A Beautiful Mind Part 23

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 Complcat Strategyst, The Complcat Strategyst, op. cit. 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.

13: Game Theory at RAND

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) Summary of RAND Research in the Mathematical Theory of Games (RM-293) (Santa Monica, Calif.: RAND, 7.13.49). (Santa Monica, Calif.: RAND, 7.13.49).

3. Arrow, interview.

4. Fred Kaplan, The Wizards of Armageddon, The Wizards of Armageddon, op. cit. op. cit.

5. Thomas C. Sch.e.l.ling, The Strategy of Conflict The Strategy of Conflict (Cambridge: Harvard University Press, 1960). (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, Games and Economic Behavior, vol. 8. (1995), pp. 26468; Carl Kaysen, interview, 2.15.96. vol. 8. (1995), pp. 26468; 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, The Compleat Strategist, op. cit. 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 a.n.a.lyses of duels, see Dixit and Skeath, op. cit.

15. Dresher and Shapley, op. cit.

16. For von Neumann's views, see Clay Blair, Jr., "Pa.s.sing of a Great Mind," Life Life (February 1957), pp. 8890, as quoted in William Poundstone, (February 1957), pp. 8890, as quoted in William Poundstone, Prisoner's Dilemma, Prisoner's Dilemma, op. cit., p. 143. 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 The Handbook of Experimental Economics (Princeton: Princeton University Press, 1995), pp. 89. (Princeton: Princeton University Press, 1995), pp. 89.

21. Albert W. Tucker, interview, 12.94.

22. See, for example, Avinash Dixit and Barry Nalebuff, Thinking Strategically, Thinking Strategically, op. cit. op. cit.

23. See, for example, Anatole Rappaport, "Prisoner's Dilemma," in John Eatwell, Murray Milgate, and Peter Newman, The New Palgrave, The New Palgrave, op. cit., pp. 199204. op. cit., pp. 199204.

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, 19491955: A Personal Reminiscence," in Toward a History of Game Theory, Toward a History of Game Theory, edited by E. Roy Weintraub (Durham, N.C.: Duke University Press, 1992). edited by E. Roy Weintraub (Durham, N.C.: Duke University Press, 1992).

29. The first version of Nash's a.n.a.lysis 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 t.i.tle in Econometrica Econometrica (January 1953), pp. 12840. Also "Rational Non-Linear Utility," RAND Memorandum, D-0793, 8.8.50. (January 1953), pp. 12840. Also "Rational Non-Linear Utility," RAND Memorandum, D-0793, 8.8.50.

30. Kaplan, op. cit.

31. Ibid.

32. Ibid.

33. Ibid., pp. 9192.

34. Ibid.

35. Bruno Augenstein, interview.

36. R. Duncan Luce and Howard Raiffa as quoted in Poundstone, op. cit., p. 168.

37. Thomas Sch.e.l.ling, The Strategy of Conflict The Strategy of Conflict (Cambridge, Ma.s.s.: Harvard University Press, 1960). (Cambridge, Ma.s.s.: Harvard University Press, 1960).

14: The Draft

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 a.s.sistant, three-quarters time, on A. W. Tucker's ONR Contract A-727.

3. See, for example, David Halberstam, The Fifties, The Fifties, op. cit. op. cit.

4. Proceedings of the International Congress of Mathematicians, August 30September 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, Was.h.i.+ngton, DC, 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, Schizophrenia Genesis, op. cit., pp. 15255; also Bruce Dohrenwind, professor of social psychology, Columbia University, interview, 1.16.98. op. cit., pp. 15255; 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, British Journal of Psychiatry, vol. 111 (1968), pp. 10971106, as quoted in Gottesman, vol. 111 (1968), pp. 10971106, as quoted in Gottesman, Schizophrenia Genesis; Schizophrenia Genesis; op. cit. op. cit.

16. Notes of telephone call from Alice Henry, secretary, department of mathematics, Princeton University, re I-A cla.s.sification 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.

15: A Beautiful Theorem

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, Proceedings of the International Congress of Mathematicians, vol. 1 (1950), p. 516, and "Real Algebraic Manifolds," vol. 1 (1950), p. 516, and "Real Algebraic Manifolds," Annals of Mathematics, Annals of Mathematics, vol. 56, no. 3 (November 1952; received October 8, 1951). For expositions of Nash's result, see John Milnor, "A n.o.bel Prize for John Nash," op. cit., pp. 1415, and Harold W. Kuhn, introduction, "A Celebration of John F. Nash, Jr.," vol. 56, no. 3 (November 1952; received October 8, 1951). For expositions of Nash's result, see John Milnor, "A n.o.bel Prize for John Nash," op. cit., pp. 1415, and Harold W. Kuhn, introduction, "A Celebration of John F. Nash, Jr.," Duke Mathematical Journal, Duke Mathematical Journal, vol. 81, no. 1 (1995), p. iii. vol. 81, no. 1 (1995), p. iii.

4. Harold Kuhn, interview, 11.30.97.

5. See, for example, June Barrow-Green, Poincare and the Three-Body Problem Poincare and the Three-Body Problem (Providence, R.I.: American Mathematical Society, 1977); also Kuhn, interview. (Providence, R.I.: American Mathematical Society, 1977); also Kuhn, interview.

6. George Hinman, interview, 10.30.97.

7. John F. Nash, Jr., Les Prix n.o.bel 1994, Les Prix n.o.bel 1994, op. cit. op. cit.

8. See, for example, E. T. Bell, Men of Mathematics, Men of Mathematics, op. cit., and Norman Levinson, "Wiener's Life," in "Norbert Wiener 18941964," op. cit., and Norman Levinson, "Wiener's Life," in "Norbert Wiener 18941964," Bulletin of the American Mathematical Society; Bulletin of the American Mathematical Society; vol. 72, no. 1, vol. 72, no. 1, part II 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.