Unequal
The Math of When Things Do and Don't Add Up
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- US$18.99
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Why the familiar equal sign is a gateway into math’s—and humanity’s—most profound questions
"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
A New Scientist Best Book of the Year
Math is famous for its equations: 1 + 1 = 2, a^2 + b^2 = c^2, or y = mx + b. 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 is a world of shapes, symmetries, and logical ideas. 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! 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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Mathematician Cheng attempts to impart crucial life lessons via the fundamentals of math in her uneven latest (after Is Maths Real?). The focus is on the meaning of "sameness" and "difference" in both equations and in life—Cheng defines sameness mathematically as when functions give exactly the same output when given an input. Explaining that "the point of math is to gain new understanding and illuminate different points of view," Cheng posits that sameness is what "counts towards an equation being true," while difference "is what counts towards it being interesting." She draws direct parallels to society—mathematical symmetry is similar to reciprocity in human relationships, for example—and she makes a case that using the ways of thinking required in math can enrich people's lives and provide a more nuanced viewpoint. Things get complicated in her survey's second half, however, when Cheng veers into an extended discussion of category theory, the abstract branch of mathematics that focuses on structures and their relationships. Only readers committed to a deep dive into mathematical arcana will be able to make sense of the connections she draws between complex equations and society. This one doesn't quite come together.
