EUCLID'S WINDOW: The Story of Geometry from Parallel Lines to Hyperspace

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.