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Unequal
The Math of When Things Do and Don’t Add Up
Description
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 only 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.
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 only 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.
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Praise
"Eugenia Cheng has opened up my mind to the wondrous world of pure mathematics in a way that I never thought was possible."
—Willow Smith, singer and actress
"Eugenia Cheng's writing is generous and precise, a soft-serve swirl of the universal and the particular. In a way that few mathematicians can, she writes for everyone."
—Ben Orlin, author of Math with Bad Drawings
"Eugenia Cheng has done it again. Not only is she a great teacher of powerful mathematics: she shows us how understanding math can help us live better lives. Once you read this book, you'll have a new perspective on equality and difference, and why both matter so much."
—Stephon Alexander, author of The Jazz of Physics
"Eugenia Cheng has humour, grace and a natural gift"
—Daniel Levitin, author of I Heard There Was a Secret Chord
"Clear, clever and friendly...even at her most whimsical, she is rigorous and insightful"
—Alex Bellos, author of The Grapes of Math