1. George W. Mackey, professor of mathematics, Harvard University, interview, Cambridge, Mass., 12.14.95.
2. See, for example, David Halberstam, The Fifties (New York: Fawcett Columbine, 1993).
3. Mikhail Gromov, professor of mathematics, Institut des Hautes-Etudes, Bures-sur-Yvette, France, and Courant Institute, interview, 12.16.97. The claim that Nash ranks among the greatest mathematicians of the postwar era is based on judgment of fellow mathematicians. The topologist John Milnor expressed a nearly universal opinion among mathematicians when he wrote: “To some, the brief paper, written at age 21, for which he has won a Nobel prize in economics, may seem like the least of his achievements.” In “A Celebration of John F. Nash, Jr.,” a special volume, Duke Mathematical Journal, vol. 81, no. 1 (Durham, N.C.: Duke University Press, 1995), the game theorist Harold W. Kuhn calls Nash “one of the most original mathematical minds of this century.”
4. Paul R. Halmos, “The Legend of John von Neumann,” American Mathematical Monthly, vol. 80 (1973), pp. 382–94.
5. Donald J. Newman, professor of mathematics, Temple University, interview, Philadelphia, 3.2.96.
6. Harold W. Kuhn, professor of mathematics, Princeton University, interview, 7.26.95.
7. John Forbes Nash, Jr., remarks at the American Economics Association Nobel luncheon, San Francisco, 1.5.96; plenary lecture, World Congress of Psychiatry, Madrid, 8.26.96.
8. John Nash, “Parallel Control,” RAND Memorandum no. 1361, 8.7.54; plenary lecture, Madrid, 8.26.96, op. cit.
9. Interviews with Newman, 3.2.96; Eleanor Stier, 3.13.96.
10. John Nash, plenary lecture, Madrid, 8.26.96, op. cit.
11. Jürgen Moser, professor of mathematics, ETH, Zurich, interview, New York City, 3.21.96.
12. Interviews with Paul Zweifel, professor of physics, Virginia Polytechnic Institute, 10.94; Solomon Leader, professor of mathematics, Rutgers University, 7.9.95; David Gale, professor of mathematics. University of California at Berkeley, 9.20.95; Martin Shubik, professor of economics, Yale University, 9.27.95; Felix Browder, president, American Mathematical Society, 11.2.95; Melvin Hausner, professor of mathematics, Courant Institute, 1.26.96; Hartley Rogers, professor of mathematics, MIT, Cambridge, 2.16.96; Martin Davis, professor of mathematics, Courant Institute, 2.20.96; Eugenio Calabi, 3.2.96.
13. Atle Selberg, professor of mathematics, Institute of Advanced Study, interview, Princeton, 8.16.95.
14. George W. Boehm, “The New Uses of the Abstract,” Fortune (July 1958), p. 127: “Just turned thirty, Nash has already made a reputation as a brilliant mathematician who is eager to tackle the most difficult problems.” Boehm goes on to say that Nash is working on quantum theory and that he invests in the stock market as a hobby.
15. John von Neumann, “Zur Theorie der Gesellschaftsspiele,” Math. Ann., vol. 100 (1928), pp. 295–320. See also Robert J. Leonard, “From Parlor Games to Social Science: Von Neumann, Morgenstern and the Creation of Game Theory, 1928–1944,” Journal of Economic Literature (1995).
16. See, for example, Harold Kuhn, ed., Classics in Game Theory (Princeton: Princeton University Press, 1997); John Eatwell, Murray Milgate, and Peter Newman, The New Palgrave: Game Theory (New York: Norton, 1987); Avinash K. Dixit and Barry J. Nalebuff, Thinking Strategically (New York: Norton, 1991).
17. Robert J. Leonard, “Reading Cournot, Reading Nash: The Creation and Stabilization of the Nash Equilibrium,” The Economic Journal (May 1994), pp. 492–511; Martin Shubik, “Antoine Augustin Cournot,” in Eatwell, Milgate, and Newman, op. cit., pp. 117–28.
18. Joseph Baratta, historian, interview, 6.12.97.
19. John Nash, “Non-Cooperative Games,” Ph.D. thesis, Princeton University Press (May 1950). Nash’s thesis results were first published as “Equilibrium Points in N-Person Games,” Proceedings of the National Academy of Sciences, USA (1950), pp. 48–49, and later as “Non-Cooperative Games,” Annals of Mathematics (1951), pp. 286–95. See also “Nobel Seminar: The Work of John Nash in Game Theory,” in Les Prix Nobel 1994 (Stockholm: Norstedts Tryckeri, 1995). For a reader-friendly exposition of the Nash equilibrium, see Avinash Dixit and Susan Skeath, Games of Strategy (New York: Norton, 1997).
20. See, for example, Anthony Storr, Solitude: A Return to the Self (New York: Ballantine Books, 1988); Robert Heilbroner, The Worldly Philosophers (New York: Simon & Schuster, 1992); E. T. Bell, Men of Mathematics (New York: Simon & Schuster, 1986); Stuart Hollingdale, Makers of Mathematics (New York: Penguin, 1989); Ray Monk, Ludwig Wittgenstein: The Duty of Genius (New York: Penguin, 1990); John Dawson, Logical Dilemmas: The Life and Work of Kurt Gödel (Wellesley, Mass.: A. K. Peters, 1997); Roger Highfield and Paul Carter, The Private Lives of Albert Einstein (New York: St. Martin’s Press, 1994); Andrew Hodges, Alan Turing: The Enigma (New York: Simon & Schuster, 1983).
21. Anthony Storr, The Dynamics of Creation (New York: Atheneum, 1972).
22. Ibid.
23. John G. Gunderson, “Personality Disorders,” The New Harvard Guide to Psychiatry (Cambridge: The Belknap Press of Harvard University, 1988), pp. 343–44.
24. Ibid.
25. Ibid.
26. Havelock Ellis, A Study of British Genius (Boston: Houghton Mifflin, 1926).
27. Rogers, interview, 2.16.96.
28. Zipporah Levinson, interview, Cambridge, 9.11.95.
29. Irving I. Gottesman, Schizophrenia Genesis: The Origins of Madness (New York: W. H. Freeman, 1991). For a contrary view, which states that cases of schizophrenia have been documented as long as 3,400 years ago, see Ming T. Tsuang, Stephen V. Faraone, and Max Day, “Schizophrenic Disorders,” New Harvard Guide to Psychiatry, op. cit.
30. Tsuang, Faraone, and Day, op. cit., p. 259.
31. Gottesman, op. cit.; Tsuang, Faraone, and Day, op. cit.; Richard S. E. Keefe and Philip D. Harvey, Understanding Schizophrenia: A Guide to the New Research on Causes and Treatment (New York: Free Press, 1994); E. Fuller Torrey, Surviving Schizophrenia: A Family Manual (New York: Harper & Row, 1988).
32. Gottesman, op. cit.
33. For an excellent summary see Michael R. Trimble, Biological Psychiatry (New York: John Wiley & Sons, 1996), p. 224.
34. Eugen Bleuler, quoted in Louis A. Sass, Madness and Modernism (New York: Basic Books, 1992), p. 14.
35. Emil Kraepelin, quoted in ibid., pp. 13–14.
36. Torrey, op. cit.
37. Gottesman, op. cit.
38. Ibid.
39. See, for example, Tsuang, Faraone, and Day, op. cit.
40. See, for example, Gottesman, op. cit.
41. Ibid.
42. See, for example, Storr, Solitude, op. cit.; Gale Christianson, In the Presence of the Creator (New York: Free Press, 1984); Richard S. Westfall, The Life of Isaac Newton (Cambridge, U.K.: Cambridge University Press, 1993).
43. George Winokur and Ming Tsuang, The Natural History of Mania, Depression and Schizophrenia (Washington, D.C.: American Psychiatric Press, 1996), pp. 253–68; Manfred Bleuler, The Schizophrenia Disorders: Long-Term Patient and Family Studies (New Haven: Yale University Press, 1978).
44. M. Bleuler, op. cit., quoted in Sass, op. cit., p. 14.
45. Storr, The Dynamics of Creation, op. cit.
46. See, for example, Gottesman, op. cit. For discussions of differences between manic depressive illness and schizophrenia, see Torrey, op. cit.; Kay Redfield Jamison, Touched with Fire: Manic-Depressive Illness and the Artistic Temperament (New York: Free Press, 1993).
47. Sass, op. cit., prologue.
48. Emil Kraepelin, Dementia Praecox and Paraphrenia (Huntington, N.Y.: R. E. Krieger, 1971), quoted in Sass, op. cit., pp. 13–14.
49. Sass, op. cit., p. 4.
50. Letter from John Nash to Emil Artin, written in Geneva, undated (1959).
51. Letter from John Nash to Alex Mood, 11.94.
52. R. Nash, interview, 1.7.96.
53. Confidential source.
54. See, for example, Mikhail Gromov, Partial Differential Relations (New York: Springer-Verlag, 1986); Heisuke Hironaka, “On Nash Blowing Up,” Arithmetic and Geometry II (Boston: Birkauser, 1983), pp. 103–11; P. Ordehook, Game Theory and Political Theory: An Introduction (Cambridge, U.K.: Cambridge University Press, 1986); Richard Dawkins, The Selfish Gene (Oxford: Oxford University Press, 1976); John Maynard Smith, Did Darwin Get It Right? (New York: Chapman and Hall, 1989); as well as Math Reviews and Social Science Citation Index, various dates.
55. Eatwell, Milgate, Newman, op. cit., p. xii.
56. Ariel Rubinstein, professor of economics, Princeton University and University of Tel Aviv, interview, 10.18.95.
57. Eatwell, Milgate, Newman, op. cit.
58. Member, School of Historical Studies, Institute for Advanced Study, interview, 1995.
59. Freeman Dyson, professor of physics, Institute for Advanced Study, interview, Princeton, 12.5.96.
60. Enrico Bombieri, professor of mathematics, Institute for Advanced Study, interview, 12.6.96.
61. See, for example, Winokur and Tsuang, op cit., p. 268.
62. Kuhn, interview, 10.94.
1. John Forbes Nash, Jr., autobiographical essay, Les Prix Nobel 1994, op. cit.
2. “Nash-Martin,” Appalachian Power & Light Searchlight, vol. 3, no. 9 (September 1924), p. 14.
3. Ibid.
4. Martha Nash Legg, interview, Roanoke, 7.31.95.
5. The history of the Nashes is based on genealogical materials, regional histories, and newspaper clippings supplied by Martha Legg and Richard Nash, including The History of Grayson County, Texas, vol. 2 (Grayson County Frontier Village, 1981) and Graham Landrum and Allan Smith, Grayson County: An Illustrated History (Fort Worth, Tex.: Historical Publishers). The facts of John Forbes Nash, Sr.’s early life are based on interviews with Martha Nash Legg as well as his obituary.
6. Obituaries of Martha Nash, Baptist Standard (1944); M. Legg, interview, 8.1.95; R. Nash, interview, San Francisco, 1.7.97.
7. M. Legg, interview, 7.31.95.
8. The history of the Martins and the facts of Virginia Martin’s early life are based on interviews with Martha Legg as well as obituaries of Emma Martin and Virginia Martin in the Bluefield Daily Telegraph.
9. Letter from John Forbes Nash, Jr., to Martha Legg, undated (1969).
10. For a short history of the marriage bar, see Claudia Goldin, “Career and Family: College Women Look to the Past,” Working Paper No. 5188 (Cambridge, Mass.: National Bureau of Economic Research, July 1995).
11. C. Stuart McGehee, The City of Bluefield: Centennial History 1889–1989 (Bluefield Historical Society).
12. Ibid.; John E. Williams, professor of psychology, Wake Forest University, interview, 8.95.
13. John Nash, Les Prix Nobel 1994, op. cit.
14. Williams, interview, 10.24.95; William Lewis, McKinsey & Partners, interview, 10.94.
15. John Nash, Les Prix Nobel 1994, op. cit.
16. M. Legg, interview, 8.3.95.
17. Ibid.
18. John G. Gunderson, “Personality Disorders,” op. cit., pp. 343–44; also Nikki Erlenmeyer-Kimling, professor of genetics and development, Columbia University, interview, 1.17.98.
19. M. Legg, interview.
20. George Thornhill, quoted in William Archer, Bluefield Daily Telegraph, 10.94.
21. Report cards, various years, supplied by Martha Legg.
22. John Nash, Les Prix Nobel 1994, op. cit.
23. M. Legg, interview, 8.1.95.
24. Eddie Steele, quoted in William Archer, Bluefield Daily Telegraph, 10.13.94.
25. Donald V. Reynolds, interview, 6.29.97.
26. Ibid.
27. Ibid.
28. M. Legg, interview, 8.2.95.
29. Ibid.
30. E. T. Bell, Men of Mathematics, op. cit.; Betty Umberger, quoted in William Archer, Bluefield Daily Telegraph, 10.13.94.
31. Janice Thresher Frazier, personal communication, 9.97.
32. The origin of this quotation is unknown.
33. M. Legg, interview, 10.94.
34. Kuhn, interview, 3.97.
35. John Nash, Les Prix Nobel 1994, op. cit.
36. Bell, op. cit.
37. Ibid.
38. Ibid.
39. Denis Brian, Einstein: A Life (New York: John Wiley & Sons, 1996).
40. Bell, op. cit.; also Kuhn, interview, 10.21.97.
41. Bell, op. cit.
42. M. Legg, interview, 8.1.95.
43. Williams, interview.
44. Donald V. Reynolds, interview.
45. Interviews with Peggy Wharton, 12.96; Robert Holland, 6.9.97; John Louthan, 6.21.97; John Williams; Reynolds.
46. Reynolds, interview.
47. Ibid.
48. Felix Browder, president, American Mathematics Society, interview, 11.2.95.
49. M. Legg, interview, 11.94.
50. Nelson Walker, quoted in William Archer, Bluefield Daily Telegraph, 10.94.
51. Edwin Elliot, quoted in William Archer, Bluefield Daily Telegraph, 11.14.94.
52. M. Legg, interview, 8.2.95.
53. Reynolds, interview; see also William Archer, “Boys Will Be Boys,” Bluefield Daily Telegraph, 11.14.94.
54. Julia Robinson, in Donald Albers, Gerald L. Alexanderson, and Constance Reid, More Mathematical People (New York: Harcourt Brace Jovanovich, 1990), p. 271.
55. Anthony Storr, The Dynamics of Creation, op. cit.
56. M. Legg, interview, 11.94.
57. Vernon Dunn, quoted in William Archer, Bluefield Daily Telegraph, 11.94.
58. Beaver High School Yearbook, 1945.
59. Interviews with Williams and Louthan.
60. M. Legg, interview, 8.1.95.
61. John Nash, Les Prix Nobel 1994, op. cit.
62. John F. Nash and John F. Nash, Jr., “Sag and Tension Calculations for Cable and Wire Spans Using Catenary Formulas,” Electrical Engineering, 1945.
63. Uncle App’s News, 7.45.
1. Nash’s interest in number theory, topology, and other branches of pure mathematics was recalled by Robert Siegel, professor of physics, College of William and Mary, interview, 10.30.97; Hans F. Weinberger, professor of mathematics, University of Minnesota, interviews, 9.6.95, 10.28.95, and 10.29.95; Paul F. Zweifel, professor of mathematics, Virginia Polytechnic Institute, interviews, 10.94 and 9.6.95; Richard J. Duffin (deceased), emeritus professor of mathematics, Carnegie-Mellon University, interviews, 10.94, 8.95, and 10.26.96.
2. See, for example, Stephan Lorant, Pittsburgh: The Story of an American City (Lenox, Mass.: author’s edition, 1980) and interviews with Nash’s contemporaries.
3. Richard Cyert, former president, Carnegie-Mellon University, interview, 10.26.95. Also Herbert Simon, Nobel Laureate, Carnegie-Mellon University, interview, 10.26.95.
4. Duffin, interview, 10.26.96; Robert E. Gleeson, professor of history, Carnegie-Mellon University, interview, 10.27.95; Glen U. Cleeton, The Story of Carnegie Tech, II: The Doherty Administration, 1936–1950 (Pittsburgh: Carnegie Press, 1965); Robert E. Gleeson and Steven Schlossman, George Leland Bach and the Rebirth of Graduate Management Education in the United States, 1945–1975 (Graduate Management Admission Council, Spring 1995); Robert E. Gleeson and Steven Schlossman, The Many Faces of the New Look: The University of Virginia, Carnegie Tech and the Reform of American Management Education in the Postwar Era (Graduate Management Admission Council, Spring 1992).
5. Interviews with Weinberger, 10.28.95; Zweifel, 10.94; George W. Hinman, professor of physics, Washington State University, 10.30.97; David R. Lide, editor, CRC Handbook of Chemistry and Physics, 10.30.97; Edward Kaplan, professor of statistics, Oregon State University, 5.21.97.
6. Interviews with Martha Nash Legg, 8.2.95; Weinberger, 10.28.95; Zweifel, 10.94.
7. Interviews with Siegel, 10.30.97; Hinman, 10.30.97.
8. John Nash, autobiographical essay, Les Prix Nobel 1994, op. cit.
9. Lide, interview, 10.30.97.
10. Hinman, interview, 10.30.97.
11. Lide, interview, 10.30.97.
12. John Nash, Les Prix Nobel 1994, op. cit.
13. Interviews with Raoul Bott, professor of mathematics, Harvard University, 11.5.95; Hinman, 10.30.97; Cathleen S. Morawetz, professor of mathematics, Courant Institute, and daughter of J. Synge, 2.29.96.
14. Duffin, interview, 10.26.95.
15. Duffin, interview, 10.94.
16. Morawetz, interview.
17. Ibid.
18. Interviews with Lide, 10.30.97, and Duffin, 10.26.95.
19. Weinberger, interview, 9.6.95.
20. Siegel, interview, 10.30.97. Siegel may have been mistaken; Bluefield had both a symphony and concert series before the war.
21. Bott, interview, 11.5.95.
22. Patsy Winter, Williamsburg, Virginia, interview, 10.30.97.
23. Weinberger, interview, 10.28.96.
24. Lide, interview, 10.30.97.
25. Interviews with Zweifel, 10.94, and Lide, 10.30.97.
26. Weinberger, interview, 10.28.95.
27. Siegel, interview, 10.30.97.
28. Hinman, interview, 10.30.97.
29. Zweifel, interview, 10.94.
30. Zweifel, interview, 1.21.98.
31. Ibid.; also interviews with Hinman, 10.30.97, and Siegel, 10.30.97.
32. Siegel, interview, 10.30.97.
33. Weinberger, interview, 10.28.95.
34. Zweifel, interview, 10.94.
35. Fletcher Osterle, professor of mechanical engineering, Carnegie-Mellon University, interview, 5.21.97.
36. Mathematical Monthly (September 1947), p. 400.
37. Leonard F. Klosinski, director, the William Lowell Putnam Mathematical Competition, interview, 10.96; Gerald L. Alexanderson, associate director, the William Lowell Putnam Mathematical Competition, interview, 10.96; Garrett Birkhoff, “The William Lowell Putnam Mathematical Competition: Early History,” and L. E. Bush, “The William Lowell Putnam Mathematical Competition: Later History and Summary of Results,” reprinted from American Mathematical Monthly, vol. 72 (1965), pp. 469–83.
38. Hinman, interview.
39. Harold Kuhn, interview, 7.97.
40. John Nash, Les Prix Nobel 1994, op. cit.
41. This scene is based on recollections of Duffin, interview, 10.94 and 10.26.95; Bott, interview, 10.94; and Weinberger, interviews, 9.6.95 and 10.28.95.
42. Duffin, interview, 10.94.
43. Bott, interview, 10.94.
44. Martin Burrow, professor of mathematics, Courant Institute, interview, 2.4.96.
45. Duffin, interviews, 10.94 and 10.26.95.
46. Duffin, interview, 10.94.
47. Bott, interview, 11.5.95.
48. Weinberger, interview, 10.28.95.
49. Siegel, interview, 10.30.97.
50. Weinberger, interview.
51. John Nash, Les Prix Nobel 1994, op. cit.
53. The Carnegie Tartan, 4.20.48.
54. Interviews with Kuhn, 10.97, and M. Legg, 8.3.95.
55. John Nash, Les Prix Nobel 1994, op. cit.
56. The perception of Harvard’s relative decline and Princeton’s ascendancy by the late 1940s was widespread among Nash’s contemporaries.
57. Duffin, interview, 10.26.95.
58. Letter from Solomon Lefschetz to Nash, 4.8.48.
59. Details about the JSK Fellowship, named after John S. Kennedy, a Princeton alumnus, are based on a memorandum from Sandra Mawhinney to Harold Kuhn, 10.27.97.
60. Graduate Catalog, Princeton University, various years; Report to the Dean of Faculty, Princeton University, various years.
61. John Nash, Les Prix Nobel 1994, op. cit.
62. Letter from S. Lefschetz to J. Nash.
63. Letter from John Nash to Solomon Lefschetz, undated, mid-April 1948.
64. Clifford Ambrose Truesdell, interview, 8.14.96.
65. Letter from J. Nash to S. Lefschetz. For the events transpiring then, see Chronicle of the Twentieth Century (Mount Kisco, N.Y.: Chronicle Publications, 1987).
66. Interviews with Charlotte Truesdell, 8.14.96, and Kaplan, 5.21.97.
67. Letter from J. Nash to S. Lefschetz, 4.26.48.
68. Clifford Truesdell, interview, 8.14.96.
69. Charlotte Truesdell, interview, 8.14.96.
1. Martha Nash Legg, interview, 8.3.95.
2. See, for example, Rebecca Goldstein, The Mind-Body Problem (New York: Penguin, 1993); Ed Regis, Who Got Einstein’s Office? (Reading, Mass.: Addison Wesley, 1987); and recollections of Nash’s contemporaries, including interviews with Harold Kuhn and Harley Rogers and letter from George Mowbry, 4.5.95.
3. F. Scott Fitzgerald, This Side of Paradise (New York: Scribner, 1920).
4. Albert Einstein, quoted in Goldstein, op. cit.
5. As recalled by her niece Gillian Richardson, interview, 12.14.95.
6. Donald Spencer, professor of mathematics, Princeton University, interview, Durango, Colorado, 11.18.95.
7. Leopold Infeld, Quest (New York: Chelsea Publishing Company, 1980).
8. Virginia Chaplin, “Princeton and Mathematics,” Princeton Alumni Weekly (May 9, 1958).
9. John D. Davies, “The Curious History of Physics at Princeton,” Princeton Alumni Weekly (October 2, 1973).
10. Harold W. Kuhn, interview, 1.97.
11. Eugene Wigner, Recollections of Eugene Paul Wigner as Told to Andrew Szanton (New York: Plenum Press, 1992).
12. Regis, op. cit.
13. Infeld, op. cit.
14. Chaplin, op. cit.; William Aspray, “The Emergence of Princeton as a World Center for Mathematical Research, 1896–1939,” in A Century of Mathematics in America, Part II (Providence, R.I.: American Mathematical Society, 1989); Gian-Carlo Rota, “Fine Hall in Its Golden Age,” in Indiscrete Thoughts (Washington, D.C.: Mathematical Association of America, 1996), pp. 3–20.
15. Davies, op. cit.
16. Solomon Lefschetz, “A Self Portrait,” typewritten, 1.54, Princeton University Archives.
17. Davies, op. cit.
18. Ibid.
19. Ibid.
20. Robert J. Leonard, “From Parlor Games to Social Science,” op. cit.
21. Davies, op. cit.
22. Woodrow Wilson, quoted in ibid.
23. George Gray, Confidential Monthly Trustees Report, Rockefeller Foundation Archives (November 1945).
24. Wigner, op. cit.
25. The account of the Institute’s history is based on Regis, op. cit.; Bernice M. Stern, A Histon of the Institute for Advanced Study 1930–1950, unpublished two-volume manuscript (1964).
26. Garrett Birkhoff, “Mathematics at Harvard 1836–1944,” in A Century of Mathematics in America, Part II, op. cit., pp. 3–58; William Aspray, “The Emergence of Princeton as a World Center for Mathematical Research, 1896–1939,” in A Century of Mathematics in America, Part II, op. cit., pp. 195–216; Gian-Carlo Rota, “Fine Hall in Its Golden Age,” in A Century of Mathematics in America, Part II, op. cit., pp. 223–36.
27. Robin E. Rider, “Alarm and Opportunity: Emigration of Mathematicians and Physicists to Britain and the United States, 1933–1945,” Historical Studies in the Physical and Biological Sciences, vol. 15, no. 1 (1984), pp. 108–71.
28. Paul Samuelson, “Some Memories of Norbert Wiener,” provided by author, undated.
29. William James, “Great Men, Great Thoughts and Environment,” Atlantic Monthly, vol. 46 (1880), pp. 441–59, quoted in Silvano Arieti, Creativity: The Magic Synthesis (New York: Basic Books, 1976), p. 299.
30. See, for example, Davies, op. cit.; Chaplin, op. cit.; Nathan Rheingold, “Refugee Mathematicians in the United States of America, 1933–1941: Reception and Reaction,” Annals of Science, vol. 38 (1981), pp. 313–38; Rider, op. cit.; Lipman Bers, “The European Mathematician’s Migration to America,” in A Century of Mathematics in America, Part II (Providence, R.I.: American Mathematical Society, 1988).
31. See, for example, Mina Rees, “The Mathematical Sciences and World War II,” in A Century of Mathematics in America, Part I; op. cit., Peter Lax, “The Flowering of Applied Mathematics in America,” in A Century of Mathematics in America, Part II, op. cit., pp. 455–66; Fred Kaplan, The Wizards of Armageddon (New York: Simon & Schuster, 1983).
32. Chaplin, op. cit.
33. Andrew Hodges, Alan Turing: The Enigma (New York: Simon & Schuster, 1983).
34. Chaplin, op. cit.
35. Ibid.
36. See Kaplan, op. cit.; William Poundstone, Prisoner’s Dilemma (New York: Doubleday, 1992); David Halberstam, The Fifties, op. cit.
37. Rees, “The Mathematical Sciences and World War II,” op. cit.; Lax, “The Flowering of Applied Mathematics in America,” op. cit., pp. 455–66.
38. Herman H. Goldstine, “A Brief History of the Computer,” in A Century of Mathematics in America, Part I, op. cit., pp. 311–22; Poundstone, op. cit., pp. 76–78, on von Neumann’s role in the development of the computer; Halberstam, op. cit., pp. 93–97, on von Neumann and the computer.
39. Hartley Rogers, professor of mathematics, MIT, interview, 1.26.96.
1. Solomon Leader, professor of mathematics, Rutgers University, interview, 6.9.95.
2. The portrait of Solomon Lefschetz is based on interviews with Harold W. Kuhn, 11.97; William Baumol, 1.95; Donald Spencer, 11.18.95; Eugenio Calabi, 3.2.96; Martin Davis, 2.20.96; Melvin Hausner, 2.6.96; Solomon Leader, 6.9.95; and other contemporaries of Nash’s at Princeton. Also consulted were several memoirs, including Solomon Lefschetz, “Reminiscences of a Mathematical Immigrant in the United States,” American Mathematical Monthly, vol. 77 (1970); A. W. Tucker, Solomon Lefschetz: A Reminiscence; Sir William Hodge, Solomon Lefschetz, 1884–1972; Phillip Griffiths, Donald Spencer, and George Whitehead, Solomon Lefschetz: Biographical Memoirs (Washington, D.C.: National Academy of Sciences, 1992); Gian-Carlo Rota, Indiscrete Thoughts, op. cit.
3. Lefschetz’s obituary in The New York Times (October 7, 1972) credits him for “developing] [the Annals of Mathematics] into one of the world’s foremost mathematical journals.”
4. “It should be noted that although Lefschetz was Jewish, he was not above engaging in a mild form of anti-semitism. He told Henry Wallman that he was the last Jewish graduate student that would be admitted to Princeton because Jews could not get a job anyway and so why bother,” Ralph Phillips, “Reminiscences of the 1930s,” The Mathematical Intelligencer, vol. 16, no. 3 (1994). Lefschetz’s attitude toward Jewish students was well known. Phillips’s impressions were confirmed by Leader, interview, 6.9.95; Kuhn, interview, 11.97; Davis, interview, 2.20.96; and Hausner, interview, 2.6.96.
5. Baumol, interview, 1.95.
6. See, for example, Gian-Carlo Rota, “Fine Hall in Its Golden Age,” op. cit. DOD personnel security application, 3.10.56, Princeton University Archives.
7. Solomon Lefschetz, “A Self Portrait,” typewritten, 1.54, Princeton University Archives.
8. Ibid., p. iii.
9. Donald Spencer, interviews, 11.28.95; 11.29.95; 11.30.95.
10. Rota, op. cit.
11. Ibid.
12. Ibid.
13. Leader, interview, 6.9.95.
14. Davis, interview, 2.6.96.
15. Hausner, interview, 2.6.96.
16. Leader, interview, 6.9.95.
17. Spencer, interviews.
18. Virginia Chaplin, “Princeton and Mathematics,” op. cit.; Davis, interview, 2.20.96; Hartley Rogers, interview, 1.26.96.
19. Ibid.
20. Hausner, interview.
21. Ibid.
22. Ibid.
23. Joseph Kohn, interview, 7.25.96.
24. Robert Kanigel, The Man Who Knew Infinity (New York: Pocket Books, 1991); G. H. Hardy, “The Indian Mathematician Ramanujan,” lecture delivered at the Harvard Tercentenary Conference of Arts and Sciences, August 31, 1936, reprinted in A Century of Mathematics (Washington, D.C.: Mathematical Association of America, 1994), p. 110.
25. Hardy, op. cit.
26. J. Davies, op. cit.; Gerard Washnitzer, professor of mathematics, Princeton University, interview, 9.25.96.
27. Graduate Catalog, Princeton University, various years; Report to the President, Princeton University, various years.
28. Letter from John Nash Forbes, Jr., to Solomon Lefschetz referring to request for private room, 4.46; Calabi, interview.
29. Interviews with Kuhn, 11.97; Washnitzer, 9.25.96; Felix Browder, 11.2.96; Calabi, 3.12.96; John Tukey, professor of mathematics, Princeton University, 9.30.97; John Isbell, professor of mathematics, State University of New York at Buffalo, 8.97; Leader, 6.9.95; Davis, 2.6.96.
30. Kuhn, interview.
31. Davis, interview.
32. Interviews with Washnitzer and Kuhn.
33. Washnitzer, interview.
34. Tukey, interview.
35. Kuhn, interview.
36. Calabi, interview.
37. Martin Shubik, “Game Theory at Princeton: A Personal Reminiscence,” Cowles Foundation Preliminary Paper 901–019, undated.
38. Interviews with Hausner; Davis; Kuhn; Spencer; Leader; Rogers; Calabi; and John McCarthy, professor of computer science, Stanford University, 2.4.96.
39. Hausner, interview, 2.6.96.
40. Interviews with Davis, Leader, Spencer; Rota, op. cit.
41. Rota, op. cit.
42. Isbell, interview.
43. Tukey, interview.
44. David Yarmush, interview, 2.6.96.
45. Princeton Alumni Directory 1997.
46. John W. Milnor, professor of mathematics and director, Institute for Mathematical Sciences, State University of New York at Stony Brook, interviews, 10.28.94 and 7.95.
47. Interviews with Kuhn, Hausner, John McCarthy.
48. Interviews with Hausner and Davis.
1. Kai Lai Chung, professor of mathematics, Stanford University, interview, 1.96; letter, 2.6.96.
2. Abraham Pais, Subtle Is the Lord: The Science and Life of Albert Einstein (New York: Oxford University Press, 1982).
3. Interviews with Charlotte Truesdell, 8.14.96; Martin Davis, 2.20.96; Hartley Rogers, 2.16.96; and John McCarthy, 2.4.96; John Forbes Nash, Jr., Personnel Security Questionnaire, 5.26.50, Princeton University Archives.
4. “Trivial,” Melvin Hausner, interview; “burbling,” Patrick Billingsley, professor of statistics, University of Chicago, interview, 8.12.97; “hacker,” Hausner, interview.
5. Rogers, interview.
6. Davis, interview.
7. Peggy Murray, former secretary, department of mathematics, Princeton University, interview, 8.25.97.
8. Davis, interview.
9. John Milnor, interview, 9.26.95.
10. John Nash, autobiographical essay, Les Prix Nobel 1994, op. cit.
11. Mentioned by many of his contemporaries, this was confirmed by Nash in a conversation with Harold Kuhn.
12. Harold Kuhn, personal communication, 8.96.
13. Eugenio Calabi, interview.
14. Ibid.
15. Interviews with Solomon Leader and Calabi.
16. Letter from John Nash to Solomon Lefschetz, 4.48.
17. Calabi, interview.
18. John Milnor, “A Nobel Prize for John Nash,” The Mathematical Intelligencer, vol. 17, no. 3 (1995), p. 5.
19. Leader, interview, 6.9.96.
20. Ibid.
21. David Gale, interview, 9.20.95.
22. Davis, interview.
23. Kuhn, interview, 9.96.
24. Hausner, interview.
25. Milner, interview, 9.26.95.
26. Norman Steenrod, letter, 1950, quoted by Harold Kuhn, introduction, “A Celebration of John F. Nash, Jr.,” Duke Mathematical Journal, vol. 81, no. 2 (1996).
27. E. T. Bell, Men of Mathematics, op. cit.
28. Steenrod, letter, 2.5.53.
29. For this assessment, I relied on Hale Trotter and Harold Kuhn.
30. Milnor, interview.
31. Kuhn, interview, 8.97.
32. Ed Regis, Who Got Einstein’s Office? op. cit.; Denis Brian, Einstein: A Life, op. cit.
33. John Forbes Nash, Jr., plenary lecture, World Congress of Psychiatry, Madrid, 8.26.96, op. cit.
34. Ibid.
35. Regis, op. cit.
36. Ibid.; also Brian, op. cit.
37. Brian, op. cit.
38. Ibid.
39. Nash, as told to Harold Kuhn; see also Brian, op. cit., for description of Kemeny’s assistantship under Einstein in 1948–49.
40. Brian, op. cit.
41. John Nash, as told to Kuhn, November 1997.
42. Ibid.
43. Ibid.
44. Ibid.
45. Calabi, interview.
46. William Browder, professor of mathematics, Princeton University, interview, 12.6.96.
47. Steenrod, letter, 2.5.53.
48. Milnor, interview, 9.26.95.
49. Interviews with Leader and Kuhn.
50. Princeton University Archives.
51. Ibid.
52. Melvin Peisakoff, interview, 6.3.97.
53. Rogers, interview.
54. Calabi, interview.
55. Hausner, interview.
56. Rogers, interview.
57. Hausner, interview.
58. Felix Browder, interview, 11.2.95.
59. Leader, interview.
60. Harold Kuhn witnessed the scene, and Mel Peisakoff confirmed that it took place.
61. Donald Spencer, interview.
62. Letter from Al Tucker to Alfred Koerner, 10.8.56.
63. The portrait of Artin is based on Gian-Carlo Rota, Indiscrete Thoughts, op. cit., as well as recollection of John Tate; Spencer, interview, 11.18.96; Hauser, interview; and materials from the Princeton University Archives.
64. Spencer, interview.
65. Kuhn, interview.
1. Albert W. Tucker, as told to Harold Kuhn, interview.
2. Interviews with Marvin Minsky, professor of science, MIT, 2.13.96; John Tukey, 9.30.97; David Gale, 9.20.96; Melvin Hausner, 1.26.96 and 2.20.96; and John Conway, professor of mathematics, Princeton University, 10.94; John Isbell, e-mails, 1.25.96, 1.26.97, 1.27.97.
3. Isbell, e-mails.
4. Letter from John Nash to Martin Shubik, undated (1950 or 1951); Hausner, interviews and e-mails.
5. William Poundstone, Prisoner’s Dilemma, op. cit.; John Williams, The Compleat Strategyst (New York: McGraw Hill, 1954).
6. Poundstone, op. cit.
7. Solomon Leader, interview, 6.9.95.
8. Martha Nash Legg, interview, 8.1.95.
9. Isbell, e-mails.
10. Hartley Rogers, interview, 1.26.96.
11. Ibid.
12. Ibid.
13. Nash may have had the idea while he was at Carnegie. This, in any case, is Hans Weinberger’s recollection, interview, 10.28.95.
14. Martin Gardner, Mathematical Puzzles and Diversions (New York: Simon & Schuster, 1959), pp. 65–70.
15. Gardner’s comment, in 1959, was that Hex “may well become one of the most widely played and thoughtfully analyzed new mathematical games of the century.”
16. Gale, interview, 9.20.95.
17. Dinner at which John Nash, David Gale, and the author were present, January 5, 1996, San Francisco.
18. Gale, interview.
19. Ibid.
20. Phillip Wolfe, mathematician, IBM, interview, 9.9.96.
21. John Milnor, “A Nobel Prize for John Nash,” op. cit.
22. Ibid.; Gardner, op. cit.
23. Gale, interview.
24. Ibid.
25. Ibid.
26. Kuhn, interview.
27. Ibid.
28. Milnor, interview, 9.26.95.
1. See, for example, Stanislaw Ulam, “John von Neumann, 1903–1957,” Bulletin of the American Mathematical Society, vol. 64, no. 3, part 2 (May 1958); Stanislaw Ulam, Adventures of a Mathematician (New York: Scribner’s, 1983); Paul R. Halmos, “The Legend of John von Neumann,” American Mathematical Monthly, vol. 80 (1973); William Poundstone, Prisoner’s Dilemma, op. cit.; Ed Regis, Who Got Einstein’s Office?, op. cit.
2. Poundstone, op. cit.
3. Ulam, “John von Neumann,” op. cit.; Poundstone, op. cit., pp. 94–96.
4. Harold Kuhn, interview, 1.10.96.
5. In remarks at a Nobel luncheon at the American Economics Association meeting on 1.5.96, Nash traced a lineage from Newton to von Neumann to himself. Nash shared von Neumann’s interest in game theory, quantum mechanics, real algebraic variables, hydrodynamic turbulence, and computer architecture.
6. See, for example, Ulam, “John von Neumann,” op. cit.
7. Norman McRae, John von Neumann (New York: Pantheon Books, 1992), pp. 350–56.
8. John von Neumann, The Computer and the Brain (New Haven: Yale University Press, 1959).
9. See, for example, G. H. Hardy, A Mathematician’s Apology (Cambridge, U.K.: Cambridge University Press, 1967), with a foreword by C. P. Snow.
10. Ulam, “John von Neumann,” op. cit.
11. Poundstone, op. cit.
12. Poundstone, Prisoner’s Dilemma, p. 190.
13. Clay Blair, Jr., “Passing of a Great Mind,” Life (February 1957), pp. 89–90, as quoted by Poundstone, op. cit., p. 143.
14. Poundstone, op. cit.
15. Ulam, “John von Neumann,” op. cit.
16. Harold Kuhn, interview, 3.97.
17. Paul R. Halmos, “The Legend of John von Neumann,” op. cit.
18. Ibid.
19. Poundstone, op. cit.
20. Halmos, op. cit.
21. Ibid.
22. Poundstone, op. cit.
23. Ulam, Adventures of a Mathematician, op. cit.
24. Ulam, “John von Neumann,” op. cit.
25. Ibid.
26. Ibid., p. 10; Robert J. Leonard, “From Parlor Games to Social Science,” op. cit.
27. Richard Duffin, interview, 10.94.
28. Halmos, op. cit.
29. Ulam, “John von Neumann,” op. cit., pp. 35–39.
30. Interviews with Donald Spencer, 11.18.95; David Gale, 9.20.95; and Harold Kuhn, 9.23.95.
31. Poundstone, op. cit.
32. Herman H. Goldstine, “A Brief History of the Computer,” A Century of Mathematics in America, Part I, op. cit.
33. John von Neumann, as quoted in ibid.
1. John von Neumann and Oskar Morgenstern, The Theory of Games and Economic Behavior (Princeton: Princeton University Press, 1944, 1947, 1953).
2. Both von Neumann and Morgenstern came to the seminar. Albert W. Tucker, interview, 10.94. See also Martin Shubik, “Game Theory and Princeton, 1940–1955: A Personal Reminiscence,” Cowles Foundation Preliminary Paper, undated, p. 3; David Gale, interview, 9.20.95; and Harold Kuhn, interview, 9.20.95.
3. A. W. Tucker, “Combinatorial Problems Related to Mathematical Aspects of Logistics: Final Summary Report” (U.S. Department of the Navy, Office of Naval Research, Logistics Branch, February 28, 1957), p. 1.
4. Melvin Hausner, interview, 2.6.96.
5. Interviews with David Yarmush, 2.6.96, and John Mayberry, 4.15.96.
6. David Gale, interview.
7. Kuhn, interview.
8. Ibid.; Hausner, interview.
9. Robert J. Leonard, “From Parlor Games to Social Science,” op. cit.
10. See, for example, H. W. Kuhn and A. W. Tucker, “John von Neumann’s Work in the Theory of Games and Mathematical Economics,” Bulletin of the American Mathematical Society (May 1958).
11. Leonard, “From Parlor Games to Social Science,” op. cit.
12. Ibid.
13. Ibid.
14. Dorothy Morgenstern Thomas, interview, 1.25.96. Morgenstern kept a portrait of the kaiser hanging in his home.
15. Letter from George Mowbry to author, 4.5.95.
16. Leonard, “From Parlor Games to Social Science,” op. cit.
17. As quoted in ibid.
18. Ibid.
19. Ibid.
20. Ibid.
21. Ibid.
22. Ibid.
23. Ibid.
24. Ibid.
25. A. W. Tucker, who knew both men well, said, “If he hadn’t been forced to write a book, it wouldn’t have gotten written,” interview, 10.94. Von Neumann was interested in economics before he met Morgenstern.
26. Leonard, “From Parlor Games to Social Science,” op. cit.
27. Ibid.
28. Von Neumann and Morgenstern, op. cit., p. 6.
29. Leonid Hurwicz, “The Theory of Economic Behavior,” The American Economic Review (1945), pp. 909–25.
30. Von Neumann and Morgenstern, op. cit., p. 7.
31. Ibid., p. 3.
32. Ibid.
33. Ibid., p. 4.
34. Ibid., p. 7.
35. Ibid., p. 2.
36. Ibid.
37. Ibid., p. 6.
38. New York Times, 3.46.
39. See, for example, Herbert Simon, The American Journal of Sociology, no. 50 (1945), pp. 558–60. Hurwicz, op. cit.; Jacob Marschak, “Neumann’s and Morgenstern’s New Approach to Static Economics,” Journal of Political Economy, no. 54 (1946), pp. 97–115; John McDonald, “A Theory of Strategy,” Fortune (June 1949), pp. 100–110.
40. Leonard, “From Parlor Games to Social Science,” op. cit.
41. Ibid.
42. Ibid.
43. Shubik, “Game Theory and Princeton,” op. cit., p. 2.
44. Von Neumann and Morgenstern, op. cit. See also Eatwell, Milgate, and Newman, op. cit.
45. Von Neumann and Morgenstern, op. cit.
46. Ibid.
47. See, for example, John C. Harsanyi, “Nobel Seminar,” in Les Prix Nobel 1994.
48. Von Neumann and Morgenstern, op. cit.
49. Ibid.
50. Ibid.
51. Harsanyi, op. cit.
1. John Forbes Nash, Jr., “The Bargaining Problem,” Econometrica, vol. 18 (1950), pp. 155–62.
2. Nash’s bargaining solution was “virtually unanticipated in the literature,” according to Roger B. Myerson, “John Nash’s Contribution to Economics,” Games and Economic Behavior, no. 14 (1996), p. 291. See also Ariel Rubinstein, “John Nash: The Master of Economic Modeling,” The Scandinavian Journal of Economics, vol. 97, no. 1 (1995), pp. 11–12; John C. Harsanyi, “Bargaining,” in Eatwell, Milgate, and Newman, op. cit., pp. 56–60; Andrew Schotter, interview, 10.25.96; Ariel Rubinstein, interview, 11.25.96; James W. Friedman, professor of economics, University of North Carolina, interview, 10.2.96.
3. “This is the classical problem of exchange and, more specifically, of bilateral monopoly as treated by Cournot, Bowley, Tintner, Fellner and others,” Nash, “The Bargaining Problem,” p. 155. As Harold Kuhn points out, Nash’s delineation of the history of the problem was undoubtedly supplied by Oskar Morgenstern, “It is now clear that Nash had not read those writers,” Harold Kuhn, “Nobel Seminar,” Les Prix Nobel 1994. For a delightful short history of exchange, including the references to pharaohs and kings, see Robert L. Heilbroner, The Worldly Philosophers, 6th edition (New York: Touchstone, 1992), p. 27.
4. John C. Harsanyi, “Approaches to the Bargaining Problem Before and After the Theory of Games: A Critical Discussion of Zeuthen’s, Hick’s and Nash’s Theories,” Econometrica, vol. 24 (1956), pp. 144–57.
5. In his now-classic reformulation of the Nash bargaining model, Ariel Rubinstein traces the bargaining problem to Edgeworth, “Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences” (London: C. Kegan Paul, 1881), reprinted in Mathematical Psychics and Other Essays (Mountain Center, Calif.: James & Gordon, 1995). Martin Shubik writes, “Even as a graduate student I was struck by the contrast between cooperative game theory, the seeds of which I regarded as already present in Edgeworth and noncooperative theory which was present in Cournot,” Martin Shubik, Collected Works, forthcoming, p. 6. For lively accounts of Edgeworth’s life and contributions, see Heilbroner, op. cit., pp. 174–76, and John Maynard Keynes, “Obituary of Francis Isidro Edgeworth, March 26, 1926,” reprinted in Edgeworth, op. cit.
6. Heilbroner, op. cit., p. 173.
7. Ibid., p. 174.
8. Edgeworth, op. cit.
9. Ibid.
10. Ibid.
11. Harsanyi, op. cit.
12. John von Neumann and Oskar Morgenstern, The Theory of Games and Economic Behavior, op. cit., p. 9. “It may also be regarded as a nonzero-sum two-person game,” Nash, “The Bargaining Problem,” op. cit., p. 155; “even though von Neumann and Morgenstern’s theory of games was an essential step toward a strong bargaining theory, their own analysis of two-person bargaining games did not go significantly beyond the weak bargaining theory of neoclassical economics,” Harsanyi, “Bargaining,” op. cit., pp. 56–57.
13. See, for example, Robert J. Leonard, “From Parlor Games to Social Science,” op. cit., for a history of the axiomatic approach, and a superb interpretive discussion of “axiomatics” in Robert J. Aumann, “Game Theory,” in John Eatwell, Murray Milgate, and Peter Newman, The New Palgrave, op. cit., pp. 26–28.
14. Von Neumann and Morgenstern used the axiomatic method to derive their theory of expected or von Neumann-Morgenstern utilities in the second, 1947, edition of Theory of Games and Economic Behavior. The first application to a problem in social sciences, I believe, was Kenneth J. Arrow’s Ph.D. thesis Social Choice and Individual Values (New York: John Wiley & Sons, 1951). Lloyd S. Shapley’s “A Value of N-Person Games,” Contributions to the Theory of Games II (Princeton: Princeton University Press, 1953), pp. 307–17, is another stellar example.
15. John Nash, “The Bargaining Problem,” op. cit., p. 155.
16. John Nash, Les Prix Nobel 1994, op. cit., pp. 276–77.
17. The sketch of Bart Hoselitz is based on an interview with his friend Sherman Robinson, professor of economics, University of Chicago, 7.95, and questionnaires, letters, and a curriculum vitae from Carnegie-Mellon University archives.
18. This bit of history about international trade theory after World War II was supplied by Kenneth Rogoff, professor of economics, Princeton University, interview.
19. John Nash, Les Prix Nobel 1994, op. cit., pp. 176–77.
20. Nash told Myerson that he was inspired by a problem posed by Hoselitz. Roger Myerson, professor of economics, Northwestern University, interview, 8.7.97.
21. Myerson, e-mail, 8.11.97.
22. Letter from John Nash to Martin Shubik, undated (written in 1950 or 1951).
23. Harold Kuhn was for many years convinced that Nash had mailed a copy of his first draft to von Neumann while he was still at Carnegie. Also interviews with David Gale, 9.20.95, and William Browder, 12.6.96.
24. After historian Robert Leonard published the established version of the origins of the paper in “Reading Cournot, Reading Nash: The Creation and Stabilisation of the Nash Equilibrium,” The Economic Journal, no. 164 (May 1994), p. 497, Nash corrected the record at a lunch with Harold Kuhn and Roger Myerson, 5.96, Kuhn, personal communication, 5.96.
25. John Nash, “The Bargaining Problem,” op. cit., p. 155.
26. John Nash, Les Prix Nobel 1994, op. cit., p. 277.
1. Harold Kuhn, interview, 4.14.97.
2. Albert William Tucker, interview, 10.94.
3. The beer party scene was reconstructed from the recollections of Melvin Hausner, 2.6.96, Martin Davis, 2.20.96, and Hartley Rogers, 1.16.96, who attended several such parties in the course of their graduate school careers.
4. Davis, interview.
5. Ibid. Amazingly, Davis was able, forty years later, to recall the entire song, a few lines of which are given here, interview.
6. Kuhn, interview, 4.16.97.
7. Ibid.
8. Henri Poincaré, quoted in E. T. Bell, Men of Mathematics, op. cit., p. 551.
9. John Nash to Robert Leonard, e-mail, 2.20.93. Further details supplied by Harold Kuhn, interview, 4.17.97.
10. “All the graduate students were afraid of him,” according to Donald Spencer, interview, 11.8.95.
11. Von Neumann’s dress and manner are described by George Mowbry in a letter, 4.5.95. Harold Kuhn, interview, 5.2.97.
12. See, for example, Norman McRae, John von Neumann, op. cit., pp. 350–56.
13. As told to Harold Kuhn, 4.17.97.
14. John Nash, Les Prix Nobel 1994, op. cit.
15. Silvano Arieti, Creativity op. cit., p. 294.
16. J. Nash to R. Leonard, e-mail.
17. Ibid.
18. The conversation between Nash and Gale was recounted by Gale in an interview, 9.20.95. Gale also suggested that Nash use Kakutani’s fixed point theorem instead of Brouwer’s to simplify the proof, a suggestion that Nash followed in the note in the National Academy of Sciences Proceedings.
19. John F. Nash, Jr., “Equilibrium Points in N-Person Games,” communicated by S. Lefschetz, 11.16.49, pp. 48–49.
20. Gale, interview.
21. Tucker, interview, 10.94.
22. Gian-Carlo Rota, interview, 12.12.95.
23. Tucker’s account of Minsky’s thesis on computers and the brain, “Neural Networks and the Brain Problem,” is given in an interview with Stephen B. Maurer published in the Two Year College Mathematics Journal, vol. 14, no. 3 (June 1983).
24. Tucker, interview.
25. Harold Kuhn, “Nobel Seminar,” Les Prix Nobel 1994, op. cit., p. 283.
26. Tucker, interview, 10.94.
27. Ibid.
28. Ibid.
29. John Nash, Les Prix Nobel 1994, op. cit.
30. Tucker, interview.
31. Letter from Albert W. Tucker to Solomon Lefschetz, 5.10.50.
32. Ibid.
33. See, for example, introduction, John Eatwell, Murray Milgate, and Peter Newman, The New Pal-grave, op. cit.
34. “It so happens that the concept of the two-person zero-sum games has very few real life applications,” John C. Harsanyi, “Nobel Seminar,” Les Prix Nobel 1994, op. cit., p. 285.
35. Ibid.
36. Nobel citation.
37. Avinash Dixit and Barry Nalebuff, Thinking Strategically, op. cit.
38. Ibid.
39. “Nowadays it almost seems to be obvious that the correct application of Darwinism to problems of social interaction among animals requires the use of non-cooperative game theory,” according to Reinhard Selten, “Nobel Seminar,” Les Prix Nobel 1994, op. cit., p. 288.
40. “Game Theory,” in Eatwell, Milgate, and Newman, op. cit., p. xiii.
41. Michael Intriligator, personal communication, 6.27.95.
42. Selten, op. cit., p. 297.
43. Von Neumann, as Nash always acknowledged, nonetheless helped to gain attention for Nash’s ideas. For example, the preface to the third edition (1953) of Theory of Games and Economic Behavior directs readers to Nash’s work on noncooperative games, p. vii.
1. T. S. Ferguson, “Biographical Note on Lloyd Shapley,” in Stochastic Games and Related Topics in Honor of Professor L. S. Shapley, edited by T. E. S. Raghavan, T. S. Ferguson, T. Parthasarathy, and O. J. Vrieze (Boston: Kluwer Academic Publishers, 1989).
2. See, for example, Carl Sagan, Broca’s Brain (New York: Random House, 1979).
3. David Halberstam, The Fifties, op. cit.
4. The description of Shapley’s experiences during the war, at Princeton, and at RAND draw on the recollections of Harold Kuhn, 11.18.96; Norman Shapiro, 2,9.96; Martin Shubik, 9.27.95 and 12.13.96; Melvin Hausner, 2.6.96; Eugenio Calabi, 3.2.96; John Danskin, 10.19.96; William Lucas, 6.27.95; Hartley Rogers, 1.26.96; John McCarthy, 2.4.96; Marvin Minsky, 2.13.96; Robert Wilson, 3.7.96; Michael Intriligator, 6.27.95.
5. Letter from John von Neumann, 1.54.
6. Solomon Leader, interview, 6.9.95.
7. Rogers, interview, 1.26.96.
8. “It was like ESP. Shapley seemed to know where all of the pieces were all of the time,” Minsky, interview.
9. Hausner, interview, 2.6.96.
10. Danskin, interview, 10.19.95.
11. Letter from Lloyd Shapley to Solomon Lefschetz, 4.4.49.
12. Interviews with Nancy Nimitz, 5.21.96, and Kuhn, 4.4.96.
13. Shapiro, interview, 12.13.96.
14. Intriligator, interview, 6.27.95.
15. Shubik, interview, 12.13.96.
16. Lloyd S. Shapley, interview, 10.94.
17. Ibid.
18. Shubik, interview, 12.13.96.
19. Interviews with Shapley, Shubik, McCarthy, Calabi.
20. Calabi, interview.
21. Ibid.
22. Ibid.
23. Shubik, interview, 9.27.95.
24. Shubik, interview, 9.27.95.
25. Letter from Nash to Martin Shubik, undated (1950 or 1951).
26. McCarthy, interview.
27. McCarthy, interview.
28. Hausner, interview, 2.6.96; M. Hausner, J. Nash, L. Shapley, and M. Shubik, “So Long Sucker — A Four-Person Game,” mimeo provided by Hausner.
29. Interviews with Shubik and McCarthy.
30. John Nash and Lloyd Shapley, “A Simple Three-Person Poker Game,” Annals of Mathematics, no. 24 (1950).
31. “To some extent there was a competition between Nash, Shapley, and me,” Shubik, interview, 12.13.96.
32. Shapley, interview.
33. Shapley, Additive and Non-Additive Set Functions, Ph.D. thesis, Princeton University, 1953. Shapley published his famous result — the so-called Shapley value — a value for n-person games, in 1953.
34. Martin Shubik, “Game Theory at Princeton,” op. cit., p. 6: “We all believed that a problem of importance was the characterization of the concept of threat in a two person game and the incorporation of the use of threat in determining the influence of the employment of threat in a bargaining situation. [Nash, Shapley, and I] worked on this problem, but Nash managed to formulate a good model of the two person bargain utilizing threat moves to start with.” Shubik is referring here to Nash’s “Two-Person Cooperative Games,” published in Econometrica in 1953 but actually written in August 1950 during Nash’s first summer at RAND.
35. Letter from Albert W. Tucker, 1953
36. Ibid.
37. Letter from Frederick Bohnenblust, spring 1953.
38. Letter from John von Neumann, 1.54.
39. Kuhn, interview, 11.18.96.
40. Shapley, interview, 10.94.
1. John McDonald, “The War of Wits,” Fortune (March 1951).
2. William Poundstone, Prisoner’s Dilemma, op. cit.; Fred Kaplan, The Wizards of Armageddon, op. cit.; The RAND Corporation: The First Fifteen Years (Santa Monica, Calif.: RAND, November 1963) and 40th Year Anniversary (Santa Monica: RAND, 1963); John D. Williams, An Address, 6.21.50; Bruce L. R. Smith, The RAND Corporation (Cambridge: Harvard University Press, 1966); Bruno W. Augenstein, A Brief History of RAND’s Mathematics Department and Some of Its Accomplishments (Santa Monica, Calif.: RAND, March 1993); Alexander M. Mood, “Miscellaneous Reminiscences,” Statistical Science, vol. 5, no. 1 (1990), pp. 40–41.
3. Herman Kahn, On Thermonuclear War (Princeton: Princeton University Press, 1960), as quoted in Poundstone, op. cit., p. 90.
4. Isaac Asimov, Foundation (New York: Bantam Books, 1991).
5. Poundstone, op. cit.
6. Kaplan, op. cit., p. 52.
7. Ibid., p. 10.
8. Oskar Morgenstern, The Question of National Defense (New York: Random House, 1959), as quoted in Poundstone, op. cit., pp. 84–85.
9. McDonald, “The War of Wits,” op. cit.
10. The account of RAND’s beginnings is based on Poundstone, op. cit.
11. Ibid., p. 93.
12. See, for example, Stanislaw Ulam, Adventures of a Mathematician, op. cit.; Richard Rhodes, The Making of the Atomic Bomb (New York: Simon & Schuster, 1986); Hodges, Alan Turing: The Enigma, op. cit.
13. Mina Rees, “The Mathematical Sciences and World War II,” op. cit.
14. The sketch of RAND’s mathematics, economics, and computer groups is based largely on interviews with RAND staff and consultants from the early Cold War period, including Kenneth Arrow, 6.26.95; Bruno Augenstein, 6.13.96; Richard Best, 5.22.96; Bernice Brown, 5.22.96; John Danskin, 10.19.95; Martha Dresher, 5.21.96; Theodore Harris, 5.24.96; Mario Juncosa, 5.21.96 and 5.24.96; William Karush, 5.96; William F. Lucas, 6.26.95; John W. Milnor, 9.95; John McCarthy, 2.4.96; Alexander M. Mood, 5.23.96; Evar Nering, 6.18.96; Nancy Nimitz, 5.21.96; Melvin Peisakoff, 6.3.96; Harold N. Shapiro, 2.20.96; Norman Shapiro, 2.29.96; Lloyd’S. Shapley, 11.94; Herbert Simon, 10.16.95; Robert Specht, 2.96; Albert W. Tucker, 12.94; Willis H. Ware, 5.24.96; Robert W. Wilson, 8.96; Charles Wolf, Jr., 5.22.96.
15. Augenstein, interview, 6.13.96.
16. R. Duncan Luce, interview, 1996.
17. The descriptions of Arrow’s contributions are taken from Mark Blaug, Great Economists Since Keynes (Totowa, N.J.: Barnes & Noble, 1985), pp. 6–9.
18. Kenneth Arrow, professor of economics, Stanford University, interview, 6.26.95.
19. McDonald, interview.
20. Richard Best, former manager of security, RAND Corporation, interview, 5.22.96.
21. Interviews with Alexander M. Mood, professor of mathematics, University of California at Irvine, former deputy director, mathematics department, RAND Corporation, 5.23.96, and Mario L. Juncosa, mathematician, RAND, 5.21.96 and 5.24.96.
22. Kaplan, op. cit., p. 51.
23. Bernice Brown, retired statistician, RAND, interview, 5.22.96.
24. Augenstein, interview.
25. Arrow, interview.
26. Chronicle of the Twentieth Century, op. cit., p. 667.
27. David Halberstam, The Fifties, op. cit.
28. Ibid.
29. Ibid., p. 46.
30. Kaplan, op. cit.
31. Martha Dresher, interview.
32. Best, interview.
33. Halberstam, The Fifties, op. cit., p. 45; Chronicle of the Twentieth Century, op. cit., p. 677.
34. Halberstam, op. cit., p. 49.
35. Chronicle of the Twentieth Century, op. cit., p. 750.
36. Best, interview.
37. Ibid.
38. Letter from Col. Walter Hardie, U.S. Air Force, to RAND, 10.25.50.
39. As told to Harold Kuhn, interview, 8.97.
40. Letter from John Nash to John and Virginia Nash, 11.10.51.
41. Best, interview.
42. The Eisenhower guidelines refer to DOD directive 52206, 1953 and Executive Order 10450, 1953.
43. Danskin, interview.
44. Robert Specht, interview, 10.96.
45. John Williams, The Compleat Strategyst, op. cit.
46. The account of mathematicians’ work habits is based on interviews with Brown, Mood, Juncosa, Danskin, and Shapiro.
47. Interviews with Mood and Juncosa.
48. Juncosa, interview.
49. Mood, interview.
50. The description of Williams is based on interviews with Best, Brown, Mood, and Juncosa; Poundstone, op. cit.; and Kaplan, op. cit.
51. Mood, interview.
52. As quoted in Poundstone, op. cit., p. 95.
53. Mood, interview.
54. Danskin, interview.
55. Arrow, interview.
56. Mood, interview.
57. Best, interview.
58. Harold Shapiro, interview.
59. Mood, interview.
60. Danskin, interview.
61. Ibid.
62. Best, interview.
1. Kenneth Arrow, interview, 6.26.95.
2. M. Dresher and L. S. Shapley, Summary of RAND Research in the Mathematical Theory of Games (RM-293) (Santa Monica, Calif.: RAND, 7.13.49).
3. Arrow, interview.
4. Fred Kaplan, The Wizards of Armageddon, op. cit.
5. Thomas C. Schelling, The Strategy of Conflict (Cambridge: Harvard University Press, 1960).
6. Ibid.
7. Arrow, interview.
8. See, for example, Martin Shubik, “Game Theory and Princeton,” op. cit.; William Lucas, “The Fiftieth Anniversary of TGEB,” Games and Economic Behavior, vol. 8. (1995), pp. 264–68; Carl Kaysen, interview, 2.15.96.
9. John McDonald, “The War of Wits,” op. cit.
10. For a humorous account of Prussian military’s romance with probability theory see John Williams, The Compleat Strategist, op. cit.
11. McDonald, op. cit.
12. Bernice Brown, interview, 5.22.96.
13. Rosters, RAND Department of Mathematics.
14. Dresher and Shapley, op. cit. For a lucid description of game theoretic analyses of duels, see Dixit and Skeath, op. cit.
15. Dresher and Shapley, op. cit.
16. For von Neumann’s views, see Clay Blair, Jr., “Passing of a Great Mind,” Life (February 1957), pp. 88–90, as quoted in William Poundstone, Prisoner’s Dilemma, op. cit., p. 143.
17. Arrow, interview.
18. See Poundstone, op. cit.; Joseph Baratta, interview, 8.12.97.
19. Arrow, interview.
20. John H. Kagel and Alvin E. Roth, The Handbook of Experimental Economics (Princeton: Princeton University Press, 1995), pp. 8–9.
21. Albert W. Tucker, interview, 12.94.
22. See, for example, Avinash Dixit and Barry Nalebuff, Thinking Strategically, op. cit.
23. See, for example, Anatole Rappaport, “Prisoner’s Dilemma,” in John Eatwell, Murray Milgate, and Peter Newman, The New Palgrave, op. cit., pp. 199–204.
24. Dixit and Nalebuff, op. cit.
25. Harold Kuhn, interview, 7.96.
26. Poundstone, op. cit.; also Kagel and Roth, op. cit.
27. John F. Nash, Jr., as quoted in Kagel and Roth, op. cit.
28. Martin Shubik, “Game Theory at Princeton, 1949–1955: A Personal Reminiscence,” in Toward a History of Game Theory, edited by E. Roy Weintraub (Durham, N.C.: Duke University Press, 1992).
29. The first version of Nash’s analysis of the role of threats in bargaining was published as a RAND memorandum, “Two-Person Cooperative Games, P-172” (Santa Monica, Calif.: RAND, 8.31.50). A final version appeared under the same title in Econometrica (January 1953), pp. 128–40. Also “Rational Non-Linear Utility,” RAND Memorandum, D-0793, 8.8.50.
30. Kaplan, op. cit.
31. Ibid.
32. Ibid.
33. Ibid., pp. 91–92.
34. Ibid.
35. Bruno Augenstein, interview.
36. R. Duncan Luce and Howard Raiffa as quoted in Poundstone, op. cit., p. 168.
37. Thomas Schelling, The Strategy of Conflict (Cambridge, Mass.: Harvard University Press, 1960).
1. Department of Mathematics, Princeton University.
2. Recommendations of 5.11.50 by Solomon Lefschetz, chairman, mathematics department, to president, Princeton University, that John Forbes Nash, Jr., be appointed research assistant, three-quarters time, on A. W. Tucker’s ONR Contract A-727.
3. See, for example, David Halberstam, The Fifties, op. cit.
4. Proceedings of the International Congress of Mathematicians, August 30-September 6, 1950, vol. 1, p. 516.
5. Letter from John Nash to Albert W. Tucker, 9.10.50. Letter from John Nash to Solomon Lefschetz, undated (probably written between April 10 and April 26, 1948), gives the clearest statement of why Nash wanted to avoid the draft: “Should there come a war involving the U.S. I think I should be more useful, and better off, working on some research project than going, say, into the infantry.”
6. Letter from Fred D. Rigby, Office of Naval Research, Washington, D.C., to Albert W. Tucker, 9.15.50.
7. Letter from J. Nash to A. W. Tucker, 9.10.50.
8. Letters from A. W. Tucker to Local Board No. 12, 9.13.50; Raymond J. Woodrow to Local Board No. 12, 9.15.50 and 9.18.50; Raymond J. Woodrow, Committee on Project Research and Inventions, Princeton University, to Local Board No. 12, Bluefield, W.Va., re occupational deferment for John F. Nash, Jr. (with reference to RAND consultancy).
9. Letter from F. D. Rigby to A. W. Tucker, 9.10.50.
10. Ibid.
11. Halberstam, op. cit.
12. Hans Weinberger, interview, 10.28.95.
13. Harold Kuhn, interview, 9.6.96.
14. Gottesman, Schizophrenia Genesis, op. cit., pp. 152–55; also Bruce Dohrenwind, professor of social psychology, Columbia University, interview, 1.16.98.
15. H. Steinberg and J. Durrel, “A Stressful Situation as a Precipitant of Schizophrenic Symptoms,” British Journal of Psychiatry, vol. 111 (1968), pp. 1097–1106, as quoted in Gottesman, Schizophrenia Genesis; op. cit.
16. Notes of telephone call from Alice Henry, secretary, department of mathematics, Princeton University, re I-A classification of John Nash and request that Dean Douglas Brown write a letter to ONR to be forwarded to the Bluefield draft board, 9.15.50.
17. “Information Needed in National Emergency,” form filled out 9.50 by John F. Nash, Jr., refers to I-A status, pending application for II-A, ONR and RAND research roles.
18. Letter from Raymond J. Woodrow, Committee on Project Research and Inventions, Princeton University, to commanding officer, Office of Naval Research, New York Branch, re deferment for John F. Nash, Jr., 9.18.50.
19. Letter from W. S. Keller, Office of Naval Research, New York Branch, to Selective Service Board No. 12, Bluefield, W.Va., re deferment for John F. Nash, Jr., 9.28.50.
20. Richard Best, interview, 5.96.
21. Melvin Peisakoff, interview, 5.96.
22. Best, interview.
23. Letter from Raymond J. Woodrow to John Nash, 10.6.50.
24. Ibid.; letter from L. L. Vivian, ONR, New York Branch, to commanding officer, ONR, New York Branch Office, re notification of Nash by draft board that active service postponed until June 30, 1951, and continued I-A status, 11.22.50.
1. Richard J. Duffin, interview, 10.26.95.
2. “He can hold his own in pure mathematics, but his real strength seems to lie on the frontier between mathematics and the biological and social sciences,” letter from Albert W. Tucker to Marshall Stone, 12.14.51.
3. John Nash, “Algebraic Approximations of Manifolds,” Proceedings of the International Congress of Mathematicians, vol. 1 (1950), p. 516, and “Real Algebraic Manifolds,” Annals of Mathematics, vol. 56, no. 3 (November 1952; received October 8, 1951). For expositions of Nash’s result, see John Milnor, “A Nobel Prize for John Nash,” op. cit., pp. 14–15, and Harold W. Kuhn, introduction, “A Celebration of John F. Nash, Jr.,” Duke Mathematical Journal, vol. 81, no. 1 (1995), p. iii.
4. Harold Kuhn, interview, 11.30.97.
5. See, for example, June Barrow-Green, Poincaré and the Three-Body Problem (Providence, R.I.: American Mathematical Society, 1977); also Kuhn, interview.
6. George Hinman, interview, 10.30.97.
7. John F. Nash, Jr., Les Prix Nobel 1994, op. cit.
8. See, for example, E. T. Bell, Men of Mathematics, op. cit., and Norman Levinson, “Wiener’s Life,” in “Norbert Wiener 1894–1964,” Bulletin of the American Mathematical Society; vol. 72, no. 1, part II, p. 8.
9. Martin Davis, interview, 2.6.96.
10. Norman Steenrod, letter of recommendation, 2.51, as quoted by Kuhn, introduction, “A Celebration of John F. Nash, Jr.,” op. cit.
11. John Nash, “Algebraic Approximations of Manifolds,” op. cit., p. 516.
12. Solomon Lefschetz, President’s Report, Princeton University Archives, 7.18.80.
13. Solomon Lefschetz, memorandum, 3.9.49, on Spencer’s appointment as visiting professor at Princeton in academic year 1948–49; Donald Spencer, interviews, 11.28.95 and 11.29.95.
14. Lefschetz, memorandum, 3.9.49.
15. Donald Clayton Spencer, Biography, 10.61, Princeton University Archives.
16. See, for example, “Analysis, Complex,” Encyclopaedia Britannica (1962).
17. Kodaira won the Fields in 1954; David C. Spencer, “Kunihiko Kodaira (1915–1997),” American Mathematical Monthly, 2.98.
18. Spencer won the Bôcher in 1947, Biography, op. cit.
19. Lefschetz, memorandum, 3.9.49.
20. Joseph Kohn, professor of mathematics, Princeton University, interview, 7.19.95.
21. Ibid. Also Phillip Griffiths, director, Institute for Advanced Study, interview, 5.26.95.
22. In his recommendation for Spencer’s appointment as visiting professor in 1949, Lefschetz remarks on his “warm and sympathetic personality.” Spencer had an unusual willingness to reach out to colleagues in trouble. He became deeply involved in helping Max Shiffman, a bright young mathematician at Stanford who was diagnosed with schizophrenia; John Moore, a mathematician who suffered a severe depression; and John Nash after Nash returned to Princeton in the early 1960s. See Spencer, op. cit.
23. Spencer, op. cit.
24. As slightly restated by Milnor, “A Nobel Prize for John Nash,” op. cit., p. 14.
25. Intersectional Nomination: Class Five; 1996 Election, John F. Nash, Jr.
26. Michael Artin, professor of mathematics, MIT, interview, 12.2.97.
27. See, for example, Michael Artin and Barry Mazur, “On Periodic Points,” Annals of Mathematics, no. 81 (1965), pp. 82–99. Milnor calls this an “important” application.
28. Barry Mazur, professor of mathematics, Harvard University, interview, 12.3.97.
29. Nash cites, for example, H. Seifert, “Algebraische Approximation von Mannigfaltigkeiten,” Math. Zeit, vol. 41 (1936), pp. 1–17.
30. Ibid.
31. Steenrod, letter, 2.51, as quoted by Kuhn, introduction, “A Celebration of John F. Nash, Jr.,” op. cit.
32. Spencer, op. cit.
33. Nash, as told to Harold Kuhn, private communication, 12.2.97. The subsequent Nash-Moser theorem has even more profound implications for celestial mechanics. See Chapter 30.
34. Albert W. Tucker, interview, 11.94. Nash still dabbled in game theory, perhaps partly to maintain his RAND connection. For example, he wrote “N-Person Games: An Example and a Proof,” RAND Memorandum, RM-615, June 4, 1951, as well as, with graduate students Martin Shubik and John Mayberry, “A Comparison of Treatments of a Duopoly Situation,” RAND Memorandum P-222, July 10, 1951.
35. Kuhn, interview.
36. Letter from Albert W. Tucker to Hassler Whitney, 4.5.55.
37. Artin supervised the honors calculus program, which, according to John Tate (interview, 6.29.97), he took very seriously. Later documents refer to Nash’s having been a poor teacher; the comments undoubtedly stem from his experiences in 1950–51.
38. “There is no doubt that the department should look towards keeping Milnor permanently as a member of our faculty,” Solomon Lefschetz, President’s Report, Princeton University Archives, 9.51.
39. Letter from A. W. Tucker to H. Whitney, op. cit.
40. William Ted Martin, professor of mathematics, MIT, interview, 9.7.95.
41. Letter from Albert W. Tucker to Marshall Stone, 2.26.51.
42. Nash told Kuhn that his desire to live in Boston played a role in his accepting the MIT position, Kuhn, personal communication, 7.97.
1. Lindsay Russell, interview, 1.14.96.
2. Patrick Corcoran, retired captain, Cambridge City Police, interview, 8.12.97.
3. Felix Browder, interview, 11.14.95.
4. Gian-Carlo Rota, professor of mathematics, MIT, interview, 10.29.94.
5. Paul A. Samuelson, professor of economics, MIT, interview, 11.94.
6. Harvey Burstein, former FBI agent who set up the campus police at MIT, interview, 7.3.97.
7. Samuelson, interview.
8. William Ted Martin, professor of mathematics, MIT, interview, 9.7.95.
9. Samuelson, interview.
10. Department of Physics, MIT, communication, 1.98.
11. Course catalog, MIT, various years.
12. Samuelson, interview.
13. Ibid.
14. Arthur Mattuck, professor of mathematics, MIT, e-mail, 6.23.97.
15. Joseph Kohn, professor of mathematics, Princeton University, interview, 7.25.95.
16. Samuelson, interview. See also Report to the President, MIT, various years.
17. Jerome Lettvin, professor of electrical engineering and bioengineering, MIT, interview, 7.25.97; Emma Duchane, interview, 6.26.97.
18. Samuelson, interview.
19. Gian-Carlo Rota, interview.
20. Hearing before Committee on Un-American Activities (HUAC), House of Representatives, Eighty-third Congress, First Session, Washington, D.C., April 22 and 23, 1953.
21. Samuelson, interview.
22. Martin, interview.
23. Ibid.
24. See, for example, Wiener’s obituary, New York Times, 3.19.64; Paul Samuelson, “Some Memories of Norbert Wiener,” 1964, Xerox provided by Samuelson; and Norbert Wiener, Ex-Prodigy (New York: Simon & Schuster, 1953) and I Am a Mathematician (New York: Simon & Schuster, 1956).
25. Samuelson, “Some Memories of Norbert Wiener,” op. cit.
26. Ibid.
27. Zipporah Levinson, interview, 9.11.95.
28. Samuelson, “Some Memories of Norbert Weiner,” op. cit.
29. Z. Levinson, interview.
30. Ibid.
31. Ibid.
32. Ibid.
33. Note from John Nash to N. Wiener, 11.17.52.
34. Letter from John Nash to Albert W. Tucker, 10.58.
35. Jerome Neuwirth, professor of mathematics, University of Connecticut at Storrs, interview, 5.21.97.
36. The sketch of Levinson is based on recollections of his widow, Zipporah Levinson; Arthur Mattuck; F. Browder, 11.2.95; Gian-Carlo Rota, 11.94; and many others. Also Kenneth Hoffman, Memorandum to President J. B. Wiesner, 3.14.74; William Ted Martin et al., obituary of Norman Levinson, 12.17.75.
37. HUAC, op. cit. See also Chapter 19.
38. Arthur Mattuck, “Norman Levinson and the Distribution of Primes,” address to MIT shareholders, 10.6.78.
1. Donald J. Newman, professor of mathematics, Temple University, interview, 12.28.95; Leopold Flatto, Bell Laboratories, interview, 4.25.96.
2. Sigurdur Helgason, professor of mathematics, MIT, interview, 2.13.96.
3. Course catalog, MIT, various years.
4. Arthur Mattuck, interview, 11.7.95.
5. Robert Aumann, professor of mathematics, Hebrew University, interview, 6.25.95.
6. Joseph Kohn, interview, 7.19.95.
7. Ibid.
8. Aumann, interview.
9. Seymour Haber, professor of mathematics, Temple University, interviews, 3.14.95 and 3.19.95.
10. George Whitehead, professor of mathematics, MIT, interview, 12.12.95.
11. Eva Browder, interview, 9.6.97.
12. Barry Mazur, interview, 12.3.97.
13. Harold Kuhn quotes Nash taking credit for introducing the tea hour at MIT in his introduction to the special volume in honor of Nash, “A Celebration of John F. Nash, Jr.,” op. cit.
14. Isadore M. Singer, professor of mathematics, MIT, interview, 12.13.95.
15. Kohn, interview.
16. Singer, interview.
17. Jerome Neuwirth, interview, 5.21.97.
18. Mattuck, interview, 2.13.96.
19. Descriptions of this legendary crowd are based on interviews with Kohn; Felix Browder, 11.2.95, 11.10.95, 9.6.97; Aumann; Neuwirth; Newman; H. F. Mattson, 10.29.97 and 11.18.97; Larry Wallen, 5.16.97 and 5.20.97; Mattuck; Paul Cohen, 1.5.96; Jacob Bricker, 5.22.97; and others.
20. F. Browder, interview, 9.6.97.
21. Haber, interview.
22. Ibid.
23. Martha Nash Legg, interview, 3.29.96.
24. Neuwirth, interview.
25. Ibid.
26. Mattuck, interview, 2.13.96.
27. Interviews with Neuwirth and F. Browder, 11.2.95.
28. Jürgen Moser, professor of mathematics, Eidgenösische Techische Hochschule, Zurich, interview, 3.23.96.
29. Marvin Minsky, professor of science, MIT, interview, 2.13.96.
30. Herta Newman, interview, 3.2.96.
31. Andrew-Browder, professor of mathematics, Brown University, interview, 6.18.97.
32. Haber, interview.
33. Flatto, interview.
34. D. Newman, interview, 2.4.96.
35. Zipporah Levinson, interview, 9.11.95.
36. Neuwirth, interview.
37. D. Newman, interview.
38. Ibid.
39. Lawrence Wallen, professor of mathematics, University of Hawaii, interviews, 5.20.97 and 6.4.97.
40. Kohn, interview.
41. H. F. Mattson, professor of computer science, Syracuse University, interview, 5.16.97; also Wallen, interview.
42. J. C. Lagarias, “The Leo Collection: Anecdote and Stories,” AT&T Bell Laboratories, 4.29.95 (Xerox).
43. Mattuck, interview, 5.21.95, and Neuwirth, interview.
44. Neuwirth, interview.
45. The sketch of Donald J. Newman is based on an interview with him and on interviews with Flatto, Kohn, Mattuck, Singer, and Harold S. Shapiro, professor of mathematics, Royal Institute of Technology, Stockholm, Sweden, e-mail, 5.21.97.
46. Singer, interview, 12.13.95.
47. Mattuck, interview, 11.7.95.
48. D. Newman, interview, 3.2.96.
49. Helgason, interview, 12.3.94; also interviews with Mattuck and Singer.
50. Flatto, interview.
51. Ibid.
52. Ibid.
53. Singer, interview.
54. Haber, interview.
55. Ibid.
56. Flatto, interview.
57. Ibid.
58. Ibid.
59. Neuwirth, interview.
60. Ibid.
61. D. Newman, interview, 3.2.96.
62. Ibid.
63. H. Newman, interview.
64. Fred Brauer, professor of mathematics, University of Wisconsin, interview, 5.22.97.
1. Harold N. Shapiro, professor of mathematics, Courant Institute, interview, 2.20.96.
2. John Milnor, interview, 9.26.95.
3. The account of the cross-country trip is based largely on recollections of Martha Nash Legg, interviews, 8.29.95 and 3.29.96, and Ruth Hincks Morgenson, interview, 6.22.97.
4. John Nash to Harold Kuhn, personal communication, 6.24.97; also Morgenson, interview.
5. M. Legg, interview.
6. Ibid.
7. Ibid.
8. Ibid.; Milnor, interview.
9. John M. Danskin, interview, 10.29.95.
10. M. Legg, interview.
11. Ibid.
12. John Milnor, “Games Against Nature,” in Decision Processes, edited by R. M. Thrall, C. H. Coombs, and R. L. Davis (New York: John Wiley & Sons, 1954).
13. “Some Games and Machines for Playing Them,” RAND Memorandum, D-l 164, 2.2.52.
14. John Nash and R. M. Thrall, “Some War Games,” RAND Memorandum, D-1379, 9.10.52.
15. G. Kalisch, J. Milnor, J. Nash, and E. Nering, “Some Experimental N-Person Games,” RAND Memorandum, RM-948, 8.25.52.
16. M. Legg, interview.
17. The description of the experiment is based on, apart from the original paper, Evar Nering, professor of mathematics, University of Minnesota, interview, 6.18.96; R. Duncan Luce and Howard Raiffa, Games and Decisions (New York: John Wiley & Sons, 1957), pp. 259–69; John H. Kagel and Alvin E. Roth, The Handbook of Experimental Economics, op. cit., pp. 10–11.
18. Kagel and Roth, op. cit.
19. Milnor, interview, 10.28.94.
20. John Milnor, “A Nobel Prize for John Nash,” op. cit.
21. See, for example, Kagel and Roth, op. cit.
22. Milnor, interview, 1.27.98.
23. Letter from John Nash to John Milnor, 12.27.64.
1. Zipporah Levinson, interview, 9.11.95.
2. Hearing before Committee on Un-American Activities, House of Representatives, Washington, D.C., 4.22.53 and 4.23.53. Unless otherwise noted, all references to the hearing are based on this transcript.
3. David Halberstam, The Fifties, op. cit.
4. Letter from Harold W. Dodds, president, Princeton University, to Colonel S. R. Gerard, Screening Division, Western Industrial Personnel Security Board, 10.14.54, Princeton University Archives.
5. See, for example, F. David Peat, Infinite Potential: The Life and Times of David Bohm (Reading, Mass.: Addison Wesley, 1997).
6. Z. Levinson, interview.
7. Ibid. See also Felix Browder, interview, 11.10.95.
8. Z. Levinson, interview.
9. Ibid.
10. The Tech, spring 1953, various issues.
11. Z. Levinson, interview.
12. Ibid.
13. William Ted Martin, interview.
14. Z. Levinson, interview.
15. Fred Brauer, e-mail, 6.23.97; Arthur H. Copeland, professor of mathematics, University of New Hampshire, e-mail, 6.24.97; Arthur Mattuck, e-mail, 6.25.97.
16. John Nash, plenary lecture, World Congress of Psychiatry, Madrid, 8.26.96, op. cit.
1. Letter from Warren Ambrose to Paul Halmos, undated (written spring 1953).
2. The portrait of Ambrose is based on the recollections of Isadore Singer, 2.13.95; Lawrence Wallen, 6.4.97; Felix Browder, 11.2.95; Zipporah Levinson, 9.11.95; William Ted Martin, 9.7.95; H. F. Mattson, 10.29.97, 11.18.97, 11.28.97; Gian-Carlo Rota, 10.94; George Mackey, 12,14.95.
3. See, for example, I. M. Singer and H. Wu, “A Tribute to Warren Ambrose,” Notices of the AMS [April 1996).
4. Robert Aumann, interview, 6.28.95.
5. Gabriel Stolzenberg, professor of mathematics, Northeastern University, interview, 4.2.96.
6. Leopold Flatto, interview, 4.15.96. See also “The Leo Collection: Anecdotes and Stories,” AT&T Bell Laboratories, 4.29.94.
7. Ibid.
8. George Mackey, interview, 12.14.95.
9. Felix Browder, interview, 11.2.95.
10. Flatto, interview.
11. Despite its apocryphal ring, the story appears to be true and has been confirmed by Nash. Harold Kuhn, personal communication, 8.97.
12. Armand Borel, professor of mathematics, Institute for Advanced Study, interview, 3.1.96.
13. F. Browder, interview.
14. Ibid.
15. Joseph Kohn, interview, 7.19.95. Phrasing the question precisely, Ambrose would have used the adverb “isometrically” — meaning “to preserve distances” — after “embedding.”
16. Shlomo Sternberg, professor of mathematics, Harvard University, interview, 3.5.96.
17. Mikhail Gromov, interview. 12.16.97.
18. John Forbes Nash, Jr., Les Prix Nobel 1994, op. cit.
19. Gromov, interview.
20. John Conway, professor of mathematics, Princeton University, interview, 10.94.
21. Jürgen Moser, e-mail, 12.24.97.
22. Richard Palais, professor of mathematics, Brandeis University, interview, 11.6.95.
23. Moser, interview.
24. Donald J. Newman, interview, 3.2.96.
25. Jürgen Moser, “A Rapidly Convergent Iteration Method and Non-linear Partial Differential Equations, I, II,” Annali della Scuola Normale Superiore di Pisa, vol. 20 (1966), pp. 265–315, 499–535.
26. See, for example, Kyosi Ito, ed., Encyclopedic Dictionary of Mathematics (Mathematical Society of Japan; Cambridge: MIT Press, 1987), p. 1076; Lars Hörmander, “The Boundary Problems of Physical Geodesy,” Archive for Rational Mechanics and Analysis, vol. 62, no. 1 (1976), pp. 1–52; and S. Klainerman, Communications in Pure and Applied Mathematics, vol. 33 (1980), pp. 43–101.
27. John Nash, “C1 Isometric Imbeddings,” Annals of Mathematics, vol. 60, no. 3 (November 1954), pp. 383–96.
28. Kohn, interview.
29. John Forbes Nash, Jr., Les Prix Nobel 1994, op. cit.
30. Rota, interview, 11.14.95.
31. Flatto, interview.
32. Jacob Schwartz, professor of computer science, Courant Institute, interview, 1.29.96.
33. Isadore Singer, interview, 12.14.95.
34. Paul J. Cohen, professor of mathematics, Stanford University, interview, 1.6.96.
35. Moser, interview, 3.23.96.
36. The Nash-Federer correspondence wasn’t saved, and Federer declined to be interviewed (personal communication, 6.25.96). The account is based on the recollections of several individuals, including Wendell Fleming (interview, 6.97), a longtime collaborator and friend of Federer.
37. Fleming, interview.
38. John Nash, “The Imbedding Problem for Riemannian Manifolds,” Annuls of Mathematics, vol. 63, no. 1 (January 1956, received October 29, 1954, revised August 20, 1955).
39. Borel, interview.
40. Letter from John Forbes Nash, Jr., to Virginia and John Nash, Sr., 4.54.
41. Rota, interview.
42. Stolzenberg, interview, 4.2.96.
43. Ibid.
44. Schwartz, interview.
45. Moser, interview.
46. Ibid.
47. Ibid.
48. Rota, interview, 10.94.
49. George Whitehead, professor of mathematics, MIT, interview, 12.12.95.
50. Flatto, interview.
51. Lawrence Wallen, interview, 6.4.97.
1. Postcard from John Nash to Arthur Mattuck, 1968. B stood for Jacob Bricker, T for Ervin D. Thorson, F for Herbert Amasa Forrester, and R for Donald V. Reynolds.
1. Letter from John Forbes Nash, Jr., to Martha Nash Legg, 11.4.65.
2. Ibid.
3. Herta Newman, interview, 3.2.96.
4. D. Newman, interview.
5. Joseph Kohn, interview, 2.15.96.
6. H. Newman, interview.
7. D. Newman, interview.
8. In his 11.4.65 letter, Nash describes Thorson as one of three “special friendships.” Thorson was working in Santa Monica, California, at Douglas Aircraft.
9. The references to T in Nash’s letters continued until at least 1968, usually in conjunction with references to B (for Bricker) and F.
10. M. Legg, interview, 3.30.96.
11. Douglas Aircraft could supply no biographical or professional information on Thorson (Donald Hanson, personal communication, 6.17.97). Nash did not recall Thorson when asked about him by Harold Kuhn (6.97). What details are known of Thorson are based solely on an obituary in the Hemet News and a brief conversation with his surviving sister, Nelda Troutman, 5.28.97.
12. Hanson, interview.
13. Ibid.
14. Troutman, interview, 5.28.97.
15. Ibid.
16. Ibid.
17. Under the Eisenhower guidelines, homosexuals were not permitted to have security clearances.
1. The description of Nash’s stay at Mrs. Grant’s house is based on interviews with Lindsay Russell, 1.14.96, 4.23.96, and 7.97.
2. Postcard from John Nash, Jr., to Virginia and John Nash, Sr., 9.52.
3. Martha Nash Legg, interview, 9.3.95.
4. Eleanor Stier, interview, 2.14.96.
5. Ibid., 3.15.96.
6. Ibid., 2.14.96 and 3.18.96.
7. Arthur Mattuck, interview, 11.7.95.
8. Eleanor’s history was taken from interviews with her, 3.1 5.95, and John David Stier, 9.20.97.
9. E. Stier, interview, 2.14.96.
10. Ibid., 3.15.96.
11. That Nash was interested in, and experimented with, various drugs was recalled by Donald Newman, interview, 3.2.96. Eleanor Stier confirmed this, interview, 3.18.96, although neither witnessed Nash’s experiments, if indeed they ever took place. Their possible significance is twofold. First, it suggests Nash’s concern with enhancing his mental powers but also his concerns about his own “manliness.”
12. E. Stier, interview, 3.13.96.
13. Ibid.
14. M. Legg, interview.
15. E. Stier, interview, 3.15.96. Confirmed by Jacob Bricker, inteview, 5.22.97, and Arthur Mattuck, interview.
16. Bricker, interview.
17. E. Stier, interview, 7.95.
18. Ibid.
19. Bricker, interview.
20. E. Stier, interview, 3.15.96.
21. John David Stier, interview, 6.29.96.
22. E. Stier, interview, 3.15.96.
23. J. D. Stier, interview, 9.20.97.
24. E. Stier, interview, 3.15.96.
25. Ibid.
26. Ibid, 3.18.96.
27. Ibid., 3.18.96, and J. D. Stier, interview, 9.20.97.
28. J. D. Stier, interview, 9.20.97.
29. A. Mattuck, interview.
30. E. Stier, interview, 3.18.96.
31. Bricker, interview; Mattuck, interview.
32. E. Stier, interview, 3.18.96.
33. Mattuck, interview.
34. E. Stier, interview, 3.18.96.
35. Ibid., 3.15.96.
36. Mattuck, interview.
37. Best, interview, 5.22.96.
38. Mattuck, interview, 5.21.97.
39. Bricker, interview.
40. E. Stier, interview.
41. Ibid., 3.18.96.
42. Ibid.
43. J. D. Stier, interview, 9.20.97.
44. Ibid.
1. Donald J. Newman, interview, 3.12.96.
2. Arthur Mattuck, interview, 5.21.97.
3. The portrait of Bricker is based on interviews with Mattuck; Newman; Herb Kamowitz; Jerome Neuwirth, 5.23.97 and 6.5.97; Leopold Flatto, 4.25.96; Lawrence Wallen, 5.20.97.
4. Jacob Bricker, interview, 5.22.97.
5. Jack Kotick, interview, 1.21.98.
6. D. Newman, interview, 3.12.96.
7. Ibid., 1.25.98.
8. Eleanor Stier, interview.
9. Letter from John Nash to Martha Nash Legg, 11.4.65.
10. Herta Newman, interview, 3.2.96.
11. Sheldon M. Novick, Henry James: The Young Master (New York: Random House, 1996).
12. Letter from J. Nash to M. Legg.
13. Alfred C. Kinsey et al., Sexual Behavior of the Human Male (Philadelphia: Saunders, 1948).
14. Letter from J. Nash to M. Legg.
15. Bricker, interview, 5.22.97.
16. Neuwirth, interviews.
17. Mattuck, interviews, 5.20.97 and 5.28.97.
18. Bricker, interview, 5.22.97.
19. Postcard from John Nash to Jacob Bricker, 8.3.67.
20. Letter from John Nash to Arthur Mattuck, 7.10.68. “Mattuckine” seems to be a reference to the Mattachine Society, the first American advocacy group for homosexuals, founded in 1951 (source: Neil Miller, Out of the Past: Gay and Lesbian History from 1869 to the Present [New York: Vintage Books, 1995], pp. 334–38).
21. Bricker, interview.
22. Bricker, interview, 1.26.98.