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Profile Books Ltd Unequal The Maths of When Things Do and Dont Add Up.
At first glance, the concept of equality in maths seems unambiguous. When we see the equality sign, we think of 'solving for x' or balancing two sides of an equation or maybe even the many famous equations that make use of this elegant, innocuous symbol.
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But between those parallel lines lies a mathematical playground of choice and abstraction, leading to far greater insight than you could have dreamed. As it turns out, sameness and difference, equality and inequality, are not nearly as straightforward as they seem.
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Unequal explores the rich and rewarding interplay between sameness and difference, from numbers to manifolds to category theory and beyond in a glorious celebration of mathematics that will change the way you look at maths - and the world around you - forever.
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But between those parallel lines lies a mathematical playground of choice and abstraction, leading to far greater insight than you could have dreamed. As it turns out, sameness and difference, equality and inequality, are not nearly as straightforward as they seem.
=/=
Unequal explores the rich and rewarding interplay between sameness and difference, from numbers to manifolds to category theory and beyond in a glorious celebration of mathematics that will change the way you look at maths - and the world around you - forever.
- GenresNonfictionMathematics
400 pages, Hardcover
Published June 5, 2025
10 people are currently reading
198 people want to read
About the author
Eugenia Cheng
17 books340 followersEugenia Cheng is a mathematician, pianist, and lecturer. She is passionate about ridding the world of math-phobia. Eugenia’s first book, How to Bake Pi, has been an international success. Molly’s Mathematical Adventure is her first children's book.
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Displaying 1 - 3 of 3 reviews
November 2, 2025
For me there is a sweet spot for science and maths books that can best be summed up by Roger Penrose’s Road to Reality. This type of book lies somewhere between an introductory text for undergraduate students and a popular science book that treats readers as able to grasp the necessary maths and physics while still being accessible to a wider audience. I came across Unequal by Eugenia Cheng in my local bookshop a couple of weeks back, and after a short browse revealed that it falls roughly into this category, I decided to give it a go.
Unequal is a dive into the world of category theory in mathematics, which is the area of maths that examines mathematical structures themselves. The author has written a number of books that infuse everyday life with esoteric mathematical concepts – her book on infinity (Beyond Infinity) is one of the best popular maths books I’ve read. However, of late her books have tended to be peppered with illustrations of real-life applications of maths that at times veer into leftist dogma which I think has put off a lot of her readers – including me. While this tendency is to some extent true of Unequal, it tails off towards the end of the book and only rises to the level of irritation in a few places (be prepared for some sweeping statements about white men).
True to its title, Unequal presents its material in a somewhat unequal way – some earlier chapters labour simple points, while later chapters feel a bit rushed, perhaps because Cheng thinks the material is too advanced and anything more than an overview would lose readers. Add to this the tendency of earlier chapters to spend too much time trying to relate concepts from category theory to real life – often unsuccessfully in my view – and I think the book could have been better, hence three stars.
There is one howler in the book that I think should be pointed out. Cheng states (on page 10 of the hardback edition) that road signs painted on road surfaces are elongated as, when they are seen from the perspective of drivers driving at speed, “the surface shrinks in the direction of travel according to how fast they’re moving”. Not true unless Cheng drives near the speed of light!
Unequal is a dive into the world of category theory in mathematics, which is the area of maths that examines mathematical structures themselves. The author has written a number of books that infuse everyday life with esoteric mathematical concepts – her book on infinity (Beyond Infinity) is one of the best popular maths books I’ve read. However, of late her books have tended to be peppered with illustrations of real-life applications of maths that at times veer into leftist dogma which I think has put off a lot of her readers – including me. While this tendency is to some extent true of Unequal, it tails off towards the end of the book and only rises to the level of irritation in a few places (be prepared for some sweeping statements about white men).
True to its title, Unequal presents its material in a somewhat unequal way – some earlier chapters labour simple points, while later chapters feel a bit rushed, perhaps because Cheng thinks the material is too advanced and anything more than an overview would lose readers. Add to this the tendency of earlier chapters to spend too much time trying to relate concepts from category theory to real life – often unsuccessfully in my view – and I think the book could have been better, hence three stars.
There is one howler in the book that I think should be pointed out. Cheng states (on page 10 of the hardback edition) that road signs painted on road surfaces are elongated as, when they are seen from the perspective of drivers driving at speed, “the surface shrinks in the direction of travel according to how fast they’re moving”. Not true unless Cheng drives near the speed of light!
November 23, 2025
This book falls into the vein of 25 Rocks which I read earlier this year. If i was being completely honest with myself, i'll put this in the "didn't finish" category because even after I finish the book, I cannot tell you the main thesis of the book other than what you can see on the front or back cover of the book.
The chapters in this book always begin with a math equation of some sort, and the grand thesis is really that not everything about math has to be about equality which we kind of implicitly assume when we see x + y = z. The book then takes the math equation or concept and then starts broaching real life topics with it, like equality doesn't have to be equal, such as when in a couple, one person prefers to cook and another prefers to clean, it doesn't make sense to force each person to equally clean and cook the same amounts. We deem it equal that they can share chores in a way that's beneficial to all and wave away the inequality that one thing or another takes up more effort.
This is fine for relatively simple concepts, but when she starts talking about harder concepts, it just loses me completely. this was not for a lack of concentration on my part, the authoress, who is also the narrator, acknowledges in parts of the audio book that listeners might just have to live with the fact that they cannot see equations and to check the enclosed pdf if they want to follow along.
I might end up checking out the dead tree version of this book at some point, but simply put, I think this is kind of the "math's version of philosophy", using math concepts to express the authoresses' philosophy. As these books goes, how well you react to it will depend on how your worldview lines up with the authoress. Mine lines up well so I think i put up till the end of the book with it because what she does say about equality in plain english is worth listening to. its maybe a stretch as to how you can use math equations or concepts to justify it, but hey, it takes all sorts.
Worth it if you're into math and want to see how stretchy it really is when it comes to asserting world views. =)
not recommended unless you are really into math.
The chapters in this book always begin with a math equation of some sort, and the grand thesis is really that not everything about math has to be about equality which we kind of implicitly assume when we see x + y = z. The book then takes the math equation or concept and then starts broaching real life topics with it, like equality doesn't have to be equal, such as when in a couple, one person prefers to cook and another prefers to clean, it doesn't make sense to force each person to equally clean and cook the same amounts. We deem it equal that they can share chores in a way that's beneficial to all and wave away the inequality that one thing or another takes up more effort.
This is fine for relatively simple concepts, but when she starts talking about harder concepts, it just loses me completely. this was not for a lack of concentration on my part, the authoress, who is also the narrator, acknowledges in parts of the audio book that listeners might just have to live with the fact that they cannot see equations and to check the enclosed pdf if they want to follow along.
I might end up checking out the dead tree version of this book at some point, but simply put, I think this is kind of the "math's version of philosophy", using math concepts to express the authoresses' philosophy. As these books goes, how well you react to it will depend on how your worldview lines up with the authoress. Mine lines up well so I think i put up till the end of the book with it because what she does say about equality in plain english is worth listening to. its maybe a stretch as to how you can use math equations or concepts to justify it, but hey, it takes all sorts.
Worth it if you're into math and want to see how stretchy it really is when it comes to asserting world views. =)
not recommended unless you are really into math.
December 27, 2025
It's exactly what the title says: an exploration of the concept of equality across different mathematical domains. It's explained well and enthusiastically; those without an advanced math background will still learn a lot. However, the sections on category theory and homotopy theory are suddenly much more advanced than the surrounding material, and will probably confuse those not already familiar with the topics, or at least haven't read Cheng's other book, The Joy of Abstraction. It makes sense since this book also focuses on abstraction and developing mathematical maturity, something Cheng does really well. Overall it's an accessible book that's easily recommendable.
Displaying 1 - 3 of 3 reviews