Consider the Octahedron

by Evelyn Lamb
By Paul Lockhart
Harvard University Press, 416 pages, $29.95
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“To be like a geometric thing,” Lockhart observes, “a real thing has to be the right size; namely, it has to be about our size ... Why? Because we’re the ones who made up the mathematics!” He goes on to postulate that our formulation of geometry would be radically different if we were the size of atoms or galaxies.

Lockhart emphasizes over and over that math is about exploration, not rote computation. He does not expect the reader to sit back and watch him have all the fun. He explains mathematical arguments thoroughly and precisely and then leaves questions in bold for the reader to tackle herself. To get the most out of the book — to learn and practice mathematical reasoning — a pencil and paper are required, especially for those who are new to creative thinking in math. Even those who are well-versed in the topics he presents will enjoy turning off their prior knowledge and trying to solve problems using only the theory in the book.

“Mathematics is a meeting place for language, pattern, curiosity, and joy,” writes Lockhart toward the end of Measurement. “And it has given me a lifetime of free entertainment.” A reader who wants to learn more about the pleasure of doing mathematics will find much to explore here.


Evelyn Lamb is a mathematician and freelance writer in Chicago. She has written for Scientific American and the Notices of the American Mathematical Society.

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