Read A Beautiful Mind Online

Authors: Sylvia Nasar

Tags: #Biography & Autobiography, #Mathematics, #Science, #Azizex666, #General

A Beautiful Mind (92 page)

Leonard, Robert J. “From Parlor Games to Social Science: Von Neumann, Morgenstern and the Creation of Game Theory, 1928–1944.”
Journal of Economic Literature
(1995).

———. “Reading Cournot, Reading Nash: The Creation and Stabilization of the Nash Equilibrium.”
The Economic Journal
(May 1994), pp. 492–511.

Lindbeck, Assar. “The Prize in Economic Science in Memory of Alfred Nobel.”
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vol. 23 (March 1985), pp. 37–56.

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Life Studies and For the Union Dead.
New York: Farrar Straus and Giroux, 1992.

Luce, R. Duncan, and Howard Raiffa.
Games and Decisions.
New York: John Wiley & Sons, 1957.

McDonald, John. “The War of Wits.”
Fortune
(March 1951).

Milnor, John. “A Nobel Prize for John Nash.”
The Mathematical Intelligencer,
vol. 17, no. 3 (1995), pp. 14–15.

Nash, John Forbes, Jr. “Sag and Tension Calculations for Cable and Wire Spans Using Catenary Formulas” (with John F. Nash, Sr.).
Electrical Engineering
(1945).

———. “Equilibrium Points in N-Person Games.”
Proceedings of the National Academy of Sciences, USA, vol.
36 (1950), pp. 48–49.

———.
Non-Cooperative Gaines,
Ph.D. thesis, Princeton University, May 1950.

———. “A Simple Three-Person Poker Game” (with Lloyd S. Shapley).
Annals of Mathematics Stndy,
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———. “The Bargaining Problem.”
Econometrica,
vol. 18 (1950), pp. 155–62.

———. “Non-Cooperative Games.”
Annals of Mathematics,
vol. 54 (1951), pp. 286–95.

———. “Real Algebraic Manifolds.”
Annals of Mathematics,
vol. 56, no. 3 (November 1952), pp. 405–21.

———. “Some Experimental N-Person Games” (with G. Kalisch, J. W. Milnor, and E. D. Nering).
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———. “Two-Person Cooperative Games.”
Econometrica,
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———. “A Comparison of Treatments of a Duopoly Situation” (with J. P. Mayberry and M. Shubik).
Econometrica,
vol. 21 (1953), pp. 141–54.

———. “Higher Dimensional Core Arrays for Machine Memories.” RAND Memorandum, D-2495, 7.22.54.

———. “LODAR.” RAND Memorandum, D-2349, 7.23.54.

———. “Continuous Iteration Method for Solution of Differential Games.” RAND Memorandum, RM-1326, 8.18.54.

———. “Parallel Control.” RAND Memorandum, RM-1361, 8.27.54.

———. “C Isometric Imbeddings.”
Annals of Mathematics,
vol. 60, no. 3 (November 1954), pp. 382–96.

———. “Results on Continuation and Uniqueness of Fluid Flow.”
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———. “A Path Space and the Stiefel-Whitney Classes.”
Proceedings of the National Academy of Sciences USA,
vol. 41 (1955), pp. 320–21.

———. “The Imbedding Problem for Riemannian Manifolds.”
Annals of Mathematics,
vol. 63, no. 1 (January 1956), pp. 20–63.

———. “Parabolic Equations.”
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vol. 43 (1957), pp. 754–58.

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———. “Le probleme de Cauchy pour les equations differentielles d’un fluide general.”
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———. “Arc Structure of Singularities.”
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———. Autobiographical essay,
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———.
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Acknowledgments
 

M
ANY PEOPLE
contributed to this book, two above all: my friend of twenty-five years, Ellen Tremper, who cheered me on and rendered invaluable assistance every step of the way, and Harold W. Kuhn, whose enthusiasm for the enterprise and intimate knowledge of John Nash and the mathematics community was a constant source of guidance and inspiration. No one could have done more.

I am deeply indebted to Alicia Larde Nash and Martha Nash Legg, without whose support I could not have embarked on this biography, much less completed it. I am also grateful to John David Stier, Eleanor Stier, and John Charles Martin Nash for their cooperation, and appreciate John Nash’s benign “attitude of Swiss neutrality” toward the undertaking.

No author was ever in better hands than those of Alice Mayhew, my editor, and Kathy Robbins, my agent — not to mention those of Simon & Schuster’s terrific publishing team, especially Robert Labrie, Victoria Meyer, Elizabeth Hayes, and Nira Weisel.

I am thankful to Amartya Sen and Phillip Griffiths for enabling me to spend a vital year as a Director’s Visitor at the Institute for Advanced Study in Princeton; Gian-Carlo Rota for a shorter but equally critical interlude at the MIT mathematics department; and Vivien Arterberry for a productive week at the RAND Corporation.

Joseph Lelyveld, Soma Golden Behr, and Glenn Kramon of
The New York Times
granted me a generous leave of absence and enthusiastic support.

My colleagues Doug Frantz at
The New York Times
and Rob Norton at
Fortune
gave much-appreciated advice and encouragement at every stage.

Avinash Dixit, Harold Kuhn, Roger Myerson, Ariel Rubinstein, and Robert Wilson patiently shared their insights about game theory and served as valuable sounding boards.

Donald Spencer, Harold Kuhn, Lars Hormander, Michael Artin, Joseph Kohn, John Milnor, Louis Nirenberg, and Jürgen Moser worked hard to help me convey the originality of Nash’s contributions to pure mathematics clearly and accurately.

Superb histories by John McDonald, William Poundstone, Fred Kaplan, and David Halberstam provided much of the context for Nash’s tenure at RAND. Ed Regis’s lively history of the Institute for Advanced Study and Rebecca Goldstein’s delightful novel
The Mind-Body Problem
were also invaluable.

Richard Jed Wyatt guided me through the vast and fascinating literature on schizophrenia. The extraordinary work of Louis Sass, Anthony Storr, John Gunderson, Kenneth Kendler, Irving Gottesman, Richard Keefe, James Glass, Kay Redfield Jamison, and E. Fuller Torrey provided inspiration as well as important information. Special thanks to Connie and Steve Lieber, the founders of the National Alliance for Research on Schizophrenia and Depression, for their interest in this project.

Psychiatrists Paul Howard, Joseph Brenner, Robert Garber, and Peter Baumecker provided firsthand descriptions of the institutions where Nash was treated and glimpses into the mysteries of clinical psychiatry.

Jorgen Weibull and other members of the economics prize committee and the Swedish Academy of Sciences were wonderfully hospitable during my visit to Stockholm and helped me decipher the seemingly inscrutable process by which the
ne plus ultra
of honors is bestowed. Sociologist Harriet Zuckerman’s landmark study of Nobel Laureates served as an excellent road map.

Lloyd Shapley’s loving and lovely phrase “a beautiful mind” became, at Kathy Robbins’s suggestion, the title of the book.

I am infinitely grateful to the hundreds of individuals — mathematicians, economists, psychiatrists, and others who knew John Nash — who supplied the memories from which I’ve woven together his remarkable story. Every fragment, however tiny, added to the vividness of the whole, and each was gratefully received and treasured. In addition to those already cited, I am particularly indebted to Paul Samuelson, Arthur Mattuck, Paul Cohen, Odette Larde, Dorothy Thomas, Peter Lax, Cathleen Morawetz, Donald Newman, Al Vasquez, Richard Best, John Moore, Armand and Gaby Borel, Zipporah Levinson, Jerome Neuwirth, Felix and Eva Browder, Leopold Flatto, John Danskin, Emma Duchane, and Joyce Davis.

Archivists and librarians at Carnegie Mellon University, Princeton University, MIT, Harvard University, the Institute for Advanced Study, the Rockefeller Archive Center, McLean Hospital, the Swiss National Archives, and the National Archive provided important material and expert guidance. Special thanks to Arlen Hastings, Momota Ganguli, and Elise Hansen at the Institute for Advanced Study for making my year at the institute so productive, and to Richard Wolfe for sharing his knowledge of the Cambridge intellectual community.

Ellen Tremper, Geoffrey O’Brien, Harold Kuhn, Avinash Dixit, Lars Hormander, Jürgen Moser, Michael Artin, Donald Spencer, Richard Wyatt, and Rob Norton read and commented on various drafts. Their painstaking efforts eliminated mistakes, improved expositions, and added important new insights. All errors that remain are, of course, mine.

My husband, Darryl McLeod, and children, Clara, Lily, and Jack, not only lived with this book and its harried author for three years, but pitched in — on the computer, in the library, around the house — when deadlines were looming and the sky seemed about to fall. For their love and patience I am most indebted.

Index
 

Abbat, John,
282

ABC conjecture,
21

Aberdeen Proving Ground,
56

Acta Mathematica,
226

Adler, Alfred,
94

AEC (Atomic Energy Commission),
74
,
80
,
107
,
110
,
122
,
134
,
216

Aeschylus,
94

Afriat, Napthali,
284

Air Force, U.S.,
105
,
107
,
110
,
121
,
134
,
135
,
187

Albert, Adrian,
236
,
244

Alchian, Armen,
119

John Alden Society,
33

algebra,
56
,
65
,
74

Gauss’s proof of the fundamental theorem of,
67

von Neumann and,
81

algebraic geometry,
96

algebraic manifolds,
123
–24,
128
–32

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