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How the World Became Geometrical

Amir Alexander

Scientific American / Farrar, Straus and Giroux

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ISBN10: 0374254907
ISBN13: 9780374254902


320 Pages



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On a cloudy day in 1413, a balding young man stood at the entrance to the Cathedral of Florence, facing the ancient Baptistery across the piazza. As puzzled passers-by looked on, he raised a small painting to his face, then held a mirror in front of the painting. Few at the time understood what he was up to; even he barely had an inkling of what was at stake. But on that day, the master craftsman and engineer Filippo Brunelleschi would prove that the world and everything within it was governed by the ancient science of geometry.

In Proof!, the award-winning historian Amir Alexander traces the path of the geometrical vision of the world as it coursed its way from the Renaissance to the present, shaping our societies, our politics, and our ideals. Geometry came to stand for a fixed and unchallengeable universal order, and kings, empire-builders, and even republican revolutionaries would rush to cast their rule as the apex of the geometrical universe. For who could doubt the right of a ruler or the legitimacy of a government that drew its power from the immutable principles of Euclidean geometry?

From the elegant terraces of Versailles to the broad avenues of Washington, DC and on to the boulevards of New Delhi and Manila, the geometrical vision was carved into the landscape of modernity. Euclid, Alexander shows, made the world as we know it possible.


Praise for Proof!

"By crafting an argument as elegant as a Euclidean proof, Amir Alexander demonstrates that ancient Greek geometry helped shape our modern political systems, from kingdoms to republics to empires. This is intellectual history at its finest: illuminating, surprising, and a cracking good read."—Steven Strogatz, Professor of Mathematics, Cornell University, and author of Infinite Powers

"Geometry is at the center of this retelling of the history of modernity. Amir Alexander brings his prodigious storytelling skills to the task, and the result is elegant, illuminating, and thoroughly entertaining."—Michael Harris, Professor of Mathematics, Columbia University

“I couldn’t stop reading Amir Alexander’s Proof!, an enlightening centuries-long tour that reveals the secret geometry inscribed in our cities, our politics, and even our gardens.”—Jordan Ellenberg, Professor of Mathematics, University of Wisconsin-Madison, and author of How Not to Be Wrong: The Power of Mathematical Thinking

“Looking with Amir Alexander at the great world cities, we now see, beneath their political regimes, the imprint of Euclidean geometry. In this dazzling book we grasp for the first time the underlying rationality and order built into the geography of ancient and Renaissance Rome, Paris (inspired by Versailles), Washington, D.C., Berlin, imperial Saigon—the list is long. Vastly different forms of government and power took inspiration from the unity made possible only by geometry.”—Margaret Jacob, Professor of History, UCLA

"Alexander’s lucid and convincingly argued book fully demonstrates how ideas ancient in origin continue to shape the contemporary world."Publishers Weekly


Read an Excerpt






By the early 1400s the Baptistery of St. John at the heart of Florence was already ancient, its origins lost in the...

About the author

Amir Alexander

Amir Alexander teaches history at the University of California, Los Angeles. He is the author of Infinitesimal, Geometrical Landscapes, and Duel at Dawn. His writing has appeared in The New York Times and the Los Angeles Times, and his work has been featured in Nature and The Guardian, on NPR, and elsewhere. He lives in Los Angeles, California.

Ronna Kovner