A Beautiful Mind Part 19

30. See, for example, Davies, op. cit.; Chaplin, op. cit.; Nathan Rheingold, "Refugee Mathematicians in the United States of America, 19331941: Reception and Reaction," Annals of Science, Annals of Science, vol. 38 (1981), pp. 31338; Rider, op. cit.; Lipman Bers, "The European Mathematician's Migration to America," in vol. 38 (1981), pp. 31338; Rider, op. cit.; Lipman Bers, "The European Mathematician's Migration to America," in A Century of Mathematics in America, A Century of Mathematics in America, Part I Part I (Providence, R.I.: American Mathematical Society, 1988). (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, Century of Mathematics in America, Part I Part I; op. cit., Peter Lax, "The Flowering of Applied Mathematics in America," in op. cit., Peter Lax, "The Flowering of Applied Mathematics in America," in A Century of Mathematics in America, A Century of Mathematics in America, Part II Part II, op. cit., pp. 45566; Fred Kaplan, op. cit., pp. 45566; Fred Kaplan, The Wizards of Armageddon The Wizards of Armageddon (New York: Simon & Schuster, 1983). (New York: Simon & Schuster, 1983).

32. Chaplin, op. cit.

33. Andrew Hodges, Alan Turing: The Enigma Alan Turing: The Enigma (New York: Simon & Schuster, 1983). (New York: Simon & Schuster, 1983).

34. Chaplin, op. cit.

35. Ibid.

36. See Kaplan, op. cit.; William Poundstone, Prisoner's Dilemma Prisoner's Dilemma (New York: Doubleday, 1992); David Halberstam, (New York: Doubleday, 1992); David Halberstam, The Fifties, The Fifties, op. cit. op. cit.

37. Rees, "The Mathematical Sciences and World War II," op. cit.; Lax, "The Flowering of Applied Mathematics in America," op. cit., pp. 45566.

38. Herman H. Goldstine, "A Brief History of the Computer," in .4 Century of Mathematics in America, Century of Mathematics in America, Part I Part I, op. cit., pp. 31122; Poundstone, op. cit., pp. 7678, on von Neumann's role in the development of the computer; Halberstam, op. cit., pp. 9397, on von Neumann and the computer. op. cit., pp. 31122; Poundstone, op. cit., pp. 7678, on von Neumann's role in the development of the computer; Halberstam, op. cit., pp. 9397, 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, American Mathematical Monthly, vol. 77 (1970); A. W. Tucker, vol. 77 (1970); A. W. Tucker, Solomon Lefschetz: A Reminiscence; Solomon Lefschetz: A Reminiscence; Sir William Hodge, Sir William Hodge, Solomon Lefschetz, 18841972; Solomon Lefschetz, 18841972; Phillip Griffiths, Donald Spencer, and George Whitehead, Phillip Griffiths, Donald Spencer, and George Whitehead, Solomon Lefschetz: Biographical Memoirs Solomon Lefschetz: Biographical Memoirs (Was.h.i.+ngton, D.C.: National Academy of Sciences, 1992); Gian-Carlo Rota, (Was.h.i.+ngton, D.C.: National Academy of Sciences, 1992); Gian-Carlo Rota, Indiscrete Thoughts, Indiscrete Thoughts, op. cit. op. cit.

3. Lefschetz's obituary in The New York Times The New York Times (October 7, 1972) credits him for "developing] the (October 7, 1972) credits him for "developing] the Annals of Mathematics] Annals of Mathematics] into one of the world's foremost mathematical journals." 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, The Mathematical Intelligencer, vol. 16, no. 3 (1994). Lefsehetz's att.i.tude 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. vol. 16, no. 3 (1994). Lefsehetz's att.i.tude 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 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 (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 A Century of Mathematics (Was.h.i.+ngton, D.C.: Mathematical a.s.sociation of America, 1994), p. 110. (Was.h.i.+ngton, D.C.: Mathematical a.s.sociation 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, Inst.i.tute 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 Subtle Is the Lord: The Science and Life of Albert Einstein (New York: Oxford University Press, 1982). (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 n.o.bel 1994, Les Prix n.o.bel 1994, op. cit. 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 n.o.bel Prize for John Nash," The Mathematical Intelligencer, The Mathematical Intelligencer, vol. 17, no. 3 (1995), p. 5. 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. F. Nash, Jr.," Nash, Jr.," Duke Mathematical Journal, Duke Mathematical Journal, vol. 81, no. 2 (1996). vol. 81, no. 2 (1996).

27. E. T. Bell, Men of Mathematics, Men of Mathematics, op. cit. op. cit.

28. Steenrod, letter, 2.5.53.

29. For this a.s.sessment, 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. Who Got Einstein's Office? op. cit.; Denis Brian, cit.; Denis Brian, Einstein: A Life, Einstein: A Life, op. cit. 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.