole -- "males and females contribute equally to parenting." In females, "parenting behavior is primed by the hormonal changes of pregnancy." What triggers paternal behavior? The lateral septum, which "is very different in males and females, being much more richly endowed with receptors for the hormone vasopressin in the male, yet this striking sex difference in the brain enables male and female prairie voles to behave the same."
De Vries (2004). "Sex differences in adult and developing brains". Endocrinology, 145(3), 1063-1068.

Neuroimaging studies and the risk of "unwittingly projecting assumptions about gender onto the vast unknown that is the brain.")
posted by away for regrooving at 12:20 AM on September 9, 2020 [1 favorite]

When I was very young (probably about 13, though I'm not sure) some nutter said some stuff about research(*) showing that one of the reasons boys (men) tended to be better at quantitative thinking than girls (women) was that they were raised to value things differently. For example, boys played by throwing balls (this necessitated being able to predict MANLY MATH THINGS like trajectories) while girls played by making believe with dolls (this necessitated empathy and pretending, you know, GIRLY/WOMANLY THINGS). I'm only a little ashamed to say that at the time, when I was but a stupid lad (in the 90s), this sort of pat thinking made sense (in a cart-vs-horse way) and seemed to justify the way of the world that was plainly evident (not least because I happened to be male and good at math).

I didn't really deprogram myself until sometime in undergrad. I do think that there's a core of truth to this line of thinking (although with entirely wrong conclusions) -- not that women can't do math, but that society encourages different sectors of the population to be allowed to be good at different things. It's the system that's flawed, not the unwitting subjects of it. The reason math-is-hard-Barbie wasn't Ken isn't because of genetic or biologic incapability, but because we have (deeply flawed human) systems that encourage these outcomes.

* - probably some dodgy study in a D-grade publication cherry picked to support the talking point
posted by axiom at 2:09 AM on September 9, 2020

probably some dodgy study in a D-grade publication cherry picked to support the talking point

I recall reading about that research... I think whoever originally described it to you perhaps did not give a very accurate representation, since (if I recall correctly) the research itself seemed to draw the conclusion that, as you say, "society encourages different sectors of the population to be allowed to be good at different things. It's the system that's flawed, not the unwitting subjects of it." As in, the study talked about men or women tending to have achieved or attained more in various areas due to what skills they've been encouraged or allowed to practice, not about them having some developmentally-derived but fundamental/structural brain differences that would prevent future attainment in the other area despite embarking on similar levels of practice.
posted by eviemath at 5:49 PM on September 9, 2020

Steven Pinker & Elizabeth Spelke debate - The Science of Gender & Science.

I think this is a decent exposition on the nature vs nurture aspects if you haven't seen it already. If nothing else, it's a nice debate.
posted by zengargoyle at 5:28 AM on September 10, 2020

May I just say, with all due respect, fuck Steven Pinker. His enabling of Epstein is just the most recent in a long line of horrible and misogynistic things he has said and done that mean he has no place in any discussion of gender.
posted by hydropsyche at 5:58 AM on September 10, 2020 [2 favorites]

Two things I think are going on here: one, she's getting people to think about logic and statements in ways so that "men are good with X -> men are natural at Y" aren't logically as valid as people make it. Totally get that and I think we here at Metafilter are pretty good about avoiding these logical traps.

The other is that she (or the book reviewers) seems to be saying we shouldn't look at mathematical ability to determine success, and instead should be looking at more social factors like cooperation. But it still seems like there's some gendered aspect to those social skills being argued.

From my own profile here: "I deny that any one knows or can know, the nature of the two sexes, as long as they have only been seen in their present relation to one another. Until conditions of equality exist, no one can possibly assess the natural differences between women and men, distorted as they have been. What is natural to the two sexes can only be found out by allowing both to develop and use their faculties freely." -John Stuart & Harriet Taylor Mill, The Subjection of Women

It doesn't matter if it's mathematical ability or social skills. I don't like the idea of arguing that success in math is defined wrong and instead we should use these other measures, which also happen to be gendered (but in the opposite direction).

Like, to me, the problem is not how we measure success in math, its society itself and this argument to "Undo Gender Stereotypes - with Math!" is not getting at the root cause that will always be the root cause forever. I guess if this helps some people see that, then yay some movement has been made in the right direction! but I guess I'm not the target audience for this one.
posted by LizBoBiz at 2:44 AM on September 23, 2020 [1 favorite]