A Beautiful Mind (83 page)

3
. Felix Browder, interview, 11.14.95.

4
. Gian-Carlo Rota, professor of mathematics, MIT, interview, 10.29.94.

5
. Paul A. Samuelson, professor of economics, MIT, interview, 11.94.

6
. Harvey Burstein, former FBI agent who set up the campus police at MIT, interview, 7.3.97.

7
. Samuelson, interview.

8
. William Ted Martin, professor of mathematics, MIT, interview, 9.7.95.

9
. Samuelson, interview.

10
. Department of Physics, MIT, communication, 1.98.

11
. Course catalog, MIT, various years.

12
. Samuelson, interview.

13
. Ibid.

14
. Arthur Mattuck, professor of mathematics, MIT, e-mail, 6.23.97.

15
. Joseph Kohn, professor of mathematics, Princeton University, interview, 7.25.95.

16
. Samuelson, interview. See also Report to the President, MIT, various years.

17
. Jerome Lettvin, professor of electrical engineering and bioengineering, MIT, interview, 7.25.97; Emma Duchane, interview, 6.26.97.

18
. Samuelson, interview.

19
. Gian-Carlo Rota, interview.

20
. Hearing before Committee on Un-American Activities (HUAC), House of Representatives, Eighty-third Congress, First Session, Washington, D.C., April 22 and 23, 1953.

21
. Samuelson, interview.

22
. Martin, interview.

23
. Ibid.

24
. See, for example, Wiener’s obituary,
New York Times,
3.19.64; Paul Samuelson, “Some Memories of Norbert Wiener,” 1964, Xerox provided by Samuelson; and Norbert Wiener,
Ex-Prodigy
(New York: Simon & Schuster, 1953) and
I Am a Mathematician
(New York: Simon & Schuster, 1956).

25
. Samuelson, “Some Memories of Norbert Wiener,” op. cit.

26
. Ibid.

27
. Zipporah Levinson, interview, 9.11.95.

28
. Samuelson, “Some Memories of Norbert Weiner,” op. cit.

29
. Z. Levinson, interview.

30
. Ibid.

31
. Ibid.

32
. Ibid.

33
. Note from John Nash to N. Wiener, 11.17.52.

34
. Letter from John Nash to Albert W. Tucker, 10.58.

35
. Jerome Neuwirth, professor of mathematics, University of Connecticut at Storrs, interview, 5.21.97.

36
. The sketch of Levinson is based on recollections of his widow, Zipporah Levinson; Arthur Mattuck; F. Browder, 11.2.95; Gian-Carlo Rota, 11.94; and many others. Also Kenneth Hoffman, Memorandum to President J. B. Wiesner, 3.14.74; William Ted Martin et al., obituary of Norman Levinson, 12.17.75.

37
. HUAC, op. cit. See also
Chapter 19
.

38
. Arthur Mattuck, “Norman Levinson and the Distribution of Primes,” address to MIT shareholders, 10.6.78.

17: Bad Boys

1
. Donald J. Newman, professor of mathematics, Temple University, interview, 12.28.95; Leopold Flatto, Bell Laboratories, interview, 4.25.96.

2
. Sigurdur Helgason, professor of mathematics, MIT, interview, 2.13.96.

3
. Course catalog, MIT, various years.

4
. Arthur Mattuck, interview, 11.7.95.

5
. Robert Aumann, professor of mathematics, Hebrew University, interview, 6.25.95.

6
. Joseph Kohn, interview, 7.19.95.

7
. Ibid.

8
. Aumann, interview.

9
. Sevmour Haber, professor of mathematics, Temple University, interviews, 3.14.95 and 3.19.95.

10
. George Whitehead, professor of mathematics, MIT, interview, 12.12.95.

11
. Eva Browder, interview, 9.6.97.

12
. Barry Mazur, interview, 12.3.97.

13
. Harold Kuhn quotes Nash taking credit for introducing the tea hour at MIT in his introduction to the special volume in honor of Nash, “A Celebration of John F. Nash, Jr.,” op. cit.

14
. Isadore M. Singer, professor of mathematics, MIT, interview, 12.13.95.

15
. Kohn, interview.

16
. Singer, interview.

17
. Jerome Neuwirth, interview, 5.21.97.

18
. Mattuck, interview, 2.13.96.

19
. Descriptions of this legendary crowd are based on interviews with Kohn; Felix Browder, 11.2.95, 11.10.95, 9.6.97; Aumann; Neuwirth; Newman; H. F. Mattson, 10.29.97 and 11.18.97; Larry Wallen, 5.16.97 and 5.20.97; Mattuck; Paul Cohen, 1.5.96; Jacob Bricker, 5.22.97; and others.

20
. F. Browder, interview, 9.6.97.

21
. Haber, interview.

22
. Ibid.

23
. Martha Nash Legg, interview, 3.29.96.

24
. Neuwirth, interview.

25
. Ibid.

26
. Mattuck, interview, 2.13.96.

27
. Interviews with Neuwirth and F. Browder, 11.2.95.

28
. Jürgen Moser, professor of mathematics, Eidgenossische Techische Hochschule, Zurich, interview, 3.23.96.

29
. Marvin Minsky, professor of science, MIT, interview, 2.13.96.

30
. Herta Newman, interview, 3.2.96.

31
. Andrew Browder, professor of mathematics, Brown University, interview, 6.18.97.

32
. Haber, interview.

33
. Flatto, interview.

34
. D. Newman, interview, 2.4.96.

35
. Zipporah Levinson, interview, 9.11.95.

36
. Neuwirth, interview.

37
. D. Newman, interview.

38
. Ibid.

39
. Lawrence Wallen, professor of mathematics, University of Hawaii, interviews, 5.20.97 and 6.4.97.

40
. Kohn, interview.

41
. H. F. Mattson, professor of computer science, Syracuse University, interview, 5.16.97; also Wallen, interview.

42
. J. C. Lagarias, “The Leo Collection: Anecdote and Stories,” AT&T Bell Laboratories, 4.29.95 (Xerox).

43
. Mattuck, interview, 5.21.95, and Neuwirth, interview.

44
. Neuwirth, interview.

45
. The sketch of Donald J. Newman is based on an interview with him and on interviews with Flatto, Kohn, Mattuck, Singer, and Harold S. Shapiro, professor of mathematics, Royal Institute of Technology, Stockholm, Sweden, e-mail, 5.21.97.

46
. Singer, interview, 12.13.95.

47
. Mattuck, interview, 11.7.95.

48
. D. Newman, interview, 3.2.96.

49
. Helgason, interview, 12.3.94; also interviews with Mattuck and Singer.

50
. Flatto, interview.

51
. Ibid.

52
. Ibid.

53
. Singer, interview.

54
. Haber, interview.

55
. Ibid.

56
. Flatto, interview.

57
. Ibid.

58
. Ibid.

59
. Neuwirth, interview.

60
. Ibid.

61
. D. Newman, interview, 3.2.96.

62
. Ibid.

63
. H. Newman, interview.

64
. Fred Brauer, professor of mathematics, University of Wisconsin, interview, 5.22.97.

18: Experiments

1
. Harold N. Shapiro, professor of mathematics, Courant Institute, interview, 2.20.96.

2
. John Milnor, interview, 9.26.95.

3
. The account of the cross-country trip is based largely on recollections of Martha Nash Legg, interviews, 8.29.95 and 3.29.96, and Ruth Hincks Morgenson, interview, 6.22.97.

4
. John Nash to Harold Kuhn, personal communication, 6.24.97; also Morgenson, interview.

5
. M. Legg, interview.

6
. Ibid.

7
. Ibid.

8
. Ibid.; Milnor, interview.

9
. John M. Danskin, interview, 10.29.95.

10
. M. Legg, interview.

11
. Ibid.

12
. John Milnor, “Games Against Nature,” in
Decision Processes,
edited by R. M. Thrall, C. H. Coombs, and R. L. Davis (New York: John Wiley & Sons, 1954).

13
. “Some Games and Machines for Playing Them,” RAND Memorandum, D-l 164, 2.2.52.

14
. John Nash and R. M. Thrall, “Some War Games,” RAND Memorandum, D-l379, 9.10.52.

15
. G. Kalisch, J. Milnor, J. Nash, and E. Nering, “Some Experimental N-Person Games,” RAND Memorandum, RM-948, 8.25.52.

16
. M. Legg, interview.

17
. The description of the experiment is based on, apart from the original paper, Evar Nering, professor of mathematics, University of Minnesota, interview, 6.18.96; R. Duncan Luce and Howard Raiffa,
Games and Decisions
(New York: John Wiley & Sons, 1957), pp. 259–69; John H. Kagel and Alvin E. Roth,
The Handbook of Experimental Economics,
op. cit., pp. 10–11.

18
. Kagel and Roth, op. cit.

19
. Milnor, interview, 10.28.94.

20
. John Milnor, “A Nobel Prize for John Nash,” op. cit.

21
. See, for example, Kagel and Roth, op. cit.

22
. Milnor, interview, 1.27.98.

23
. Letter from John Nash to John Milnor, 12.27.64.

19: Reds

1
. Zipporah Levinson, interview, 9.11.95.

2
. Hearing before Committee on Un-American Activities, House of Representatives, Washington, D.C., 4.22.53 and 4.23.53. Unless otherwise noted, all references to the hearing are based on this transcript.

3
. David Halberstam,
The Fifties,
op. cit.

4
. Letter from Harold W. Dodds, president, Princeton University, to Colonel S. R. Gerard, Screening Division, Western Industrial Personnel Security Board, 10.14.54, Princeton University Archives.

5
. See, for example, F. David Peat,
Infinite Potential: The Life and Times of David Bohm
(Reading, Mass.: Addison Wesley, 1997).

6
. Z. Levinson, interview.

7
. Ibid. See also Felix Browder, interview, 11.10.95.

8
. Z. Levinson, interview.

9
. Ibid.

10
.
The Tech,
spring 1953, various issues.

11
. Z. Levinson, interview.

12
. Ibid.

13
. William Ted Martin, interview.

14
. Z. Levinson, interview.

15
. Fred Brauer, e-mail, 6.23.97; Arthur H. Copeland, professor of mathematics, University of New Hampshire, e-mail, 6.24.97; Arthur Mattuck, e-mail, 6.25.97.

16
. John Nash, plenary lecture, World Congress of Psychiatry, Madrid, 8.26.96, op. cit.

20: Geometry

1
. Letter from Warren Ambrose to Paul Halmos, undated (written spring 1953).

2
. The portrait of Ambrose is based on the recollections of Isadore Singer, 2.13.95; Lawrence Wallen, 6.4.97; Felix Browder, 11.2.95; Zipporah Levinson, 9.11.95; William Ted Martin, 9.7.95; H. F. Mattson, 10.29.97, 11.18.97, 11.28.97; Gian-Carlo Rota, 10.94; George Mackey, 12.14.95.

3
. See, for example, I. M. Singer and H. Wu, “A Tribute to Warren Ambrose,”
Notices of the AMS
(April 1996).

4
. Robert Aumann, interview, 6.28.95.

5
. Gabriel Stolzenberg, professor of mathematics, Northeastern University, interview, 4.2.96.

6
. Leopold Flatto, interview, 4.15.96. See also “The Leo Collection: Anecdotes and Stories,” AT&T Bell Laboratories, 4.29.94.

7
. Ibid.

8
. George Mackey, interview, 12.14.95.

9
. Felix Browder, interview, 11.2.95.

10
. Flatto, interview.

11
. Despite its apocryphal ring, the story appears to be true and has been confirmed by Nash. Harold Kuhn, personal communication, 8.97.

12
. Armand Borel, professor of mathematics, Institute for Advanced Study, interview, 3.1.96.

13
. F. Browder, interview.

14
. Ibid.

15
. Joseph Kohn, interview, 7.19.95. Phrasing the question precisely, Ambrose would have used the adverb “isometrically” — meaning “to preserve distances” — after “embedding.”

16
. Shlomo Sternberg, professor of mathematics, Harvard University, interview, 3.5.96.

17
. Mikhail Gromov, interview. 12.16.97.

18
. John Forbes Nash, Jr.,
Lcs Prix Nobel 1994,
op. cit.

19
. Gromov, interview.

20
. John Conway, professor of mathematics, Princeton University, interview, 10.94.

21
. Jürgen Moser, e-mail, 12.24.97.

22
. Richard Palais, professor of mathematics, Brandeis University, interview, 11.6.95.

23
. Moser, interview.

24
. Donald J. Newman, interview, 3.2.96.

25
. Jürgen Moser, “A Rapidly Convergent Iteration Method and Non-linear Partial Differential Equations, I, II,”
Annali della Scuola Normale Superiore di Pisa,
vol. 20 (1966), pp. 265–315, 499–535.

26
. See, for example, Kyosi Ito, ed.,
Encyclopedic Dictionary of Mathematics
(Mathematical Society of Japan; Cambridge: MIT Press, 1987), p. 1076; Lars Hörmander, “The Boundary Problems of Physical Geodesy,”
Archive for Rational Mechanics and Analysis,
vol. 62, no. 1 (1976), pp. 1–52; and S. Klainerman,
Communications in Pure and Applied Mathematics,
vol. 33 (1980), pp. 43–101.