1. George Pólya, How to Solve It: A New Aspect of Mathematical Method (Princeton, N.J.: Princeton University Press, 1971), 208.

2. Personal communication with author.

3. G. H. Hardy, A Mathematician’s Apology (New York: Cambridge University Press, 1967), 82–85.

4. Stephen Weinberg, Dreams of a Final Theory (New York: Pantheon, 1992), 67.

5. Constance Reid, Hilbert (New York: Springer, 1970), 220.

6. See R. Courant and D. Hilbert, Methoden der Mathematischen Physik, 2 vols. (Berlin: Springer, 1968).

7. Schrödinger to Wien, February 22, 1926, printed in Jagdish Mehra, The Historical Development of Quantum Theory, 5 vols. (New York: Springer, 1987), vol. 5, part 2, p. 583.

8. Marguerite Kay, Bruegel (New York: Paul Hamlyn, 1969).

9. James Gleick, Genius: The Life and Science of Richard Feynman (New York: Pantheon, 1992), 378.

10. See Donald J. Albers, G. L. Alexanderson, and Constance Reid, International Mathematical Congresses: An Illustrated History, 1893–1986 (New York: Springer, 1986).

11. William Dunham, Journey through Genius: The Great Theorems of Mathematics (New York: John Wiley and Sons, 1990), 10.

12. See Tobias Dantzig, Number: The Language of Science (Garden City, N.Y.: Doubleday, 1954).

13. Rudin to J. W. Cannon, January 1993.

14. See J. W. Cannon, “Mathematics in Marble and Bronze: The Sculpture of Helaman Rolfe Pratt Ferguson,” Mathematical Intelligencer 13 (1991): 37.

15. “One Saturday Gerhard Gauss was making out the weekly payroll, . . . unaware that his young son was following the proceedings. Coming to the end of his long computations, Gerhard was startled to hear the little boy pipe up, ‘Father, the reckoning is wrong, it should be. . . .’ A check of the account showed that the boy [Karl Friedrich Gauss] was correct.” E. T. Bell, Men of Mathematics (New York: Simon and Schuster, 1937), 221.

16. See Karl Friedrich Gauss, General Investigations of Curved Surfaces of 1827 and 1825, trans. James Caddall Morehead and Adam Miller Hiltebeitel (Princeton: Princeton University Press, 1902).

17. Bell, Men of Mathematics, 500–503.

18. See Bell, Men of Mathematics, ch. 26; Bernhard Riemann, Collected Works, ed. Heinrich Weber (New York: Dover, 1953).

19. Riemann, Collected Works, 275.

20. See H. Poincaré, Oeuvres, 6 vols. (Paris: Gauthier-Villars, 1953), 6:183, for the original text, or J. W. Cannon, “The Recognition Problem: What Is a Topological Manifold?” Bulletin of the American Mathematical Society 84 (1978): 835, for a rough translation of the complete passage.

21. See J. W. Milnor, “On the Total Curvature of Knots,” Annals of Math 52, no. 2 (1950): 248–57.

22. See the list of all Fields Medalists in Albers, Alexanderson, and Reid, International Mathematical Congresses.

23. See R. H. Bing, The Collected Papers of R. H. Bing, ed. Sukhjit Singh, Steve Armentrout, and Robert J. Daverman, 2 vols. (Providence: American Mathematical Society, 1988).

24. R. Lashof, ed., “Problems in Differential and Algebraic Topology: The Conference in Seattle, 1963,” Annals of Math 81 (1965): 565–91.

25. Leslie C. Glaser, “On a Well-known Method for Trying to Obtain a Noncombinatorial Triangulation of Sⁿ for n ≥ 5,” Duke Mathematics Journal 35 (1968): 147–54.

26. Leslie C. Glaser, “On Double Suspensions of Arbitrary Nonsimply Connected Homology n-spheres,” in Topology of Manifolds, ed. James C. Cantrell and C. H. Edwards Jr. (Chicago: Markham, 1970), 5–17.

27. See M. A. Štan’ko, “Approximation of Imbeddings of Compacta in Codimensions Greater Than Two,” Dokl. Adad. Nauk SSSR 198 (1971): 783–86 or in Societ Math. Dokl. 12 (1971): 906–9; and M. A. Štan’ko, “Approximation of Compacta in Eⁿ in Codimensions Greater Than Two,” Mat. Sbornik 90, no. 132 (1973): 625–36 or in Math USSR Sbornik 19 (1973): 615–26.

28. Štan’ko, “Approximation of Imbeddings of Compacta,” 783–86.

29. M. A. Štan’ko, “Approximation of Imbeddings of Manifolds in Codimension One,” Mat. Sbornik 23 (1974): 456–66.

30. See F. D. Ancel and J. W. Cannon, “The Locally Flat Approximation of Cell-like Embedding Relations,” Annals of Mathematics 109 (1979): 61–86.

31. See Robert D. Edwards, “The Topology of Manifolds and Cell-like Maps,” in Proceedings of the International Congress of Mathematicians, Helsinki, 1978 (Hungary: Academia Scientiarum Fennica, 1980), 111–27.

32. See J. L. Bryant and others, “Topology of Homology Manifolds,” Bulletin of the American Mathematical Society 28 (April 1993): 324–28.

33. Donald J. Albers, Gerald L. Alexanderson, and Constance Reid, More Mathematical People: Contemporary Conversations (New York: Harcourt Brace Jovanovich, 1990), 3.

34. Lipman Bers, “Quasiconformal Mappings and Teichmüller’s Theorum,” in Analytic Functions, ed. R. Nevannlina and others (Princeton, N.J.: Princeton University Press, 1960), 90.

35. See Albers, Alexanderson, and Reid, More Mathematical People, 324–43.

36. See Albers, Alexanderson, and Reid, More Mathematical People, 283–303.

37. Bell, Men of Mathematics, 204.

38. See Henri Poincaré, The Value of Science (New York: Dover, 1958), 11–12, for the entire quotation.

39. See Wendell Berry, Recollected Essays, 1965–1980 (San Francisco: North Point Press, 1981), 154.

J. W. Cannon

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