A Fields medalist recounts his lifelong transnational effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

The Shape of a Life: One Mathematician's Search for the Universe's Hidden Geometry

Biographies & Memoirs

Yau, Shing-Tung

Nadis, Steve

Professionals & Academics

Yale University Press

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.

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

Science & Math

Mathematics

Basic Books

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.

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

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.

Astronomy & Space Science

In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard's mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics--in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose.
The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics--an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce's successors--William Fogg Osgood and Maxime Bôcher--undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators--students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling.
A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.

A History in Sum: 150 Years of Mathematics at Harvard (1825–1975)

History

Americas

Harvard University Press

Contains papers presented at a conference organized by the editors of the "Journal of Differential Geometry" which featured speakers representing algebraic geometry and mathematical physics, among other areas.

Surveys in Differential Geometry: Proceedings of the Conference on Geometry and Topology Held at Harvard University, April 27-29, 1990 (Supplement to the Journal of Differential Geometry, No. 1)

Lehigh University

Hsiung, Chuan-Chih

Conference on Geometry and Topology

Amer Mathematical Society

These three parts contain the proceedings of the AMS Summer Institute on Differential Geometry, held at the University California, Los Angeles in July 1990. This was the largest AMS Summer Institute ever, reflecting the wide-ranging and intense research activity in the subject. The parts contain many extensive survey articles presenting perspectives on relatively broad topics; these articles would be accessible to advanced graduate students. In addition, the authors of the research articles were encouraged to survey the relevant literature. The three parts together offer the deepest and most comprehensive survey of recent research in differential geometry available today.

Differential Geometry (Proceedings of Symposia in Pure Mathematics ; V. 54 Part 1, 2, 3)

GREENE, ROBERT

One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it&nbsp; Mathematics is far more than just the language of science. It is a critical underpinning of nature. The famed physicist Albert Einstein demonstrated this in 1915 when he showed that gravity--long considered an attractive force between massive objects--was actually a manifestation of the curvature, or geometry, of space and time. But in making this towering intellectual leap, Einstein needed the help of several mathematicians, including Marcel Grossmann, who introduced him to the geometrical framework upon which his theory rests. &nbsp; In The Gravity of Math, Steve Nadis and Shing-Tung Yau consider how math can drive and sometimes even anticipate discoveries in physics. Examining phenomena like black holes, gravitational waves, and the Big Bang, Nadis and Yau ask: Why do mathematical statements, derived solely from logic, provide the best descriptions of our physical world? &nbsp; The Gravity of Math offers an insightful and compelling look into the power of mathematics--whose reach, like that of gravity, can extend to the edge of the universe.

The Gravity of Math: How Geometry Rules the Universe

From the beginning harmonic maps were studied in connection with the theory of minimal surfaces. In 1985, the authors presented a series of lectures at the University of California at San Diego on the subject of harmonic maps. Most of these lectures are collected here as Part I. Part I of the book is devoted to harmonic maps defined on Riemann surfaces. Part II was added much more recently, and comprises part of the thesis of the first author, the work of N. Korevaar and the second author, and applications to geometry by the authors. The final chapter is due to J. Jost and the second author. This book presents some of the latest research on this topic from two of the foremost researchers in the field.

Lectures on Harmonic Maps (Conference Proceedings and Lecture Notes in Geometry & Topology, Vol. 2)

Schoen, Richard

In the Spring of 1984, the authors gave a series of lectures in the Institute for Advanced Studies in Princeton. These lectures, which continued throughout the 1984-1985 academic year, are published in this volume. Lectures on Differential Geometry was originally printed in Chinese, and widely circulated in China. This greatly anticipated English translation is an essential reference tool for Differential Geometry. Differential Geometry has progressed rapidly in this century. This book describes the major achievements in this field.

Lectures on Differential Geometry (Conference Proceedings and Lecture Notes in Geometry and Topology)

Intl Pr of Boston Inc

See the best price to sell, buy, or rent books by Yau, Shing-Tung. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Yau, Shing-Tung

See the best price to sell, buy, or rent books by Yau, Shing-Tung. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

The Shape of a Life: One Mathematician's Search for the Universe's Hidden Geometry

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

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

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

A History in Sum: 150 Years of Mathematics at Harvard (1825–1975)

Surveys in Differential Geometry: Proceedings of the Conference on Geometry and Topology Held at Harvard University, April 27-29, 1990 (Supplement to the Journal of Differential Geometry, No. 1)

Differential Geometry (Proceedings of Symposia in Pure Mathematics ; V. 54 Part 1, 2, 3)

The Gravity of Math: How Geometry Rules the Universe

Lectures on Harmonic Maps (Conference Proceedings and Lecture Notes in Geometry & Topology, Vol. 2)

Lectures on Differential Geometry (Conference Proceedings and Lecture Notes in Geometry and Topology)