A Beautiful Mind
Page 65
26. Ibid.
27. Alicia Nash, personal communication, 11.29.97.
28. E-mail from J. Nash to H. Kuhn, 6.6.96.
29. Ibid., 9.94.
30. John Nash, personal communication, 3.22.96.
31. H. Kuhn, interview, 8.95.
32. Interviews with John David Stier, 9.20.97; Eleanor Stier, 7.95; Arthur Mattuck, 11.7.95.
33. Martha Nash Legg, interview, 3.1.96.
34. J. D. Stier, interview.
35. Ibid.
36. E. Stier, interview.
37. J. D. Stier, interview.
38. E-mail from J. Nash to H. Kuhn, 9.26.95.
Select Bibliography
Bell, E. T. Men of Mathematics. New York: Simon & Schuster, 1986.
Blaug, Mark. Great Economists Since Keynes. Totowa, N.J.: Barnes & Noble Books, 1985.
Bleuler, Manfred. The Schizophrenic Disorders: Long-Term Patient and Family Studies. New Haven: Yale University Press, 1978.
Boehm, George W. “The New Uses of the Abstract.” Fortune (July 1958).
Brian, Denis. Einstein: A Life. New York: John Wiley & Sons, 1996.
Buchwald, Art. I’ll Always Have Paris. New York: G. P. Putnam & Sons, 1996.
A Century of Mathematics in America. Providence, R.I.: American Mathematical Society, 1988.
Chaplin, Virginia. “Princeton and Mathematics.” Princeton Alumni Weekly (May 9, 1958).
Chronicle of the Twentieth Century. Mt. Kisco, N.Y.: Chronicle Publications, 1987.
Community of Scholars: Institute for Advanced Study Faculty and Members, 1930–1980, A. Princeton: Institute for Advanced Study, 1980.
Davies, John D. “The Curious History of Physics at Princeton.” Princeton Alumni Weekly (October 2, 1973).
Davison, Peter. The Fading Smile: Poets in Boston from Robert Frost to Robert Lowell to Sylvia Plath, 1955–1960. New York: Knopf, 1994.
Diagnostic and Statistical Manual for Mental Disorders, 3rd ed. Washington, D.C., American Psychiatric Association, 1987.
Dixit, Avinash K., and Barry J. Nalebuff. Thinking Strategically New York: W. W. Norton, 1991.
Dixit, Avinash, and Susan Skeath. Games of Strategy. New York: W. W. Norton, 1997.
Eatwell, John, Murray Milgate, and Peter Newman, eds. The New Palgrave: Game Theory: New York: W. W. Norton, 1989.
Ewing, John H., ed. A Century of Mathematics. Washington, D.C.: The Mathematical Association of America, 1994.
Gardner, Howard. Creating Minds. New York: Basic Books, 1993.
Gardner, Martin. Mathematical Puzzles and Diversions. New York: Simon & Schuster, 1959.
Glass, James M. Delusion. Chicago: University of Chicago Press, 1985.
Goldstein, Rebecca. The Mind-Body Problem. New York: Penguin, 1993.
Gottesman, Irving I. Schizophrenia Genesis: The Origins of Madness. New York: W. H. Freeman & Co., 1991.
Grob, Gerald N. The Mad Among Us. Cambridge: Harvard University Press, 1994.
Halberstam, David. The Fifties. New York: Fawcett Columbine, 1993.
Hale, Nathan G., Jr. The Rise and Crisis of Psychoanalysis in the United States. New York: Oxford University Press, 1995.
Halmos, Paul R. “The Legend of John von Neumann.” American Mathematical Monthly, vol. 80 (1973), pp. 382–94.
Hardy, G. H. A Mathematician’s Apology, with foreword by C. P. Snow. Cambridge, U.K.: Cambridge University Press, 1967.
Heilbroner, Robert. The Worldly Philosophers. New York: Simon & Schuster, 1992.
Hironaka, Heisuke. “On Nash Blowing Up,” Arithmetic and Geometry II Boston: Birkhauser, 1983.
Hollingdale, Stuart. Makers of Mathematics. New York: Penguin, 1989.
Ito, Kyosi, ed. Encyclopedic Dictionary of Mathematics, vols. I, II, and III, 3rd ed. Mathematical Society of Japan; Cambridge: MIT Press, 1987.
Jamison, Kay Redfield. Touched with Fire: Manic-Depressive Illness and the Artistic Temperament. New York: The Free Press, 1993.
“John von Neumann 1903–1957.” Bulletin of the American Mathematical Society (May 1958).
Kafka, Franz. The Castle, with introduction by Irving Howe. New York: Scholastic Books, 1992.
———. The Metamorphosis. New York: Shocken Books, 1995.
Kagel, John H., and Alvin E. Roth. The Handbook of Experimental Economics. Princeton: Princeton University Press, 1995.
Kanigel, Robert. The Man Who Knew Infinity: A Life of the Cenius Ramanujan. New York: Pocket Books, 1992.
Kaplan, Fred. The Wizards of Armageddon. Stanford: Stanford University Press, 1983.
Keefe, Richard S. E., and Philip D. Harvey. Understanding Schizophrenia: A Guide to the New Research on Causes and Treatment. New York: The Free Press, 1994.
Kuhn, Harold W. Introduction, “A Celebration of John F. Nash, Jr.,” Duke Mathematical Journal vol. 81, no. 1 (1995), pp. i-v.
———. “Nobel Seminar: The Work of John Nash in Game Theory, December 8, 1994,” Les Prix Nobel 1994. Stockholm: Norstedts Tryckeri, 1995.
Larde, Enrique. The Crown Prince Rudolf: His Mysterious Life After Maverling. Pittsburgh: Dorrance, 1994.
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.” Journal of Economic Literature, vol. 23 (March 1985), pp. 37–56.
Lowell, Robert. “Waking in the Blue.” 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, vol. 24 (1950).
———. “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). Decision Processes, ed. R. M. Thrall, C. H. Coombs, and R. L. Davis. New York: John Wiley & Sons, 1954.
———. “Two-Person Cooperative Games.” Econometrica, vol. 21 (1953), pp. 405–21.
———. “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.” Bulletin of the American Mathematical Society, vol. 60 (1954), pp. 165–66.
———. “A Path Space and the Stiefel-Whitney Classes.” Proceedings of the National Acade
my 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.” Proceedings of the National Academy of Sciences USA, vol. 43 (1957), pp. 754–58.
———. “Continuity of Solutions of Parabolic and Elliptic Equations.” American Journal of Mathematics, vol. 80 (1958), pp. 931–58.
———. “Le probleme de Cauchy pour les equations differentielles d’un fluide general.” Bull. Soc. Math., France, vol. 90 (1962), pp. 487–97.
———. “Analyticity of Solutions of Implicit Function Problems with Analytic Data.” Annals of Mathematics, vol. 84 (1966), pp. 345–55.
———. “Arc Structure of Singularities.” Duke Mathematical Journal, vol. 81, no. 1 (1996), pp. 31–38.
———. Autobiographical essay, Les Prix Nobel 1994. Stockholm: Norstedts Tryckeri, 1995.
———. Plenary lecture, World Congress of Psychiatry, Madrid, 8.26.96 (unpublished).
Nicholi, Armand M., Jr. The New Harvard Guide to Psychiatry. Cambridge: The Belknap Press of Harvard University, 1988.
“Norbert Wiener 1894–1964.” Bulletin of the American Mathematical Society, vol. 72, no. 1, part ii (1964).
Poundstone, William. Prisoners’ Dilemma. New York: Doubleday, 1992.
Regis, Ed. Who Got Einstein’s Office? Reading, Mass.: Addison-Wesley, 1987.
Reid, Constance. Courant in Gottingen and New York. New York: Springer Verlag, 1976.
Rota, Gian-Carlo. Indiscrete Thoughts. Boston: Birkhauser, 1997.
Sass, Louis A. Madness and Modernism. New York: Basic Books, 1992.
Schelling, Thomas C. The Strategy of Conflict. Cambridge: Harvard University Press, 1960.
Storr, Anthony. Solitude: A Return to the Self. New York: Ballantine Books, 1988.
———. The Dynamics of Creation. New York: Atheneum, 1972.
Torrey, E. Fuller. Surviving Schizophrenia: A Family Manual. New York: Harper & Row, 1988.
Trimble, Michael R. Biological Psychiatry. New York: John Wiley & Sons, 1996.
Ulam, Stanislaw. Adventures of a Mathematician. New York: Scribner, 1983.
U.S. House of Representatives. Hearings. Committee on Un-American Activities, April 22 and 23, 1953.
von Neumann, John, and Oskar Morgenstern. Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1944, 1947, 1953.
Williams, John. The Compleat Strategyst. New York: McGraw Hill, 1954.
Winokur, George, and Ming Tsuang. The Natural History of Mania, Depression and Schizophrenia. Washington, D.C.: American Psychiatric Press, 1996.
Zuckerman, Harriet. Scientific Elite: Nobel Laureates in the United States. London: The Free Press, 1977.
Acknowledgments
MANY 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