Euclid’s Window : The Story of Geometry from Parallel Lines to Hyperspace (Book) Authors:Leonard Mlodinow Manufacturer:Free Press Released:09 April, 2002 Rating: A

When most people think of math, they think of raw numbers, boring classes in high school or college, and geeky people calculating things quickly. People don’t think of geometry, which is very much a foundation of much of the mathematics which is performed today. In Euclid’s Window, Leonard Mlodinow makes math history interesting by telling the story of the people behind geometry, starting with Euclid and ending with modern string and M-theory.

Leonard starts at the very beginnings of Geometry, tracing back the roots of Euclid’s Elements and the times of Pythagoras’s gang of mathemeticians. He presents them in their full glory, giving a tip of the hat to how well greek society was and how it helped foster mathematics revolutions. He continues to the downfall/descruction of high math concepts (thanks a lot, romans) through the dark ages, and how math came to be reborn. The story continues through Gauss and the discovery of non-Euclidian spaces, and eentually continues through to Einstein and Witten, eventually ending with superstring theory and M-theory. The connection between physics and geometry is at first downplayed (as Euclidian space is not related to real-world physics much) and then emphasized. He very much gives a biography of the key players to drive the story, handing it off from one historic figure to another through lesser known mathemeticians linked in a remarkable way. At no point do you think you have lost the story, or is it jarring.

One of the best parts of this book are the explanations of math concepts. Leonard is generally witty, using real-world examples when appropriate, and making excellent use of figures to get his point across. At the same time he never goes too far into the math, covering only the basic concepts the reader needs to know in order to grasp the scientific significance of the advances in mathematics and physics. Every point in the book which seems confusing when presented at first is covered with an example which, even when covering basic concepts, are a joy to read. Many examples employ Alexei and Nikolai, the author’s sons, which add some sort of charm.

I sped through this book, reading it whenever chance allowed. It was split into parts which are further split into chapters, but read very much like a novel. The writing style employed is well suited to the material, and I hope that I can read more from this author. It is very rare that a book on mathematics is written so well and such a joy to read. I emphatically recommend this book to anyone who has even a passing interest in geometry or mathematics history. This book is grade A.