The Shape of Inner Space

AUTHORS' STATEMENT by SHING-TUNG YAU and STEVE NADIS
There is a certain irony running through this book that one of the smallest things you can possibly imagine — six-dimensional geometric spaces that may be more than a trillion times smaller than an electron — could, nevertheless, be one of the defining features of our universe, exerting a profound influence that extends to every single point in the cosmos. This book is, in many ways, the story of those spaces, which physicists have dubbed "Calabi-Yau manifolds." It tells how one of us, Yau, managed to prove the existence, mathematically, of those spaces, despite the fact that he had originally set out to prove that such spaces could not possibly exist. It then goes on to explain how this mathematical proof, which had initially been ignored by physicists (partly because it was steeped in difficult, nonlinear arguments), nevertheless made its way into the center of string theory, which now stands as the leading theory of the universe and our best hope yet of unifying all the particles and forces observed — and yet to be observed--in nature.

American Journal of Physics
“The Shape of Inner Space is a portrait of a beautiful branch of geometric analysis as seen through the eyes of one of its pioneers, Fields medal winner Shing-Tung Yau… After describing the sequence of events that led him to the United States and to his enamoration with geometry, Yau explains as only a master could the conjecture by Calabi and the subsequent discovery of Calabi-Yau manifolds that are the centerpiece of this book. The reader is thrown into a world of complex manifolds, geometric analysis, and differential equations, yet the book is written so that the persistent layperson could follow all of the main ideas.”