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 ... 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 ... A theory doesn’t have to be perfect to be useful. I’d say the same for Cheng’s manifesto on gender.

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 ... She does acknowledge, however, that congressive behaviours are currently more common among women, and that society encourages men to be more ingressive. And, though she carefully explains the ways in which anyone can exercise congressive power and influence, a cynical reader is likely to wonder why, even in this egalitarian system, it still seems likely that ingressive people (mostly men) are going to go on making tonnes of money, while congressive people (mostly women) will be putting others first ... Still, if we were ever going to imagine a whole new theory of people, now is as good a time as any to start.

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 ... 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 ... Her approach to mathematics is open-ended, exploratory, collaborative and rather life-affirming ... 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 ... 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 ... not groundbreaking, but it does certainly highlight the merit of taking new approaches to old problems.

...Cheng is clear, focused and precise. Despite it’s nominally nerdy take, x + y reads considerably faster than most books of equivalent length ... The book is also a foray into the broader question of whether a mathematical frame of mind (as opposed to necessarily mathematics per se) can help untangle (if not necessarily solve) complex social problems ... Math has neither objectives nor ethics: the results just are. But society does: it is trying to optimize something and people will disagree, quite legitimately in many cases, about both what that something is and what is optimum. Cheng writes that 'congressive behavior is better for society'; I happen to agree out of both principle and practicality, but 'better' is not itself a mathematical concept. Cheng’s 'whole new theory of people' requires inclusion of non-mathematical considerations which are to some extent judgmental ... That being said, x + y is a rare combination of precision, passion and optimism. Whether via math or just clear and rigorous thinking, knotty issues benefit from discussions like this.

Can mathematics break down barriers to entry—in markets, in society—imposed by gender? Mathematician and math popularizer Cheng takes a positive view ... A carefully developed argument that urges us to discuss character traits without reference to gender.