Journey Into Geometries

Journey into Geometries

Introduction to Projective Geometry

This lucid introductory text offers both analytic and axiomatic approaches to plane projective geometry. Strong reinforcement for its teachings include detailed examples and numerous theorems, proofs, and exercises, plus answers to all odd-numbered problems. In addition to its value to students, this volume provides an excellent reference for professionals. 1970 edition.

The Shape of a Life

A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer 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 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 remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe “Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist