A Beautiful Mind
Page 61
7. George Boehn, “The New Uses of the Abstract,” Fortune, July 1958.
8. Constance Reid, Courant in Göttingen and New York: The Ston of an Improbable Mathematician (New York: Springer Verlag, 1976).
9. Ibid.
10. Ibid.
11. Lax, interview.
12. Boehm, “The New Uses of the Abstract,” op. cit.
13. Nash told Harold Kuhn that he kept a car in New York City that year and that parking it caused him innumerable headaches, personal communication, 7.97.
14. Postcard from John Nash to Virginia and John Nash, Sr., 8.11.56.
15. Natasha Brunswick, interview, 9.25.95.
16. Tilla Weinstein, professor of mathematics, Rutgers University, interview, 8.25.97.
17. Morawetz, interview.
18. Lars Hörmander, professor of mathematics, University of Lund, interview, 2.13.97.
19. Lax, interview.
20. Hörmander, interview.
21. John Isbell, e-mail, 3.28.95.
22. Boehm, “The New Uses of the Abstract,” op. cit.
23. Stanislaw Ulam, “John von Neumann, 1903–57,” Bulletin of the American Mathematical Society, vol. 64, no. 3, part ii (May 1958).
24. John Nash, “Continuity of Solutions of Parabolic and Elliptic Equations,” American Journal of Mathematics, vol. 80 (1958), pp. 931–54.
25. See Chapters 2 and 16.
26. John Nash, “Continuity of Solutions of Parabolic and Elliptic Equations,” op. cit.
27. Louis Nirenberg, professor of mathematics, Courant Institute, interview, 10.94. See also Lax, interview.
28. Ibid.
29. Ibid.
30. Lax, interview.
31. Ibid.
32. Nirenberg, interview.
33. Hörmander, interview.
34. Ibid.
35. Lax, interview.
36. Nirenberg, interview.
37. Armand Borel, professor of mathematics. Institute for Advanced Study, interview, 3.1.96.
38. Lax, interview.
39. Morawetz, interview; Gian-Carlo Rota, interview, 10.94.
40. Paul R. Garabedian, professor of mathematics, Courant Institute, interview, 2.20.96.
41. “Ennio De Giorgi, 1928–1996” and “Interview with Ennio De Giorgi,” Notices of the American Mathematical Society, 10.97.
42. John Nash, Jr., Les Prix Nobel 1994, op. cit.
43. Rota, interview.
44. Lax, interview.
45. Letter from John Nash to Robert Oppenheimer, 7.10.57.
46. Ibid.
47. John Nash, plenary lecture, World Congress of Psychiatry, Madrid, 8.26.96, op. cit.
48. Institute for Advanced Study, directories, various years.
49. Letter from J. Nash to R. Oppenheimer.
50. John Nash, plenary lecture, op. cit.
31: The Bomb Factory
1. Richard Emery, attorney, interview, 4.4.96.
2. Ibid.
3. Postcard from John Nash to Virginia Nash, 9.57.
4. Emma Duchane, interview, 6.26.96.
5. Alicia Nash, interview, 7.1.97.
6. Duchane, interview.
7. Hartley Rogers, interview, 2.16.96.
8. Zipporah Levinson, interview, 9.11.95.
9. A. Nash, interview, 10.94.
10. Nash’s chief result was initially published in a note — submitted by Marston Morse of the Institute for Advanced Studies on 6.10.57 — in the Proceedings of the National Academy of Sciences, no. 43 (1957), pp. 754–58. The full paper was submitted to the American Journal of Mathematics nearly a year later, on 5.26.58, and published in vol. 80 (1958), pp. 931–58.
11. Elias Stein, professor of mathematics, Princeton University, interview, 12.2.95.
12. Lennart Carleson, professor of mathematics, University of Stockholm, interview, 10.3.95.
13. Ibid.
14. Stein, interview.
15. Ibid.
16. Ibid.
17. Paul R. Garabedian, interview, 2.20.96.
18. George Boehm, “The New Mathematics,” two-part series, Fortune (June and July 1958).
19. Martha recalled Nash’s telling her that he was considering accepting a post at Caltech in order to raise the likelihood of an offer from Harvard, possibly because Harvard and MIT had an informal nonraiding policy. Martha Nash Legg, interview, 3.30.96.
20. Letter from John Nash to Albert W. Tucker, 10.58.
21. At that time, tenure was normally not awarded until the candidate’s seventh year. At MIT, unlike some other institutions, tenure was paired with promotion to full, not associate, professor.
22. Gian-Carlo Rota, interview, 10.94.
23. John Forbes Nash, Jr., Les Prix Nobel 1994, op. cit.
24. Awards, Honors and Prizes, 8th edition, vol. II (Detroit: Gale Research, 1989), p. 129.
25. Lars Hörmander, interview, 2.13.97.
26. Confidential source.
27. Proceedings, International Congress of Mathematicians, 1958 (Providence, R.I.: American Mathematical Society, 1960).
28. Jürgen Moser, interview, 3.21.96.
29. Proceedings, International Congress of Mathematicians, op. cit.
30. Confidential source.
31. Confidential source.
32. Moser, e-mail, 12.24.97.
33. Peter Lax, interview, 2.6.96.
34. Moser, interview, 3.21.96.
35. Ibid.
36. For the history of the Bôcher Prize, see the Web site for the American Mathematical Society.
37. Letter from Lars Hörmander to author, 1.3.96; Hörmander, interview, 2.13.97.
38. Hörmander, e-mail, 12.16.97.
39. Ibid.
32: Secrets
1. John Forbes Nash, Jr., plenary lecture, World Congress of Psychiatry, Madrid, 8.26.96, op. cit.
2. G. H. Hardy, The Mathematician’s Apology (Cambridge, U.K.: Cambridge University Press, 1967), with a foreword by C. P. Snow.
3. Paul S. Cohen, interview, 1.5.96.
4. Stanislaw Ulam, “John von Neumann, 1903–1957,” op. cit., p. 5.
5. Hardy, op. cit.
6. Felix Browder, interview, 11.10.95.
7. Harold Kuhn, interview, 7.95.
8. Ibid.
9. John Nash, plenary lecture, op. cit.
10. Elias Stein, interview, 12.28.95.
11. Cohen, interview.
12. E. T. Bell, Men of Mathematics, op. cit.
13. Enrico Bombieri, interview, 12.6.95.
14. Bell, op. cit.
15. Andrew Wiles, professor of mathematics, Princeton University, personal communication, 6.97.
16. Lars Hörmander, interview, 2.13.97.
17. F. Browder, interview.
18. John Forbes Nash, Jr., Les Prix Nobel 1994, op. cit.
19. Bell, op. cit.
20. Ibid.
21. Ibid.
22. Jacob Schwartz, professor of computer science, Courant Institute, interview, 1.29.96.
23. Jerome Neuwirth, interview, 5.27.97.
24. Stein, interview.
25. Ibid.
26. Richard Palais, professor of mathematics, Brandeis University, interview, 11.6.95.
27. Bell, op. cit.
28. Atle Selberg, interview.
29. Eugenio Calabi, interview, 3.2.96.
30. Letter from John Nash to Martha Nash Legg, 11.4.65.
31. Stein, interview.
32. Hörmander, interview.
33. Harold Kuhn, e-mail, 7.97.
34. Paul A. Samuelson, interview.
35. William led Martin, interview, 9.7.95.
36. Robert Solow, professor of economics, MIT, interview, 1.95.
37. Martin, interview.
38. Cathleen Morawetz, interview, 2.29.96.
39. Alicia Nash, interview, 1.3.97.
40. Ibid.
41. John Nash, personal communication, 3.22.96.
42. Eva Browder, interview, 9.6.97.
43. Ibid.
44. A.
Nash, interview
45. F. Browder, interview.
46. John Moore, professor of mathematics, Princeton University, interview, 10.5.95.
33: Schemes
1. Alicia Nash, interview, 7.1.97.
2. Ibid.
3. Letter from John Nash to Albert W. Tucker, early October 1958.
4. George Mackey, interview, 1.21.96.
5. Letter from C. Ralph Bunchcr, professor of biostatistics and epidemiology, University of Cincinnati Medical Center, to author, 5.20.96.
6. A. Nash, interview.
7. John Nash, letter to A. Tucker, 10.58.
8. Ibid.
9. Martha Nash Legg, interview, 3.29.96.
10. Paul A. Samuelson, interview,,3.13.96.
11. Saunders McLane, former chairman, department of mathematics, University of Chicago, interview, 3.4.96.
12. Shlomo Sternberg, interview, 3.5.96.
13. Ibid. Also membership application, Institute for Advanced Studies, tall 1958.
14. Letter from Albert W. Tucker to John Nash, 10.8.58.
15. Letter from Albert W. Tucker to Sloan Foundation, 10.8.58.
16. Letter from Albert W. Tucker to Guggenheim Foundation, 11.26.58.
17. Gian-Carlo Rota, interview, 11.14.95.
18. Robert Solow, emeritus professor of economics, MIT, interview, 1.95.
19. Letter from John Nash to Virginia Nash, 10.15.58.
20. New York Times, 11.14.63.
21. Paul S. Cohen won the Fields in 1966 and the Bôcher in 1964. The sketch of Paul Cohen is based on interviews with Raoul Bott, 11.95 and 11.5.96; Lennart Carleson, 10.18.95; Elias Stein, 12.28.95; Felix Browder, 11.2.95; Adriano Garsia, professor of mathematics, University of California at San Diego, 12.31.95; Lars Hörmander, 2.13.97; Jiirgcn Moser, 3.21.96; Jerome Neuwirth, 5.27.97.
22. Cohen, interview, 1.5.96.
23. Stein, interview, 12.28.95.
24. Ibid.
25. Garsia, interview, 12.31.95.
26. Cohen, interview.
27. Garsia, interview; Neuwirth, interview, 5.27.97.
28. F. Browder, interview, 11.10.95.
29. Ibid., 11.2.95.
34: The Emperor of Antarctica
1. Richard Emery, interview, 4.4.96. The party scene described by Emery is also based on the recollections of Jürgen and Gertrude Moser, John and Karen Tate, Adriano Garsia, Gian-Carlo Rota, and Alicia Nash.
2. Alicia Nash, interview, 2.7.96.
3. Paul S. Cohen, interview, 1.5.96.
4. Al Vasquez, professor of mathematics, City University of New York, interview, 6.17.97.
5. Raoul Bott, interview, 11.5.95.
6. Emma Duchane, interview, 6.26.97.
7. Letter from C. Ralph Buncher to author, 5.20.96; also letter from Henry Y. Wan, professor of economics, Cornell University, to author, 6.5.96. Tony Phillips, professor of mathematics. State University of New York at Stony Brook, interview, 8.26.97, recalled Nash’s question to the class.
8. Ramesh Gangolli, professor of mathematics, University of Washington, interview, 6.12.95. Also, Alberto R. Galmarino, professor of mathematics. Northeastern University, interview, 6.95.
9. Atle Selberg, interviews, 8.16.95 and 1.23.96.
10. Gian-Carlo Rota, interview, 10.29.94; Gangolli, interview; Galmarino, interview. Martha Nash Legg put this episode later, but Gangolli and Galmarino recall that Nash didn’t meet his classes for the last couple of weeks of the term which ended 1.21.59 and Rota recalled that Nash stopped by his apartment before “driving south.”
11. Jerome Neuwirth, interview, 6.4.97; also Garsia, interview, 12.31.95.
12. Hartley Rogers, interview, 2.16.96.
13. Duchane, interview, 4.30.96.
14. Confidential source.
15. Vasquez, interview.
16. Kate Tate, interview, 8.11.97.
17. John Nash, plenary lecture, op. cit.
18. A. Nash, interview.
19. Cohen, interview.
20. Vasquez, interview.
21. Harold Kuhn, interview, 8.94.
22. Cohen, interview.
23. Neuwirth, interview.
24. Moser, interview, 3.23.96.
25. William Ted Martin, interview, 9.7.95.
26. Felix Browder, interview, 11.2.95; Paul A. Samuelson, interview, 10.94.
27. John Danskin, interview, 10.19.96.
28. The account of this incident is based on interviews with the following sources: Sigurdur Helgason, 2.13.96; F. Browder; Samuelson, 10.94 and 3.15.96; Harold Kuhn, interview, 1.95. Browder, who later became chairman of the Chicago department, recalled seeing the letter in the files. Efforts by the current chairman to locate it proved fruitless.
29. Vasquez, interview.
30. Eugenio Calabi, interview, 3.2.96.
31. Ibid.
32. Selberg, interview.
33. Program, 554th Meeting, Columbia University, New York, February 28, 1959, Bulletin of the American Mathematical Society, vol. 65 (1959), p. 149.
34. Harold N. Shapiro, interview, 2.29.96.
35. Peter Lax, interview, 2.6.96.
36. Donald J. Newman, interview, 3.2.96.
37. Cathleen Morawetz, interview, 2.29.96.
38. F. Browder, interview.
35: In the Eye of the Storm
1. Alicia Nash, interview, 7.1.97.
2. Emma Duchane, interview, 6.26.97.
3. A. Nash, interview.
4. Donald V. Reynolds, interview, 6.29.97.
5. A. Nash, interview.
6. Duchane, interview.
7. Martha Nash Legg, interview, 3.29.96.
8. Duchane, interview.
9. A. Nash, interview.
10. Duchane, interview.
11. A. Nash, interview.
12. Duchane, interview.
13. Ibid.
14. William Ted Martin, interview, 9.7.95.
15. Gian-Carlo Rota, interview, 10.29.94.
16. Letter from John Nash to Virginia Nash, 3.12.59.
17. Letter from John Nash to Martha Nash Legg, 3.12.59.
18. A. Nash, interview, 7.1.97.
19. Al Vasquez, interview, 6.17.97.
20. Duchane, interview.
21. Ibid.
22. Paul S. Cohen, interview, 1.5.96.
23. Gertrude Moser, interview, 8.25.95.
24. Kay Whitehead, professor of mathematics, Tufts University interview, 12.12.95.
36: Day Breaks in Bowditch Hall
1. Paul S. Cohen, interview, 1.5.96.
2. Adriano Garsia, interview, 12.31.95.
3. Cohen, interview.
4. My description of how MIT’s psychiatric sendee likely handled Nash’s commitment is based on interviews with Benson Rowell Snyder, who was hired by President Julius Stratton to reorganize the service, interview, 7.24.97; Wade Rockwood, interview, 7.26.97; Merton J. Kahne, professor, MIT, interview, 5.15.96; Harvey Burstein, former FBI agent who was brought in by Stratton to expand MIT’s campus police, interview, 7.3.97.
5. The description of how Nash was taken to McLean against his will is based on a contemporaneous account by a former dean of Tufts Medical School, A. Warren Stearns, who interviewed Nash shortly after his commitment (letter fron Stearns to Bernard Bradley, 4.14.59), and a further elaboration by Nash (E-mail, 5.15.98).
6. Snyder, interview.
7. For a portrait of McLean as it was in the 1950s, I relied on an official history by S. B. Sutton, A Histon’ of McLean Hospital (Washington, D.C.: American Psychiatric Press, 1986); annual reports; firsthand accounts by Sylvia Plath, Robert Lowell, and Ray Charles, as well as Suzanna Kaysen’s more recent report, Girl, Interrupted; and interviews with individuals associated with McLean in that era, including Paul Howard, former associate psychiatrist in chief and director of the clinical service, 2.15.95; Kahne; Joseph Brenner, 7.23.97; Arthur Cain, psychiatrist, 8.20.97; Alfred Pope, senior neuropathologist, McLean Hospital, and professor of neuropathology, Harvard Medical School, 12.13.95 and 2.16
.96.
8. Robert Garber, former president, American Psychiatric Association, interview, 5.6.96.
9. Sylvia Plath, The Bell Jar, op. cit.; Ray Charles, Brother Rav (New York: Da Capo, 1978, 1992).
10. Letter from A. W. Stearns to B. Bradley, 5.14.53.
11. Zipporah Levinson, interview, 9.11.95.
12. Emma Duchane, interview, 6.26.97.
13. Robert Lowell was hospitalized at McLean at the end of April 1959. Lowell was confined to Bowditch, as he had been two years earlier when he wrote “Day Breaks at Bowditch Hall,” one of the poems in To the Union Dead. Several of Nash’s visitors, including Gian-Carlo Rota, Isadore Singer, and Arthur Mattuck, recall encounters with Lowell, and therefore it seems that Nash, too, was confined to Bowditch. Since we have no firsthand reports from Nash, I have made use of Lowell’s impressions from 1957 and 1959, augmented by the impressions of some of Lowell’s visitors, including his wife, writer Elizabeth Hardwrck, letter, 8.8.97; poet Stanley Kunitz, interview, 8.2.97; and Lowell’s executor, Frank Bidart, interview, 7.27.97. See also Ian Hamilton, Robert Lowell: A Biography (New York: Random House, 1982); Paul Mariani, The Lost Puritan, op. cit., and interview, 7.28.97; Peter Davison, The Fading Smile: Poets in Boston, 1955–1960, from Robert Frost to Robert Lowell to Sylvia Plath (New York: Knopf, 1994), and interview, 8.11.97.
14. “I’ve been conditioning here for about a month,” letter from Robert Lowell to Edmund Wilson, 5.19.59, from Bowditch House; “In the hospital I spent a mad month or more rewriting everything in my three books,” letter from Robert Lowell to Elizabeth Bishop, 7.24.59.
15. Elizabeth Hardwick, personal communication, 9.8.97.
16. Arthur Mattuck, e-mail, 8.8.97.
17. “The house I was in was divided between ex-paranoid boys and senile old men,” letter from Robert Lowell to Peter Taylor, 3.15.58.
18. Letter from R. Lowell to E. Bishop, 3.15.58.
19. Ibid.; also “Waking in the Blue,” Robert Lowell, Life Studies and For the Union Dead (New York: Farrar, Straus and Giroux, 1992). Quotes in this and the following paragraphs are taken from “Waking” unless otherwise noted.
20. From “Waking in the Blue”; also Duchane, interview.
21. Letter from R. Lowell to E. Bishop; also “Waking in the Blue.”
22. Seymour Krim, “The Insanity Bit,” in View of a Nearsighted Cannoneer (New York: E. P. Dutton, 1968).