A Beautiful Mind Part 24

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 194849; 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, "a.n.a.lysis, Complex," Encyclopaedia Britannica Encyclopaedia Britannica (1962). (1962).

17. Kodaira won the Fields in 1954; David C. Spencer, "Kunihiko Kodaira (19151997)," American Mathematical Monthly, American Mathematical Monthly, 2.98. 2.98.

18. Spencer won the Bocher 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, Inst.i.tute 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 s.h.i.+ffman, 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 n.o.bel Prize for John Nash," op. cit., p. 14.

25. Intersectional Nomination: Cla.s.s 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, Annals of Mathematics, no. 81 (1965), pp. 8299. Milnor calls this an "important" application. no. 81 (1965), pp. 8299. 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, Math. Zeit, vol. 41 (1936), pp. 117. vol. 41 (1936), pp. 117.

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 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 Ha.s.sler 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 doc.u.ments refer to Nash's having been a poor teacher; the comments undoubtedly stem from his experiences in 195051.

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.

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, Was.h.i.+ngton, 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, New York Times, 3.19.64; Paul Samuelson, "Some Memories of Norbert Wiener," 1964, Xerox provided by Samuelson; and Norbert Wiener, 3.19.64; Paul Samuelson, "Some Memories of Norbert Wiener," 1964, Xerox provided by Samuelson; and Norbert Wiener, Ex-Prodigy Ex-Prodigy (New York: Simon & Schuster, 1953) and (New York: Simon & Schuster, 1953) and I Am a Mathematician I Am a Mathematician (New York: Simon & Schuster, 1956). (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 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.