A Beautiful Mind

by Sylvia Nasar

  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.

  2: Carnegie Institute of Technology

  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 Ston 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 Ston of Carnegie Tech, II: The Doherty Administration, 1936–19S0 (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.

  52. See Chapter 9.

  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.

&n
bsp; 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.

  3: The Center of the Universe

  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 //(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, Crcativih: 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 I (Providence, R.I.: American Mathematical Society, 1988).

  31. See, for example, Mina Rees, “The Mathematical Sciences and World War II,” in ,4 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 .4 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.

  4: School of Genius

  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). Lefsehetz’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 Ramanuj
an,” 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 901019, 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.

  5: Genius

  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).