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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 equations: 1 + 1 = 2, a^2 + b^2 = c^2, or y = mx + b. Much of the time it can seem like that's all mathematics is: 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. Eugenia Cheng is scientist in residence at the School of the Art Institute of Chicago and honorary visiting fellow at City, University of London. She has authored numerous titles, including winner of the LA Times Book Prize Is Math Real?, How to Bake Pi, Beyond Infinity, The Art of Logic, and x + y. Cheng lives in Chicago, Illinois.
Math is famous for its equations: 1 + 1 = 2, a^2 + b^2 = c^2, or y = mx + b. Much of the time it can seem like that's all mathematics is: 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. Eugenia Cheng is scientist in residence at the School of the Art Institute of Chicago and honorary visiting fellow at City, University of London. She has authored numerous titles, including winner of the LA Times Book Prize Is Math Real?, How to Bake Pi, Beyond Infinity, The Art of Logic, and x + y. Cheng lives in Chicago, Illinois.
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Reviews
"Eugenia Cheng's consideration of equivalence and equality in math and in life could be applied to the identity she presents in this audiobook: Her narration is always easy to listen to, but WHAT she narrates is not; the two are not equal. Her voice and English accent are likable; her manner is warm, friendly, and engaging; her performance is clear and gently musical. Even the frequent difficult sections, which she acknowledges may be incomprehensible, are pleasant, though they may not hold the unmathematical listener's attention. Her connections of math to life aren't always convincing or immediately compelling but are worth consideration. To those able, or even just willing, to follow along, Cheng smooths the way, even among the impenetrably complex. W.M. � AudioFile 2025, Portland, Maine"
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