A Mathematician’s Manifesto for Rethinking Gender
By Eugenia Cheng
Eugenia Cheng is a mathematician, a musician and a writer. In her newest book, “X+Y: A Mathematician’s Manifesto for Rethinking Gender,” she introduces mathematical structure to the debate on gender in order to clarify and focus the conversation in helpful, nondivisive ways.
Specifically, Cheng draws from her field of category theory the concept of characterizing things by their relation to other things rather than by explicit descriptions of their makeup. In its simplest form, that means describing a human as a parent or worker rather than by unique identifiers or DNA sequences. But in this case, she wants to do that with something we already consider abstract, namely gendered behavior traits. Instead of defining people and their daily activities explicitly by gender, she’s devised a notation — the words “ingressive” and “congressive” — that describes the social behavior of people while ignoring the specific individuals behind those behaviors.
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.
To set up this “removing by adding” metaphor, she discusses mathematical notions that have done similar things. For example, she argues that by introducing the concept of i — the square root of negative one — and the accompanying notion of a complex plane, we may have temporarily made things more confusing, but we get so much clarity from it (the geometric understanding of the nth roots of unity, for example) that the added complexity pays off. It adds clarity even as it adds a dimension to our thinking, or to her point, perhaps because it adds a dimension to our thinking and gives us more room to move.
The first half of the book is devoted to preparing the reader for the big reveal: the added structure to the concept of binary gendered people and roles that will add a dimension to our thinking and reveal better approaches to our discussions. By relating personal stories, historical examples and mathematical analogies, 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.
Armed with her new notation, Cheng goes on to describe examples of group or individual behavior as ingressive, which broadly means individualistic, or congressive, which broadly means communitarian, in the realms of mathematics, musical competitions or business meetings.
Cheng is not neutral. She definitely prefers a world that is less ingressive and more congressive. She identifies as someone who had to learn to adapt to the ingressive world of mathematics but has since found a better path, and she suggests we’d all be better off doing what she’s done.
What would that look like? She has advice. The last few chapters of the book are devoted to responding congressively to ingressive situations. And although she acknowledges that some people who have already made it in an ingressive world will not benefit from a more congressive one, she urges the reader to try anyway.
It’s easy to criticize this book. What good are two new words for stuff we already associate with male behavior or female behavior? For that matter, some of her advice for behaving congressively sounds a lot like signing up for emotional labor that — yes, I’ll say it — women already do too much of. More generally, just because she seems aware of institutional power doesn’t mean she has a viable approach to dealing with it.
And yet, as a female mathematician who also grappled with the exact environment that she describes so well, I realize she’s put her finger on something that I hadn’t been able to articulate before, and her new notation helps. I’ve been by turns a mathematics professor, hedge fund quant and data scientist, working in nearly-all-male environments. It doesn’t appeal to me to describe my discomfort in those environments as a result of sexism, because to be honest I mostly didn’t feel singled out for being a woman (although sometimes I did). I simply felt as if the environment was unappealing, and would be deeply unappealing to anyone who wanted to feel like part of a generous community. I can now say it efficiently: I want to work in congressive environments, and I want to work with other people who also want to work in congressive environments. It feels like progress to be able to say this without reference to gender.
This is an important topic and an important time to find better ways to have conversations. So even if there are weaknesses in this paradigm, most of them are identified and admitted by Cheng herself. She even suggests a generous reading of her manifesto, again by analogy: “In mathematics a theory is judged by the breadth of examples it unifies and the amount of light it sheds on those examples.” A theory doesn’t have to be perfect to be useful. I’d say the same for Cheng’s manifesto on gender.