American Scientist

X + Y: A Mathematician’s Manifesto for Rethinking Gender. Eugenia Cheng. 272 pp. Basic Books, 2020. $28.

As an undergraduate math major taking a course in Real Analysis, I belonged to a study group consisting of myself and five male students majoring in physics. One day one of them remarked, “Adriana, the guys were talking the other day, and we realized that since you are smart, funny, and cool, and not afraid to show it, then you must be a man!” Sadly, my reaction was to read this as a compliment and feel flattered, because—like many women in male-dominated fields such as mathematics—I felt that the best I could hope for was to be good enough to be considered “one of the guys.” It took years for me to fully process how insulting that comment was.

In her new book, X + Y, Eugenia Cheng introduces a surprising tool—abstract mathematics—for achieving insight into situations like the one I had found myself in—situations involving gender, inequality, and the designation of certain character traits as inherent to one group and not others. When desirable character traits are viewed as being inherently male (as occurred in my anecdote), then the expectation is that women should act more like men to be successful or respected, and women who present the traits are labeled “masculine” (as I had been). Cheng has a knack for extracting such ideas and presenting them in an abstract way that highlights problems with our thinking. For instance, she points out that when character traits associated with men are overvalued, there are two common responses: to say that gender differences are innate, or to say that they are learned; the common resulting inference is that if the differences are innate, women can’t be as successful as men, and if they are learned, women should learn to be more like men. But such an analysis ignores two things: that there are more than two gender identities, all of which probably include some people who do not want to emulate stereotypically masculine behavior; and that such behavior may not actually be essential to, or even particularly valuable for, success.

Cheng challenges us to use a logical, theoretical mathematical framework to rethink such paradigms as “leaning in” and other forms of what has been called assimilationist thinking (the idea that the disadvantaged group can gain favor by acting more like the privileged group), and to reexamine our ideas about “gender differences,” success, confidence, and ambition. An important part of the problem, she says, is that we have been thinking about gender in a one-dimensional way; only by thinking along other dimensions can we find a way to achieve true gender equality.

In category theory, which is Cheng’s research area, abstract mathematicians describe things by the role they play in a given context rather than by their intrinsic characteristics. Doing so offers flexibility by allowing one to focus on what is relevant in a situation while ignoring other details for the time being. This is the approach Cheng proposes we take to gender inequality: to refrain from talking about intrinsic characteristics associated with gender and focus instead on a different dimension—the roles that certain behaviors play in various aspects of society. If we focus on roles and behaviors, she says, then we can treat people of all genders the same, by using the way a person behaves and relates to others as the basis for our decisions about how to treat that person.

To help bypass the problem that some “ways of relating” may be associated with a particular gender, Cheng recommends adopting a new vocabulary for describing behavior. She proposes the term ingressive behaviors for actions that involve “focusing on oneself over society and community, imposing on people more than taking others into account, emphasizing independence and individualism, [being] more competitive and adversarial than collaborative, [and] tending toward selective or single-track thought processes.” By contrast, congressive behaviors involve “focusing on society and community over self, taking others into account more than imposing on them, emphasizing interdependence and interconnectedness, [being] more collaborative and cooperative than competitive, [and] tending toward circumspect thought processes.” Particularly in the United States, ingressive behaviors are generally associated with men and congressive behaviors with women. But Cheng is careful to note that a person may behave ingressively in one context and congressively in another. Her view is that focusing on behavior is less divisive and more productive than talking about gender, and that taking an ungendered approach will thus likely help us move toward greater gender equality.

I particularly appreciated the introduction of this ingressive/congressive dimension, because I am an educator who recognizes that our educational system favors and fosters ingressive traits, and I have been actively working to make classrooms more congressive. In addition, I am an immigrant from the congressive culture of Venezuela into the inherently ingressive culture of the United States. At this particular moment in history, as climate change and a pandemic are raging across the planet, it is especially important that we think of ways of fostering and developing congressive traits. Now more than ever, we need to move away from individualism and toward a focus on the collective good. In the later chapters of X + Y, Cheng makes a beautiful case for this view by describing congressive individuals and cultures and inviting us to dream of what could be. She also explores ways of making education and science less ingressive.

Cheng’s mathematical take on gender is unique, but some of these ideas are not entirely new. Some social scientists have taken a similar approach, using slightly different language, to such matters as education across different cultural backgrounds. I believe that all cultures and ethnicities would be better served if we placed greater value on congressive behavior.

Cheng makes a great point of being congressive herself, welcoming the reader into her world of thought. Her writing is always a pleasure to read, and I finished the book feeling as though I had had a conversation with a very smart friend—a conversation that was both deeply personal and wonderfully abstract. All of us—mathematicians in particular—could benefit from emulating her honesty and vulnerability.