x + y: A Mathematician's Manifesto for Rethinking Gender

Written by Eugenia Cheng

Narrated by Moira Quirk

A brilliant mathematician examines the complexity of gender and society and forges a path out of inequality.
Why are men in charge? After years in the male-dominated field of mathematics and in the female-dominated field of art, Eugenia Cheng has heard the question many times. In x + y, Cheng argues that her mathematical specialty -- category theory -- reveals why. Category theory deals more with context, relationships, and nuanced versions of equality than with intrinsic characteristics. Category theory also emphasizes dimensionality: much as a cube can cast a square or diamond shadow, depending on your perspective, so too do gender politics appear to change with how we examine them. Because society often rewards traits that it associates with males, such as competitiveness, we treat the problems those traits can create as male. But putting competitive women in charge will leave many unjust relationships in place. If we want real change, we need to transform the contexts in which we all exist, and not simply who we think we are.
Praise for Eugenia Cheng
"[Eugenia Cheng's] tone is clear, clever and friendly . . . she is rigorous and insightful. . . . [She is] a lucid and nimble expositor."

--- Alex Bellos, New York Times Book Review

"Dr. Cheng . . . has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board."

--- Natalie Angier, New York Times

• Language: English
• Publisher: Hachette Audio
• Release date: Aug 25, 2020
• ISBN: 9781549183966

Eugenia Cheng

Eugenia Cheng is a Pure Mathematician, Scientist in Residence at the School of the Art Institute of Chicago and Honorary Visiting Fellow of Pure Mathematics at City, University of London. A Cambridge graduate, she previously taught at the Universities of Cambridge, Chicago and Nice. She is also a concert pianist, fluent in French, and the author of several bestsellers, including How to Bake Pi and x + y.

Reviews for x + y

[paven-14534 · Rating: 3 out of 5 stars]

Some great ideas and a valuable perspective, but it fails on me not grasping the category.

I wonder what audience it targets. For me who is already a feminist it did not add anything new. And the maths part could have been evolved more.

With that said I really liked it, as it was kind of unique. I hope she writes a second edition with more category theory and math.

[tytania-2 · Rating: 3 out of 5 stars]

Mathematician Eugenia Chang suggests ways to remedy gender-related disparities in representation, pay, etc. by changing the *characteristics* that we reward and value, irrespective of gender. So for example, theory: men are more confident, they speak up more, they get noticed more, they get valued more, they get paid more. Common wisdom redress: teach girls to be more confident. Get women to speak up more. Get men to quiet down and listen to women. Chang's suggestion: Why are we paying people just for confidence and speaking up? The people not speaking up so much - often but not always women - are often bringing just as much value to the table; why aren't we nurturing and rewarding them for the value they bring, instead of trying to make them more like men?

I think I got the gist of it there. To remove gender from the picture, Chang suggests two new adjectives to take the place of 'masculine' and 'feminine.' I'll quote her definitions here:

Ingressive: focusing on oneself over society and community, imposing on people more than taking others into account, emphasizing independence and individualism, more competitive and adversarial than collaborative, tending toward selective or single-track thought processes

Congressive: focusing on society and community over self, taking others into account more than imposing on them, emphasizing interdependence and interconnectedness, more collaborative and cooperative than competitive, tending toward circumspect thought processes

Chang suggests that we picture a society where congressiveness is valued more than ingressiveness. Not 'as much as,' but 'more than.' Here I feel Chang and I part company, and that her argument could have been stronger if, in a congressive mindset (!), she could have acknowledged that maybe we need the strengths of both personality types to make a good world. But she makes no bones about where she stands: congressive is *better*.

I like to think that I do not impose on people and am not particularly adversarial. Those are negative personality traits you could argue we could all do with less of, or do without. But what's wrong with valuing one's independence? With single-track thought processes? There is definitely a time and place for laser focus. If Chang had merely said, let's make space for your more collaborative and wholistic-thinker types to flourish, I would have been much more receptive. I certainly love leaving gender out of it. That takes away space for men to get defensive, more 'ingressively' inclined females such as myself from getting similarly defensive (not that I ever would), and for anyone to decry 'reverse sexism.' Just focus on the individuals being marginalized, and why, and how to fix.

[sunyidean · Rating: 4 out of 5 stars]

I've thought a lot about this book and how to review it. I'm not sure I can give it the review it deserves and I'm not sure I have given it the star rating it deserves, but I can always edit both later.

For now, here are my fragments:

The info in the book was great. Cheng has some fantastic historical tidbits. For example, I had no idea Florence Nightingale was a mathematician whose use of statistics was instrumental in the changes she enacted as a nurse, and Cheng's illuminating discussion on a female coder who created a company that specifically to employ young women with children and paid them on a job done basis, not a per hour basis, to allow them flexibility and encourage job efficiency. It worked, her business boomed.

I also think Cheng's discussion on how unsupportive environments favour confident people, while supportive environments favour less confident people (I'm oversimplifying her arguments) was absolutely fascinating. It paints a picture of men creating a society in which everyone struggles needlessly, solely because a difficult environment elevates a handful of such men who--under better circumstnaces--would be *over* confident and overly aggressive. I have thoughts on that which aren't suitable for a review but suffice to say, it's interesting to think about. It would also explain the situation above (re jobs and women.)

She offers a general analysis that there is no point forcing 50/50 m/f participation unless we ALSO set up the environment to support women, because women will continue to underperform even when appropriately represented. That's fair and probably true, and feeds into the insidious myth that women haven't "earnt" the equality men so reluctantly give them.

But fundamentally, I do not think gender can be discussed in a mathematical way, and that's where the book falls down for me.

The problem of gender as a construct (and it is a problem, there is little that is uniformly positive about gender) is one which is linguistic and philosophical in nature.

Cheung says she set out to essentially define and create what "genderfree" feminism looks like. There is no such thing. And in any case, feminism is not about destroying gender or supporting gender; it is not about equality and it is not about finding solutions which "don't upset" the men (one of her goals.)

Feminism is about centering women in a world and society which centers men, however that centering may look, however you define men or women. It is about rejecting the context and structures and frameworks that give patriarchy an unfair, unethical, and illogical dominance in society, and which harm the vast majority of humans (regardless of gender or sex or background or whatever.) Most people will benefit from feminism, but feminism does not fight for most people primarily; it fights for women. If others benefit, fine, but that wasn't the goal.

This is an unpopular view, because people are stuck in patriarchal mindsets which make anything outside that seem threatening and evil. There is actually nothing wrong with a cause being focused. No one approaches cancer charities and screams at them for not collecting money to end Alzheimer's, and in a similar vein to the example above, if a cancer charity stumbles on research which benefits other sicknesses, cool! But that wasn't its goal. Get your pitchforks ready for cancer research, eh?

Likewise there is zero reason to scream at feminism because it doesn't carry a torch for every civil rights cause. (The concept of rights itself is patriarchal, but that's a whole other bag of shite.)

In summary, for me this interesting and earnest and lovely little book carries a fundamental flaw: mathematics is, I feel, a science of idealism, a world of imaginary numbers and abstract theories. Real life doesn't stop for such idealism, though, and the depth and complexity of this discussion cannot be carried by maths alone, as has been attempted here.

I'm going to regret this review later I'm sure.