A Beautiful Mind Part 20

39. Nash, as told to Harold Kuhn; see also Brian, op. cit., for description of Kemeny's a.s.sistants.h.i.+p under Einstein in 194849.

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, 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. 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.

6: Games

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, Prisoner's Dilemma, op. cit.; John Williams, op. cit.; John Williams, The Compleat Strategist The Compleat Strategist (New York: McGraw Hill, 1954). (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 Mathematical Puzzles and Diversions (New York: Simon & Schuster, 1959), pp. 6570. (New York: Simon & Schuster, 1959), pp. 6570.

15. Gardner's comment, in 1959, was that Hex "may well become one of the most widely played and thoughtfully a.n.a.lyzed 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 n.o.bel 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.

7: John von Neumann

1. See, for example, Stanislaw Ulam, "John von Neumann, 19031957," Bulletin of the American Mathematical Society, Bulletin of the American Mathematical Society, vol. 64, no. 3, part 2 (May 1958); Stanislaw Ulam, vol. 64, no. 3, part 2 (May 1958); Stanislaw Ulam, Adventures of a Mathematician Adventures of a Mathematician (New York: Scribner's, 1983); Paul R. Halmos, "The Legend of John von Neumann," (New York: Scribner's, 1983); Paul R. Halmos, "The Legend of John von Neumann," American Mathematical Monthly, American Mathematical Monthly, vol. 80 (1973); William Poundstone, vol. 80 (1973); William Poundstone, Prisoner's Dilemma, Prisoner's Dilemma, op. cit.; Ed Regis, op. cit.; Ed Regis, Who Got Einstein's Office?, Who Got Einstein's Office?, op. cit. op. cit.

2. Poundstone, op. cit.

3. Ulam, "John von Neumann," op. cit.; Poundstone, op. cit., pp. 9496.

4. Harold Kuhn, interview, 1.10.96.

5. In remarks at a n.o.bel luncheon at the American Economics a.s.sociation 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 John von Neumann (New York: Pantheon Books, 1992), pp. 35056. (New York: Pantheon Books, 1992), pp. 35056.

8. John von Neumann, The Computer and the Brain The Computer and the Brain (New Haven: Yale University Press, 1959). (New Haven: Yale University Press, 1959).

9. See, for example, G. H. Hardy, A Mathematician's Apology (Cambridge, A Mathematician's Apology (Cambridge, U.K.: Cambridge University Press, 1967), with a foreword by C. P. Snow. 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, Prisoner's Dilemma, p. 190. p. 190.

13. Clay Blair, Jr., "Pa.s.sing of a Great Mind," Life Life (February 1957), pp. 8990, as quoted by Poundstone, op. cit., p. 143. (February 1957), pp. 8990, 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, Adventures of a Mathematician, op. cit. 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. 3539.

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, A Century of Mathematics in America, Part I Part I, op. cit. op. cit.

33. John von Neumann, as quoted in ibid.

8: The Theory of Games

1. John von Neumann and Oskar Morgenstern, The Theory of Games and Economic Behavior The Theory of Games and Economic Behavior (Princeton: Princeton University Press, 1944, 1947, 1953). (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, 19401955: 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.