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MODERN MATHEMATICS 1900 to 1950 Michael J. Bradley, Ph.D.
Modern Mathematics: 1900 to 1950 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 Library of Congress Cataloging-in-Publication Data Bradley, Michael J. (Michael John), 1956– Modern mathematics : 1900 to 1950 / Michael J. Bradley. p. cm.—(Pioneers in mathematics) Includes bibliographical references and index. ISBN 0-8160-5426-6 (acid-free paper) 1. Mathematicians—Biography. 2. Mathematics—History—20th century. I. Title. QA28.B736 2006 510.92'2—dc22 2005036152 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 1 This book is printed on acid-free paper.
CONTENTS Preface Acknowledgments Introduction
CHAPTER
1
David Hilbert (1862–1943): Problems for a New Century Early Years Invariant Theory Algebraic Number Theory Geometry Mathematical Problems for the Twentieth Century Analysis and Theoretical Physics Foundations of Mathematics and the Infinite Wars and Retirement Conclusion Further Reading
CHAPTER
vii ix xi
1 2 3 4 6 7 8 10 12 13 14
2
Grace Chisholm Young (1868–1944): Mathematical Partnership Early Life and Education Partners in Life and in Mathematics Independent Work on Infinite Derivatives Final Years of Her Career Conclusion Further Reading
15 16 17 21 22 23 24
CHAPTER
3
Wacław Sierpinski ´ (1882–1969): Number Theory and the Polish School of Mathematics Early Work in Number Theory Research on Set Theory Polish School of Mathematics Further Research in Number Theory Conclusion Further Reading
CHAPTER
Early Years Invariant Theory Struggle for Faculty Appointment Ideal Theory International Influence Noncommutative Algebras Honors and Recognitions Last Years in America Conclusion Further Reading
41 42 43 45 46 47 48 49 49 50 51
5
Srinivasa Iyengar Ramanujan (1887–1920): Indian Number Theorist Societal Influences The Notebook Years, 1904–1914 Years in England, 1914–1919 Return to India, 1919–1920 Conclusion Further Reading
CHAPTER
26 29 32 34 38 38
4
Amalie Emmy Noether (1882–1935): Abstract Algebraist
CHAPTER
25
53 54 56 60 64 65 66
6
Norbert Wiener (1894–1964): Father of Cybernetics Child Prodigy Harmonic Analysis
69 70 72
Research during the War Years Cybernetics Conclusion Further Reading
CHAPTER
7
John von Neumann (1903–1957): Mathematics for Science and Technology Early Research in Set Theory Quantum Theory Game Theory Operator Theory Atomic Weapons and Nuclear Energy Computer Architecture and Numerical Analysis Automata Theory Conclusion Further Reading
CHAPTER
83 84 86 87 89 89 91 94 95 96
8
Grace Murray Hopper (1906–1992): Computer Software Innovator Early Life and Education Programming and Debugging the Mark Series of Computers Compilers and COBOL Programming Return to Active Duty in the Navy Conclusion Further Reading
CHAPTER
76 78 80 81
99