Proof!: How the World Became Geometrical

by Amir Alexander

Overview

An eye-opening narrative of how geometric principles fundamentally shaped our world

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.

Product Details

ISBN-13:	9780374254902
Publisher:	Farrar, Straus and Giroux
Publication date:	09/10/2019
Pages:	320
Sales rank:	1,022,400
Product dimensions:	6.00(w) x 9.10(h) x 1.20(d)

About the Author

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.

Editorial Reviews

Alexander is especially fascinated by the way powerful people took hold of a geometrical way of thinking and used it for their own ends . . . In always clear and lively prose, [he] devotes particular enthusiasm to [Versailles] . . . Alexander’s account acquires thematic sinew as he traces the historical quest for some sort of rational city.” —Dan Hofstadter, The Wall Street Journal

“If you think geometrical figures are abstract artefacts of the human mind, think again . . . Entertaining, enlightening and admirably well-focused.” —Simon Ings, The Telegraph (UK)

"Lively . . . Bracingly enthusiastic . . . A deep immersion into geometric determinism at its most entertaining." —Kirkus

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

"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

From the Publisher

2019-06-23
A lively explanation of how geometry structures aspects of the natural and human worlds.

In this bracingly enthusiastic account of geometry's role in shaping a variety of institutions, Alexander (History/UCLA; Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, 2014, etc.) turns to Euclid's Elements and its complete world of mathematical proofs, founded on indisputable postulates and proven through impeccable logic. (The book isn't overrun with mathematics, but when it is unavoidable, the author is clear in his language.) Geometry revealed truths stripped of anything erroneous, unessential, and transitory, truths that were deployed by such luminaries as Copernicus, Galileo, and Leon Battista Alberti, setting the scientific agenda. Geometry is everywhere, underlying the natural and human-made worlds, infusing even our social arrangements. Guided by the art and architectural works of Alberti, which demonstrated "that the seemingly limitless variety one encounters in nature was in fact governed by the fixed eternal laws of geometry," Alexander applies that thought to the royal gardens of, in particular, France. Gardens were central to the monarchy's public presentation, ideology, identity, power, and legitimacy, especially so at Versailles, where Louis XIV's hierarchical state was reflected in the layout of the vast but tightly ordered gardens. "At the apex of this universe was, inevitably, the king in his palace, whose rule was as inescapable and unchallengeable as geometry itself," writes the author. This modernizing state was governed by a rational and efficient central bureaucracy, which is how the story moves forward beyond the monarchy into city planning. "The geometrical ideal of an efficient rational state found expression…on the bustling streets of capital cities—the homes of state bureaucracies." This is the case in Rome, Paris, St. Petersburg, and Berlin, where harmony and order reflect the organs of state. The stamp of Versailles can also be found in New Delhi and Washington, D.C., the latter being a fine example of geometry accommodating several nodes of power.

A deep immersion into geometric determinism at its most entertaining.

Kirkus Reviews