Unequal: The Math of When Things Do and Don't Add Up

by Eugenia Cheng

Why the familiar equal sign isn’t just a marker of sameness but a gateway into math’s—and humanity’s—most profound questions

Math is famous for its 1 + 1 = 2, a2 + b2 = c2, or y = mx + b. Much of the time it can seem like that’s all mathematics following steps to show that what’s on one side of an equation is the same as what’s on the other.

In Unequal, Eugenia Cheng shows that’s just part of the story, and the boring part to boot. Mathematics isn’t about showing how numbers and symbols are the same. It isn’t even just about numbers and symbols at all, but a world of shapes, symmetries, logical ideas, and more. And in that world, the boundary between things being equal and unequal is a gray area, or perhaps a rainbow of beautiful, vibrant, subtly nuanced color.

As Unequal shows, once you go over that rainbow, almost everything can be considered equal and unequal at the same time, whether it’s shapes (seen from the right perspective, a circle is the same as an ellipse), words (synonyms), or people—even numbers! It all depends on what features we care about. And it’s up to us what we do about it. That’s because mathematics isn’t a series of rules, facts, or answers. It’s an invitation to a more powerful way of thinking.

Genres: Nonfiction, Mathematics, Science

401 pages, Kindle Edition

Published September 2, 2025

About the author

Eugenia 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.

Reviews

[Sam von Dresden · Rating 3 out of 5]

I liked reading this, but there is way too much shared content with her other book, Is Math Real. It’s additionally not entirely clear what the through-line of the work is, as the author seems to jump around a lot to different topics without there being a strong degree of continuity between them.

In brief, I like this author a lot, but Unequal is certainly not her best work. I’d give a much stronger recommendation to ‘Is Math Real’.

[Chris Miller · Rating 4 out of 5]

Have you ever gone to a party, a dinner, or a grill at a friend or neighbor's? Now imagine someone saying, 'Boy, we were working with some quadratic equations the other night, and it was so fun.' If so, there was probably a short silence, and someone else said, 'I saw the cutest cat video the other day,' and there went the conversation. I believe Dr. Chen is working very hard to change that perspective. As with her other book, 'Is Math Real?,' she is reaching out to a math-phobic or apathetic public and providing insights and instruction to enable people to understand and marvel at certain concepts and processes that show math is important and has meaning to our lives. It isn't always easy, but she gets her ideas across in meaningful and memorable ways. She spends a great deal of time in this book showing and explaining ideas on the cutting edge of math, and how they apply to our world. It is a terrific book.

[Andy Oram · Rating 4 out of 5]

It's hard to summarize the thesis of this book, but I certainly learned interesting math in a fun way, and came to understand the goals of mathematics in a more nuanced way. Cheng uses mathematics as a metaphor and guide to dealing with social and political issues in more subtle ways, but the metaphors also worked in reverse (an appropriate outcome for a book built around symmetries): the references to current day-to-day issues helped me understand the very abstract and complex math.

[Mairead · Rating 3 out of 5]

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