Available today at 9 a.m.

Additional Options

Mathematics Library: S.C. Kleene

On May 14, 1999, the former mathematics library was renamed the Stephen Cole Kleene Mathematics Library.

Stephen Cole Kleene (pronounced “KLAY-nee” by Steve himself) was born on January 5, 1909 in Hartford, Connecticut. He received a Bachelor of Arts degree from Amherst College in 1930, and a Ph.D. from Princeton University in 1934 under the tutelage of Alonzo Church. He joined the Wisconsin faculty in 1935 as an Instructor and in 1937 was promoted to assistant professor. During the next several years he spent time at the Institute for Advanced Study in Princeton, taught at Amherst College, and served in the U.S. Navy, earning the rank of lieutenant commander during World War II.

He returned to Madison in 1946, was promoted to full professor in 1948, and remained on the faculty for the remainder of his career. He became the Cyrus Colton MacDuffee Professor of Mathematics in 1964 and retired from that position and the UW-Madison in 1979. He was professor emeritus until his death on January 25, 1994.

Kleene Bibliography

  1. “Proof by cases in formal logic.” Annals of Mathematics, vol. 35 (1934):529-544.
  2. “A Theory of Positive Integers in Formal Logic.” Ph.D. diss., Princeton University, September, 1933. Revised June 1934. American Journal of Mathematics, vol. 57 (1935): 153-173 & 219-244.
  3. “The inconsistency of certain formal logics.” with J.B. Rosser, Annals of Mathematics, vol. 36 (1935), pp. 630-636.
  4. “General recursive functions of natural numbers.” Mathematische Annalen, vol. 112 (1936): 727-742. Reprinted with addendum in: Undecidable; Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions. ed. by Martin Davis, Raven Press Books, 1965.
  5. “Lambda definability and recursiveness.” Duke Mathematical Journal, vol. 2 (1936): 340-353.
  6. “A note on recursive functions.” Bulletin of the American Mathematical Society, vol. 42 (1936): 544-546.
  7. “Formal definitions in the theory of ordinal numbers.” with Alonzo Church, Fundamenta Mathematica, vol. 28 (1937): 11-21.
  8. “On notation for ordinal numbers.” Journal of Symbolic Logic, vol. 3 (1938): 150-155.
  9. “A postulation basis for probability.” with H.P. Evans, American Mathematical Monthly, vol. 46 (1939): 141-148.
  10. “On the term ‘analytic’ in logical syntax.” Preprinted for the members of the Fifth International Congress for the Unity of Science, Cambridge, Mass., September 1939, from the Journal of Unified Science (Erkenntnis), vol. 9 (1939): 189-192.
  11. “Recursive predicates and quantifiers.” Transactions of the American Mathematical Society, vol. 53 (1943): 41-73. Reprinted with addendum in: Undecidable; basic papers on undecidable propositions, unsolvable problems and computable functions. ed. by Martin Davis, Raven Press Books, 1965.
  12. “On the forms of the predicates in the theory of constructive ordinals.” American Journal of Mathematics, vol. 66 (1944): 41-58.
  13. “On the interpretation of intuitionistic number theory.” Journal of Symbolic Logic, vol. 10 (1945): 109-124.
  14. “On the intuitionistic logic.” Library of the Tenth International Congress of Philosophy, Amsterdam, August 11-18, 1948, Vol. I, Proceedings of the Congress, ed. by E.W. Beth, H.J. Pos, and J.H.A. Hollak. North Holland Publishing Co., Amsterdam, 1949, pp. 741-743.
  15. “Analysis of lengthing of modulated repetitive pulses.” Proceedings of the Institute of Radio Engineers, vol. 35 (1947): 1049-1053.
  16. “A symmetric form of Gödel’s theorem.” Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen. Series A, Mathematical Sciences, vol. 53, (1950): 800–802. Equivalently, Indagationes Mathematicae, vol. 12 (1950): 244-246.
  17. “Recursive functions and intuitionistic mathematics.” Proceedings of the International Congress of Mathematicians, vol. 1, Cambridge, Mass., 1950. American Mathematical Society, Providence, R. I., 1952, pp. 679-685.
  18. “Permutability of inferences in Gentzen’s calculi LK and LJ.” Two papers on the predicate calculus. Memoires of the American Mathematical Society, no. 10, American Mathematical Society, Providence, R.I., 1952, pp. 1-26.
  19. “Finite axiomatizability of theories in the predicate calculus using additional predicate symbols.” Two papers on the predicate calculus. Memoires of the American Mathematical Society, no. 10, American Mathematical Society, Providence, R.I., 1952, pp. 27-68.
  20. Introduction to Metamathematics. D. Van Nostrand Co., Inc., New York, N. Y., 1952.
  21. “The upper semi-lattice of degrees of recursive unsolvability.” with Emil Post. Annals of Mathematics, vol. 59 (1954): 379-407.
  22. “Arithmetical predicates and function quantifiers.” Transactions of the American Mathematical Society, vol. 79 (1955): 312-340.
  23. “On the forms of the predicates in the theory of constructive ordinals II.” American Journal of Mathematics, vol. 77 (1955): 405-428.
  24. “Hierarchies of number-theoretic predicates.” Bulletin of the American Mathematical Socitey, vol. 61 (1955): 193-213.
  25. “Representation of events in nerve nets and finite automata.” In: Automata Studies, ed. by C.E. Shannon and J. McCarthy. Annals of Mathematics Studies, no. 34. Princeton University Press, Princeton, N. J., 1956, pp. 3-41.
  26. “A note on computable functionals.” Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen. Series A, Mathematical sciences, vol. 59 (1956). Equivalently, Indagationes Mathematicae, vol. 18 (1956):275-280.
  27. Sets, Logic, and Mathematical Foundations: a summer institute for teachers of secondary and college mathematics, sponsored by the National Science Foundation. Notes compiled by H. William Oliver. Williamstown, Mass.,Williams College, 1956.
  28. “Foundations of Mathematics.” Encyclopedia Britannica. (1957 – 1973).
  29. “Decision Procedure.” Ibid.
  30. “Realizability.”Summaries of Talks Presented at the Summer Institute of Symbolic Logic, Cornell University, vol. 1, 1957, pp.100-104. Second edition, Communications Research Division, Institute for Defense Analysis, 1960, pp. 100-104. Reprinted in: Constructivity in mathematics; proceedings. Studies in Logic and the Foundations of Mathematics, ed. by A. Heyting, North-Holland Publishing Co., Amsterdam 1959, pp. 285-289.
  31. “Recursive functionals of higher finite types.” Ibid (1957): 148-154, with errata vol. 3 p. 429. Second Edition, Ibid (1960): 148-154.
  32. “A note on function quantification.” with John Addison. Proceedings of the American Mathematical Society, vol. 8 (1957): 1002-1006.
  33. “Extension of an effectively generated class of functions by enumeration.” Colloquium Mathematicum, vol. 6 (1958): 67-78.
  34. “Recursive functionals and quantifiers of finite types I.” Transactions of the American Mathematical Society, vol. 91 (1959): 1-52.
  35. “Countable functionals.” In: Constructivity in mathematics: proceedings. ed. by A. Heyting, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1959, pp. 81-100.
  36. “Quantification of number-theoretic functions.” Compositio Mathematica, vol. 14 (1959): 23-40.
  37. “Mathematical logic: constructive and non-constructive operations.” Proceedings of the International Congress of Mathematicians, 1958. Cambridge University Press, New York, 1960, pp. 137-153.
  38. “Realizability and Shanin’s algorithm for the constructive deciphering of mathematical sentences.” Logique et Analyse, vol. 3 (1960): 154-165.
  39. Mathematical Logic, Course I. National Science Foundation Summer Institute, Bowdoin College, 1961. Notes on lectures compiled by Edward Pols.
  40. “Disjunction and existence under implication in elementary intuitionistic formalisms.” Journal of Symbolic Logic 27 (1962): 11-18.
  41. “Turing-machine computable functionals of finite types I.” Logic, methodology, and philosophy of science; proceedings. International Congress for Logic, Methodology, and Philosophy of Science 1960. Stanford University Press, Stanford, Calif., 1962, pp. 38-45.
  42. “Turing-machine computable functionals of finite types II.” Proceedings of the London Mathematical Society, vol. 12 (1962): 245-258.
  43. “Lambda-definable functionals of finite types.” Fundementa Mathematicae, vol. 50 (1962): 281-303.
  44. “Herbrand-Gödel-style recursive functionals of finite types.” In: Recursive Function Theory. ed. by J.C.E. Dekker. Proceedings of Symposia in Pure Mathematics, no. 5, American Mathematical Society, Providence, R.I., 1962, pp. 49-75.
  45. “Recursive functionals and quantifiers of finite types II.” Transactions of the American Mathematical Society, vol. 108 (1963): 106-142.
  46. “An addendum: Disjunction and existence under implication in elementary intuitionistic formalisms.” Journal of Symbolic Logic, vol. 28 (1963): 154-156. [See # 40 above]
  47. “Computability.” The Voice of American Forum Lectures, Philosophy of Science Series, no. 6 & 8. Washington, DC: Voice of America, 1964. Reprinted in Philosophy of Science Today, ed. by Sidney Morgenbesser, Basic Books 1967, pp. 36-45.
  48. Foundations of Intuitionistic Mathematics; especially in relation to recursive functions. with Richard Vesley, Studies in Logic and the Foundations of Mathematics, North Holland Publishing Co., Amsterdam, 1965.
  49. “Classical extensions of intuitionistic mathematics.” In: Logic, Methodology, and Philosophy of Science. ed. by Y. Bar-Hillel. Proceedings of the 1964 International Congress for Logic, Methodology, and Philosophy of Science. Studies in Logic and the Founations of Mathematics, North-Holland Publishing Co., Amsterdam, 1965, pp. 31-44.
  50. “Logical calculus and realizability.” Studia Logico-Mathematica et Philosophica: in Honorem Rolf Nevanlinna. Acta Philosophica Fennica, no. 18, 1965, pp.71-80.
  51. Mathematical Logic. John Wiley & Sons, Inc., New York-London-Sydney 1967. First Corrected printing 1968.
  52. “Constructive functions in the foundations of intuitionistic mathematics.” In: Logic, Methodology, and Philosophy of Science; Proceedings of the Third International Congress for Logic, Methodology, and Philosophy of Science, Amsterdam, 1967. ed. by B. Van Rootselaar and J.F. Staal. Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1968, pp. 137-144.
  53. “On the normal form theorem.” In: Les Fonctions Recursives et leur Applications: Colloque International Organize par l’Association Mathematique Bolyai Janos avec le souiten du Conseil International des Union Scientifiques, Tihany, Hongrie, 4-7 September 1967, Texte des Conferences publie par l’Institut Blaise Pascal du Centre National de la Recherch Scientifique [Paris] et l’Association Mathematique Bolyai Janos, Budapest, 1969, pp. 71-83.
  54. Formalized Recursive Functionals and Formalized Realizability. Memoirs of the American Mathematical Society, no. 89, American Mathematical Society, Providence, R.I. 1969.
  55. “The new logic.” A Sigma-Xi-RESA National Lecture, southeast Tour, Spring 1969. American Scientist, vol. 57 (1969): 333-347.
  56. “Realizability: a retrospective survey.” Cambridge Summer School in Mathematical Logic, Cambridge, England, August 1-21, 1971, edited by A.R.D. Mathias and H. Rogers, Lecture Notes in Mathematics, no. 337, Springer-Verlag, Berlin, 1973, pp. 95-112.
  57. “Brief Mathematical autobiography.” edited and translated into Italian for Scienziati e Tecnologi Contemporanei, Arnoldo Mondadori Editore, Milan, vol. 2, (1974): 109-111.
  58. “The work of Kurt Gödel.” Journal of Symbolic Logic, vol. 41 (1976): 761-778. Reprinted in: Gödel’s theorem in focus, ed. by S.G. Shanker, Croom Helm Philosophers in Focus Series, Croom Helm, London, 1988, pp. 48-73.
  59. “Recursive functionals and quantifiers of finite types revisited I.” In: Generalized Recursion Theory II: Proceedings of the 1977 Oslo symposium, edited by J. E. Fenstad, R. O. Gandy, and G. E. Sacks. Studies in Logic and the Foundations of Mathematics, no. 94, North-Holland, Amsterdam-New York, 1978, pp. 185-222.
  60. “An addendum to: ‘The work of Kurt Gödel’.”Journal of Symbolic Logic, vol. 43 (1978): 613. [See # 58 above]
  61. “Origins of recursive function theory.” In: 20th Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 1979, IEEE, New York, 1979, pp. 371-382.
  62. “Recursive functionals and quantifiers of finite types revisited II.” In: The Kleene Symposium: Proceedings of the Symposium held June 18-24, 1978 at Madison, Wisconsin, U.S.A., ed. by Jon Barwise, H. Jerome Keisler, and Kenneth Kunen. Studies in Logic and the Foundations of Mathematics, no.101, North-Holland, Amsterdam-New York, 1980, pp. 1-29.
  63. “The theory of recursive functions, approaching its centennial.” Bulletin of the American Mathematical Society, vol. 5 (1981): 43-61.
  64. “Algorithms in various contexts.” In: Algorithms in Modern Mathematics and Computer Science: Proceedings, Urgench, Uzbek SSR, September 16-22, 1979. ed. by A.P. Ershov and D. Knuth , Lecture Notes in Computer Science, no.122, Springer, Berlin-New York, 1981, pp. 355-360.
  65. “Origins of recursive function theory.” Annals of the History of Computing, vol. 3 (1981): 52-67.
  66. “Recursive functionals and quantifiers of finite types revisited III.” In: Patras Logic Symposion: Proceedings of the Logic Symposion held at Patras, Greece, August 18-22, 1980. ed. by George Metakides. Studies in Logic and the Foundations of Mathematics, no. 109, North-Holland, Amsterdam-New York, 1982, pp. 1-40.
  67. “Recursive functionals and quantifiers of finite types revisited IV: Unimonotone functions of finite types.” In: Recursion Theory. ed by A. Nerode and R. Shore. Proceedings of Symposia in Pure Mathematics, no. 42, American Mathematical Society, Providence, RI, 1985, pp. 119-138.
  68. “Collected Works [Kurt Gödel].” Edited with S. Feferman, J.W. Dawson, G.H. Moore, R.M. Solovay, and J. van Heijenoort. Oxford University Press, New York, 1986. Introductory notes & translations vol. 1, pp. 126-139, 256; vol. 3 pp. 30-35.
  69. “Reflections on Church’s thesis.” Notre Dame Journal of Formal Logic, vol. 28 (1987): 490-498.
  70. “Kurt Gödel.” Biographical Memoirs, vol. 56, National Academy of Sciences of the United States of America, Washington, D.C., National Academy Press, 1987, pp. 134-179.
  71. “Gödel’s impression on students of logic in the 1930s.” In: Gödel remembered; Gödel-Symposium, Salzburg 10-12 July 1983. ed. by Paul Weingartner and Leopold Schmetterer, History of Logic, no. 4, Bibliopolis, Naples, 1987, pp. 49-64.
  72. “The role of logical investigations in mathematics since 1930.” In: A Century of Mathematics in America Part I. ed. by Peter Duren, Richard A. Askey, and Uta C. Merzbach. History of Mathematics, no. 1, American Mathematical Society, Providence, RI., 1988, pp. 85-91.
  73. “Turing’s analysis of computability, and major applications of it.” In: The universal Turing machine: a half-century survey. ed. by Rolf Herken. Oxford Science Publishing Co., Oxford University Press, New York, 1988, pp. 17-54.
  74. “Recursive functionals and quantifiers of finite types revisited V.” Transactions of the American Mathematical Society, vol. 325 (1991): 593-630.
  75. “The writing of Introduction to metamathematics.” In: Perspectives on the History of Mathematical Logic. ed. by Thomas Drucker. Birkhäuser, Boston, 1991, pp. 161-168.

Interviews

  • Crossley, J.N., Reminiscences of logicians, Algebra and Logic: Papers from the 1974 Summer Research Institute of the Australian Mathematical Society, Monash University, Australia. Lecture Notes in Mathematics 450, Springer-Verlag, Berlin, 1975, pp. 1-62.
  • Smail, Laura. Oral History Project, University of Wisconsin – Madison, 1981.
  • Aspray, William. The Princeton Mathematics Community in the 1930s: An Oral-History Project. An interview with J. Barkley Rosser and Stephen C. Kleene in Madison, Wisconsin on 26 April 1984.

Works About Kleene

  • “A biographical sketch of Stephen C. Kleene.” The Kleene Symposium: Proceedings of the Symposium held June 18-24, 1978 at Madison, Wisconsin, U.S.A., ed. by Jon Barwise, H. Jerome Keisler, and Kenneth Kunen. Studies in Logic and the Foundations of Mathematics, no.101, North-Holland, Amsterdam-New York, 1980, pp. vii-ix.
  • “A summary of Kleene’s work in recursion theory.” Ibid. pp. x-xi.
  • Mac Lane, Saunders. “Stephen Cole Kleene – a reminiscence.” Annals of Pure and Applied Logic, vol. 81 (1996): 3-7.
  • Maclane, Saunders. “Stephen Cole Kleene.” Biographical memoirs. vol. 75, National Academy of Sciences of the United States of America, Washington, D.C. : National Academy Press, 1998, pp. 154-163.
  • MacTutor History of Mathematics archive. “Stephen Cole Kleene.” December 1996.
  • Shoenfield, J.R.”The mathematical work of S.C. Kleene.” Bulletin of Symbolic Logic, vol. 1 (1995): 9-43.