A Beautiful Mind (82 page)

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)
(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).

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 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, 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,
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.

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,
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.

16: MIT

1
. Lindsay Russell, interview, 1.14.96.

2
. Patrick Corcoran, retired captain, Cambridge City Police, interview, 8.12.97.