Library Journal
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"Euclid's work [is] a work of beauty whose impact rivaled that of the Bible, whose ideas were as radical as those of Marx and Engels. For with his book Elements Euclid opened a window through which the nature of our universe has been revealed." Strong words, but Mlodinow backs them up with this surprisingly exciting history of how mathematicians and physicists discovered geometric space beyond Euclid's three dimensions. Each advance in mathematical geometry has been followed by unexpected discoveries proving that the strange mathematics actually describe measurable physical properties. Mlodinow, a physicist and a former faculty member at the California Institute of Technology, has also written TV screenplays for Star Trek: The Next Generation and other shows. He has a good sense of popular science writing, and he personalizes geometric abstractions by endowing them with the personalities of his adolescent sons, Alexei and Nicholai. Euclid, Descartes, Gauss, Einstein, and Witten are among the mathematicians profiled, and each of them also emerges with a distinct personality based on the style of their writing and historical anecdotes. This engaging history does an excellent job of explaining the importance of the study of geometry without making the reader learn any geometry. For all math and science collections. Amy Brunvand, Univ. of Utah Lib., Salt Lake City (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.

Book list
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Mlodinow's spry account of geometry stresses the stature of the greatest math book of all time, Euclid's Elements. Although the three-dimensional space he described in it doesn't truly represent the shape of nature, Euclid compensated by codifying an attitude essential to rational thinking--to wit, distrust intuition and therefore don't accept unjustified assumptions. Unfortunately, Euclid himself made one unjustified assumption, the parallel postulate, which worked fine in the flat-Earth mathematical world that existed until Carl Friedrich Gauss dismantled it in the nineteenth century. Gauss invented a new geometry of curved or hyperbolic space, a feat that Mlodinow honors in such amusing asides as his remark on Kant's defense of Euclid: "Gauss did not dismiss Kant's work out of hand. He read it, then dismissed it." Such japes lighten and popularize Mlodinow's approach to the further demolition of Euclid by Gauss' student Georg Riemann, whose work critically contributed to the theory of general relativity. Mlodinow's lively exposition concludes with string theorists' claim that geometry possesses no fewer than 11 dimensions. Gilbert Taylor

Publishers Weekly
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Mlodinow's background in physics and educational CD-ROMs fails to gel in this episodic history of five "revolutions in geometry," each presented around a central figure. The first four Euclid, Descartes, Gauss and Einstein are landmarks, while the fifth, Edward Witten, should join their ranks if and when his M-theory produces its promised grand unification of all fundamental forces and particles. Mlodinow conveys a sense of excitement about geometry's importance in human thought, but sloppiness and distracting patter combine with slipshod presentation to bestow a feel for, rather than a grasp of, the subject. Certain misses are peripheral but annoying nonetheless confusing Keats with Blake, repeating a discredited account of Georg Cantor's depression, etc. Some of them, however, undermine the heart of the book's argument. Strictly speaking, Descartes, Einstein and Witten didn't produce revolutions in geometry but rather in how it's related to other subjects, while Gauss arguably produced two revolutions, one of which non-Euclidean geometry is featured, while the other differential geometry though equally necessary for Einstein's subsequent breakthrough, is barely developed. Mlodinow completely ignores another revolution in geometry, the development of topology, despite its crucial role in Witten's work. Occasionally Mlodinow delivers succinct explanations that convey key insights in easily graspable form, but far more often he tells jokes and avoids the issue, giving the false, probably unintentional impression that the subject itself is dull or inaccessible. More substance and less speculation about the Greeks could have laid the foundations for an equally spirited but far more informative book. 11 figures, two not seen by PW. (Apr.) Forecast: The Free Press may be looking for a math popularizer in the mold of Amir Aczel, but Mlodinow falls short. Don't look for big sales here. (c) Copyright PWxyz, LLC. All rights reserved