About The Book

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

Editorial Reviews

"How do you know where you are?" asks Leonard Mlodinow in his charming mathematical history, Euclid's Window. This question and others about space and time grew out of simple observations of the environment by a select group of thinkers whose lives and brains Mlodinow dissects. Starting with Euclid, geometry has flowed out over the centuries, describing the universe, and, Mlodinow argues, making modern civilization possible. This is not just a history of geometry--it's a timeline of reason and abstraction, with all the major players present: Euclid, Descartes, Gauss, Einstein, and Witten, each represented by a minibiography. Lots of examples pepper the narrative to help readers achieve their own "eureka!" And it's impossible not to be staggered at the mathematical feats of these geniuses, accomplished as many of them were in the absence of anything but observation and intense thought. Each story builds satisfactorily on the last, until at the end of this delightful book, one has a sense of having climbed a peak of understanding. A working knowledge of basic geometry is helpful but not essential for enjoying Euclid's Window, and Mlodinow's chatty style lends itself remarkably well to explaining these deep and revolutionary concepts. --Adam Fisher from Amazon

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 from Booklist

About Author

Leonard Mlodinow

Mlodinow was born in Chicago, Illinois, in 1959, of parents who were both Holocaust survivors. His father, who spent more than a year in the Buchenwald death camp, had been a leader in the Jewish resistance under Nazi rule in his hometown of Częstochowa, Poland. As a child, Mlodinow was interested in both mathematics and chemistry, and while in high school was tutored in organic chemistry by a professor from the University of Illinois. As recounted in his book, Feynman's Rainbow, his interest turned to physics during a semester he took off from college to spend on a kibbutz in Israel, during which he had little to do at night beside reading The Feynman Lectures on Physics, which was one of the few English books he found in the kibbutz library. While a doctoral student at the University of California, Berkeley, and on the faculty at Caltech, he developed (with N. Papanicolaou) a new type of perturbation theory for eigenvalue problems in quantum mechanics. Later, as an Alexander von Humboldt Fellow at the Max Planck Institute for Physics and Astrophysik in Munich, Germany, he did pioneering work (with M. Hillery) on the quantum theory of dielectric media. Apart from his research and books on popular science, he also wrote the screenplay for the film Beyond the Horizon (currently in production) and has been a screenwriter for television series, including Star Trek: The Next Generation and MacGyver. He co-authored (with Matt Costello) a children's chapter book series entitled The Kids of Einstein Elementary. Between 2008 and 2010, Mlodinow worked on a book with Stephen Hawking, entitled The Grand Design. A step beyond Hawking's other titles, The Grand Design is said to explore both the question of the existence of the universe and the issue of why the laws of physics are what they are. Mlodinow currently teaches at Caltech and is in discussions about producing a book with the controversial spiritualist Deepak Chopra.