Publishers Weekly
In this brief, accessible foray, popular math/science writer Berlinski (Newton’s Gift) breathes life into an ancient mathematician and the world of axioms and theorems he created—a geometric world that became the basis for much of modern math, from analytic geometry to the idea of curved space-time. To Berlinski, Euclid’s fourth-century B.C., 13-volume Elements is a manifestation of his “intense demand for an idealized world.” In small, precise steps, Euclid spells out five axioms, or assumptions, about points, lines, and angles, and what it means when two things are “equal”—everything needed to describe shapes in space. Berlinski writes, “In every generation, a few students have found themselves ravished by the Elements”; so too will even the most math-averse be enthralled by Berlinski’s rich, vibrant language: Euclid’s “shady” fifth axiom, concerning parallel lines, is “the little lunatic locked in a padded cell,” “all mad glitter and glow”; equilateral triangles are “squat brutes” that “do nothing and go nowhere,” while isosceles triangles “have the power to soar.” Berlinski’s book succeeds not only as a history of geometry but also as an exploration of the power of ideas, masterfully replacing cold abstraction with humor and humanity. 13 b&w images. Agent: Susan Ginsburg, Writers House. (Feb.)
From the Publisher
"An impressively concise distillation of the wizardry that transforms points, lines, and planes into sheer genius." ---Booklist Starred Review
JUNE 2013 - AudioFile
The ancient Greek Euclid put his stamp on math through THE ELEMENTS, his classic work on geometry. There's a poetic quality to this discussion of his work, aided by quotes at the beginning of each chapter and some discussion of the philosophy behind the calculations. Arthur Morey's gentle voice brings those elements a sense of grace. There's also some historical material. Most of the book, though, is geometry. A PDF provides illustrations, and Morey's voice makes the explications clear. Still, listeners who are “math phobes” should steer clear. For math lovers who are a bit rusty, though, this could be a good refresher. J.A.S. © AudioFile 2013, Portland, Maine
Kirkus Reviews
A playful yet deep excursus through Euclid's Elements, from veteran mathematician Berlinski (One, Two, Three: Absolutely Elementary Mathematics, 2011, etc.). It is a pleasure to follow the author as he grasps the logistical tail of Euclid's mathematics and follows it to this day. He delves into the trials of the Beltrami pseudosphere, the hyperbolic triangle, the Poincare disk and the Erlangen Program and its classification of different kinds of geometry. It is a profound investigation, as math was synthesized and refined and Euclid broke out with his axiomatic system ("composed of small, mincing, but precise and delicate, logical steps") as a way of seeing, a way of life. He fashioned an axiomatic organization that stylized abstraction to devise all the propositions of geometry via a handful of theories. The first four books of the Elements ("by far and away the most successful of mathematical textbooks") are the pivots, but the drama comes from the simple waxing complexity of the formulations, especially the fifth, where discomfort sets in. Euclid may not have been happy with these interrogations of his common notions, axis, proof and theorems, but Euclidean geometry lasted for 2,000 years. Nearly a third of the book tackles the parallel postulate and the coming of analytic geometry, with David Hilbert's brainstorms being critical referents. Berklinski also provides a list of Euclid's definitions (e.g., "A point is that which has no part"). The author's storytelling is clear, crisp and emotive, and he brings Euclid's little-known life alive.
