The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions

Shing-Tung Yau
Steve Nadis
0465020232, 978-0465020232



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.

Of course, none of this could have been foretold more than a half century ago when a man named Eugenio Calabi--the first half of the Calabi-Yau duo--proposed that there could be multidimensional spaces with properties so special that many mathematicians, including one of this book's authors, considered them "too good to be true." Calabi had not been thinking about physics at the time, in the early 1950s, when he advanced the famous conjecture named after him. Following the proof of the Calabi conjecture, we have learned many new and wonderful things in both physics and mathematics--all of which suggest that Calabi-Yau spaces are not only too good to be true, as the skeptics used to say, but that they may be even better.


Brian Greene, Professor of Mathematics & Physics, Columbia University; author of The Fabric of the Cosmos and The Elegant Universe
The Shape of Inner Space provides a vibrant tour through the strange and wondrous possibility that the three spatial dimensions we see may not be the only ones that exist. Told by one of the masters of the subject, the book gives an in-depth account of one of the most exciting and controversial developments in modern theoretical physics.”

Joe Polchinski, Professor of Physics, University of California - Santa Barbara; author of String Theory, Vols. 1 & 2
“Einstein’s vision of physical laws emerging from the shape of space has been expanded by the higher dimensions of string theory. This vision has transformed not only modern physics, but also modern mathematics. Shing-Tung Yau has been at the center of these developments. In this ambitious book, written with experienced science writer Steve Nadis, Yau tells of his own mathematical experiences, and of the parallel efforts in string theory and in mathematics to understand the nature of space.”

Simon Donaldson, Royal Society Research Professor in Pure Mathematics and President of the Institute for Mathematical Science, ImperialCollegeLondon
The Shape of Inner Space has a distinctive style: in part autobiography, in part an account of developments in geometric analysis and string theory over the past 40 years, and comments on future directions. It gives a unique insight into the thoughts of one of the most important and influential mathematicians of our times.”

Edward Witten, Professor, Institute for Advanced Study
“Shing-Tung Yau and Steve Nadis take the reader on a fascinating tour of many contemporary topics in geometry and physics. Readers will find many challenging ideas to explore in this book, and even specialists will enjoy Yau’s reminiscences about his education and work.”

Steven Strogatz, New York Times Opinionator contributor and professor of mathematics, Cornell University
“A fascinating first-hand account of how the math underlying string theory was discovered. Fields medalist Yau and ace science writer Nadis have teamed up to show the rest of us the deep geometry that just might lie at the heart of the universe. It’ll twist you into knots of pleasure!”

John Coates, Sadleirian Professor of Pure Mathematics, University of Cambridge
"This remarkable book by Shing-Tung Yau and Steve Nadis gives the layman a remarkable glimpse into the mysterious inner world of one of the most beautiful and important parts of mathematics."

Andrew Strominger, Professor of Physics, Harvard University
“This book tells an inspiring story about how progress in science is made by breaking traditional boundaries in disciplines. It's really the only book of its kind—and, of course, written by someone who not only witnessed but also inspired and produced many of the major developments in this field over an exhilarating period of four decades.”


Publishers Weekly
“With the help of Astronomy magazine contributing editor Nadis, Yau relates the saga of [his] groundbreaking work which provided the foundations of string theory. Yau confidently draws readers into a realm of abstract concepts, from multiple dimensions to the exotic spaces called ‘manifolds,’ or Calabi-Yau spaces, whose curvature gives space its shape. From here it’s a hop, skip, and a jump to the geometry of space around the Big Bang, black holes, and the end of the universe.”

New Scientist
“It is a testimony to [Yau’s] careful prose (and no doubt to the skills of co-author Steve Nadis) that this book so compellingly captures the essence of what pushes string theorists forward in the face of formidable obstacles. It gives us a rare glimpse into a world as alien as the moons of Jupiter, and just as fascinating…. Yau and Nadis have produced a strangely mesmerizing account of geometry’s role in the universe.”

“Physicists investigate one cosmos, but mathematicians can explore all possible worlds. So marvels Fields medalist Shing-Tung Yau…. Relating how he solved a major theoretical problem in string theory in the 1970s, Yau explains how the geometries of the vibrating multidimensional strings that may characterize the Universe have implications across physics.”

Science Books & Films
“Concepts are introduced in a clear way, preceding more detailed discussions. The subjects examined include topology, geometries, general relativity, quantum physics, the standard model of particles, and other topics relevant to the pursuit of the understanding of extra dimensions in our universe. Among the volume’s especially interesting discussions are the possible experimental tests of the theory, the potential semistability of our universe, the five candidate string theories, and black-hole entropy.”

David Eicher,
“[A] masterwork on its subject…. The book is an entertaining read, written with the absorbing style that characterizes Nadis’ feature stories in Astronomy…. Those interested in cosmology and nature as a whole will be delighted with this new work!”

New York Journal of Books
The Shape of Inner Space provides the opportunity to look over the shoulder of a giant in mathematics.”

David Gross, Frederick W. Gluck Professor of Theoretical Physics, University of California – Santa Barbara; Nobel Prize-winning physicist
The Shape of Inner Space takes one on a marvelous journey that explores many beautiful areas of modern geometry and physics, and the people behind recent discoveries. It is a journey that I highly recommend to the intellectually curious.”

Product Description

String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.

Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

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