A Beautiful Mind (79 page)

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unpublished two-volume manuscript (1964).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 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 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).

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 essav,
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.

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.