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x + y: Can maths solve the problem of gender bias?

Mathematician Eugenia Cheng’s ideas on gender are fascinating but don’t always add up

x + y: A Mathematician’s Manifesto for Rethinking Gender
Author: Eugenia Cheng
ISBN-13: 978-1788160407
Publisher: Profile
Guideline Price: £16.99

At the core of x + y is a thoroughly unique approach to thinking differently about gender and the ways in which we tend, both individually and collectively, to limit ourselves and one another as a result of gendering. Mathematician Eugenia Cheng takes her expertise in mathematics – specifically category theory, an area “built on the idea that we can understand a lot more about something or someone by looking at their relationships with those around them” – and rather surprisingly applies it to gender in a book that, while impressive, does not successfully break truly new ground as it promises.

Cheng has an innovative mind, and as you read it is wonderful to witness her unique approach to thinking and problem-solving in action. It gives the reader liberating permission to think about enormous questions without becoming intimidated. For those of us (arguably most of us) who are not mathematically proficient, or who have carried a sense of resentment towards maths since our school days, there is an intense sense of joy and curiosity in Cheng’s method. Her approach to mathematics is open-ended, exploratory, collaborative and rather life-affirming.

She argues that “we would benefit from having ungendered terminology with which to think and talk about” human characteristics and behaviours (the lack of which has contributed to the deeply unhelpful habits and intellectual tradition which perpetuate social and formal systems), which could be far better and more egalitarian for everyone. She is not interested in slapping a band-aid on the problem, but in rebuilding entirely, though the book does not quite succeed in this mission.

Much to her credit, Cheng devotes he last section of x + y to outlining what she sees as potential solutions to the problems the book focuses on, citing astutely that critical approaches within academia devote themselves to critique without offering constructive alternatives. This engenders pessimism and often even hopelessness. Cheng’s project in this book is wholly positive and constructive; in an era characterised by a sense that everything is going wrong, it is unremittingly hopeful.


Cheng argues that instead of defining characteristics as “masculine” (eg assertiveness) and “feminine” (eg sensitivity), we should instead focus on what she calls “ingressive” and “congressive” people. The definitions provided for these terms are lengthy, but ingressive people tend to be self-interested and congressive people tend to be more concerned for others.

She stresses that ingressive and congressive people may be of any gender. By associating the characteristics of ingressive individuals with masculinity and congressive individuals with femininity, we not only set up a system that ignores the fact that there are far more overlaps in characteristics between men and women on average than there are differences.

We also, argues Cheng, eliminate the possibility of progress by taking a combative perspective, and suggests that the interests of the one can only be championed by taking from the other: “If we object to the idea that ‘men are better’, it’s not that helpful to declare instead that ‘women are better’.” Cheng suggests that her new way of looking at gender provides a potential solution without navigating the traditional pitfalls of gender discourse.

The nature of modern academic expertise is that something (or many somethings) can easily become lost in the execution of a hugely ambitious project

Ultimately, though, she replaces one binary with what looks in practice very much like another binary. If the point is that our language doesn’t capture specificity, then another binary is not a clear solution to the problem, and language of greater specificity may surely benefit from the input of fields such as psychology.

One can wonder over the extent to which Cheng’s is more a nominal change than a substantive one. The fact remains that Cheng depicts ingressive traits as obstacles to the flourishing of congressive people, and her blank slate approach to psychology (itself insufficiently unexamined and highly questionable) suggests that since ingressive and congressive traits and behaviours are learned, they can be unlearned to make way for congressive environments that will be better for everyone.


x + y  is essentially a type of book that has fallen out of fashion: a treatise, a concerted and earnest attempt to look at a very complicated subject in a holistic way and make some incredibly interesting and insightful points in so doing. However, there are several reasons we don’t see many treatises as they are traditionally understood – one being that they tend to be written by polymaths, and are truly interdisciplinary. The nature of modern academic expertise is that something (or many somethings) can easily become lost in the execution of a hugely ambitious project.

Cheng states explicitly in the introduction to the book that she is “not a biologist, psychologist, philosopher, historian, sociologist, gender theorist, biographer, neuroscientist. [She is] a mathematician”, and declares her intent to write the book from the perspective of a pure mathematician. The result is fascinating but unconvincing overall. It borrows heavily from the fields mentioned above, utilising concepts and terminology from these disciplines without doing precisely what Cheng states is so fundamental in mathematics: going back to first principles.

The book is a fascinating, disarmingly accessible read and a wonderful example of what academics should in general do much more of

Cheng talks about concepts like implicit bias without providing any real groundwork for how the term is understood within psychology. She advocates ungendering our language as a means to “escape from those cultural restriction” so “everyone can be freed to benefit from the love and help of others”, but does not seriously examine the contributions of philosophy of language with sufficient depth to clarify whether a nominal change can truly represent a meaningful one.

x + y is a book about ontology which does not use that word once. In talking about social structure, Cheng employs immense concepts from within critical theory (like power) without showing the reader a deep understanding of critical theory or whether such concepts are up to the heavy lifting she requires of them. Consequently, there are several premises simply taken as true before the author moves on to structuring her argument atop or around them.

Still, the book is a fascinating, disarmingly accessible read and a wonderful example of what academics should in general do much more of: wade into the potential pragmatic applications of their specialist knowledge and make their discipline accessible to others. For Cheng’s project to have been successful, she would necessarily have needed to write an interdisciplinary book, branch outside her own particular discipline, and also engage deeply in several of the others she mentions above.

x + y is not groundbreaking, but it does certainly highlight the merit of taking new approaches to old problems.