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What makes mathematicians tick? How do their minds process formulas and concepts that, for most of the rest of the world’s population, remain mysterious and beyond comprehension? Is there a connection between mathematical creativity and mental illness?In The Mind of the Mathematician, internationally famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind. Together they explore the behavior and personality traits that tend to fit the profile of a mathematician. They discuss mathematics and the arts, savants, gender and mathematical ability, and the impact of autism, personality disorders, and mood disorders. These topics, together with a succinct analysis of some of the great mathematical personalities of the past three centuries, combine to form an eclectic and fascinating blend of story and scientific inquiry. (2007)
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The Mind of the Mathematician THE JOHNS HOPKINS UNIVERSITY PRESS BAlTIMORE Michael FitzgeraLd and loan James © 2007 Michael Fitzgerald and loan James All rights reserved. Published 2007 Printed in the United States of America on acid-free paper 9 87 6 5 432 The Johns Hopkins University Press 2715 North Charles Street Baltimore, Maryland 21218-4363 www.press.jhu.edu Library of Congress Cataloging-in-Publication Data Fitzgerald, Michael, 1946The mind of the mathematician / Michael Fitzgerald and loan James. p.cm. Includes bibliographical references and index. ISBN-13: 978-0-8018-8587-7 (hardcover: acid-free paper) ISBN-lO: 0-8018-8587-6 (hardcover: acid-free paper) 1. Mathematicians-Psychology. 2. Mathematics-Psychological aspects. 3. Mathematical ability. 4. Mathematical ability-Sex differences. I. James, I. M. (loan Mackenzie), 1928- II. Title. BF456.N7F582007 510.1' 9-dc22 2006025988 A catalog record for this book is available from the British Library. Contents Preface Vll Introduction ix PART I } TOUR OF THE LITERATURE Chapter 1. Mathematicians and Their World Chapter 2. Mathematical Ability 3 24 Chapter 3. The Dynamics of Mathematical Creation PART II } 42 TWENTY MATHEMATICAL PERSONALITI ES Chapter 4. Lagrange, Gauss, Cauchy, and Dirichlet 67 Chapter 5. Hamilton, Galois, Byron, and Riemann 88 Chapter 6. Cantor, Kovalevskaya, Poincare, and Hilbert 105 Chapter 7. Hadamard, Hardy, Noether, and Ramanujan 131 Chapter 8. Fisher, Wiener, Dirac, and G6del References Index 175 163 149 Preface Psychologists have long been fascinated by mathematicians and their world. In this book we start with a tour of the extensive literature on the psychology of mathematicians and related matters, such as the source of mathematical creativity. By limiting both mathematical and psychological technicalities, or explaining them when necessary, we seek to make our review of research in this field easily readable by both mathematicians and psychologists. In the belief that they might also wish to learn about some of the human beings who helped to create modern mathematics, we go on to profile twenty well-known mathematicians of the past whose personalities we find particularly interesting. These profiles serve to illustrate our tour of the literature. Among the many people we have consulted in the course of writing this book we would particularly like to thank Ann Dowker, Jean Mawhin, Allan Muir, Daniel Nettle, Brendan O'Brien, Susan Lantz, and Mikhail Treisman. We also wish to thank Ohio University Press, Athens, Ohio (www.ohio .edu/oupress), for granting permission to reprint an excerp