E-Book Content
MATHEMATICS FRONTIERS 1950 to the Present Michael J. Bradley, Ph.D. Mathematics Frontiers: 1950 to the Present Copyright © 2006 by Michael J. Bradley, Ph.D. All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval systems, without permission in writing from the publisher. For information contact: Chelsea House An imprint of Infobase Publishing 132 West 31st Street New York NY 10001 ISBN-10: 0-8160-5427-4 ISBN-13: 978-0-8160-5427-5 Library of Congress Cataloging-in-Publication Data Bradley, Michael J. (Michael John), 1956– Mathematics frontiers : 1950 to [the] present / Michael J. Bradley. p. cm.—(Pioneers in mathematics) Includes bibliographical references and index. ISBN 0-8160-5427-4 (acid-free paper) 1. Mathematicians—Biography. 2. Mathematics—History—20th century. I. Title. QA28.B7357 2006 510.92'2—dc22 2005036154 Chelsea House books are available at special discounts when purchased in bulk quantities for businesses, associations, institutions, or sales promotions. Please call our Special Sales Department in New York at (212) 967-8800 or (800) 322-8755. You can find Chelsea House on the World Wide Web at http://www.chelseahouse.com Text design by Mary Susan Ryan-Flynn Cover design by Dorothy Preston Illustrations by Jeremy Eagle Printed in the United States of America MP FOF 10 9 8 7 6 5 4 3 2 This book is printed on acid-free paper. CONTENTS Preface Acknowledgments Introduction CHAPTER 1 Julia Robinson (1919–1985): Discoveries in Number Theory and Mathematical Logic Student of Mathematics Decision Problems in Arithmetic Game Theory and Politics Hilbert’s 10th Problem Honors and Service to the Profession Conclusion Further Reading CHAPTER vii ix xi 1 2 3 4 5 9 11 11 2 J. Ernest Wilkins, Jr. (1923– ): Mathematician, Scientist, and Engineer Early Achievements Mathematics Professor Scientist and Engineer Gamma Rays Professor Again Temporary Retirement Conclusion Further Reading 13 14 15 16 17 19 20 21 22 CHAPTER 3 John Nash (1928– ): Nobel Prize–Winning Game Theorist Education and Early Years Revolutionizing Game Theory Research on Manifolds and Fluid Flows Struggles with Paranoid Schizophrenia Awarded the Nobel Prize Conclusion Further Reading CHAPTER Geometrical Puzzles and Finite Groups The Game of Life Analysis of Numbers Spheres, Lattices, and Codes Conclusion Further Reading 37 38 40 44 46 48 49 5 Stephen Hawking (1942– ): The Mathematics of Black Holes Early Life and Education Investigations of Black Holes Hawking Radiation and the Information Paradox The End of Physics and the No-Boundary Proposal Popular Science for General Audiences Science for Scientists Conclusion Further Reading CHAPTER 24 25 30 33 34 35 35 4 John H. Conway (1937– ): Inventor of the Game of Life CHAPTER 23 51 52 53 55 57 58 59 61 62 6 Shing-Tung Yau (1949– ): Surfaces in Differential Geometry 65 Student of Mathematics Solutions to Open Problems in Differential Geometry 66 66 Analyzing Properties of Manifolds Recent Work in Geometry Conclusion Further Reading CHAPTER 7 Fan Chung (1949– ): Professor of Internet Mathematics Student of Mathematics Industrial Mathematician Telecommunications Networks and Algorithms Academic Researcher Spectral Graph Theory and Internet Mathematics Conclusion Further Reading CHAPTER 75 76 77 79 81 83 85 85 8 Andrew Wiles (1953– ): Number Theorist Who Proved Fermat’s Last Theorem Early Interest in Mathematics Research on Elliptic Curves Modular Forms and Iwa