Stephen Cole Kleene Explained

Stephen Kleene
Birth Date:5 January 1909
Birth Place:Hartford, Connecticut, U.S.
Death Place:Madison, Wisconsin, U.S.
Field:Mathematics
Work Institutions:University of Wisconsin–Madison
Alma Mater:Amherst College
Princeton University
Doctoral Advisor:Alonzo Church
Doctoral Students:Robert Constable
Joan Moschovakis
Yiannis Moschovakis
Nels David Nelson
Dick de Jongh
Prizes:Leroy P. Steele Prize (1983)
National Medal of Science (1990)

Stephen Cole Kleene (; January 5, 1909 – January 25, 1994) was an American mathematician and logician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science.[1] Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented regular expressions in 1951 to describe McCulloch-Pitts neural networks, and made significant contributions to the foundations of mathematical intuitionism.[2] [3]

Biography

Kleene was born to Alice Lena Cole, a published poet, and Gustav Adolph Kleene, a professor of economics at Trinity College, in Hartford, Connecticut.[4] [5] Gustav's parents were immigrants from Germany.[6]

Kleene was awarded a bachelor's degree from Amherst College in 1930. He was awarded a Ph.D. in mathematics from Princeton University in 1934, where his thesis, entitled A Theory of Positive Integers in Formal Logic, was supervised by Alonzo Church.[7] In the 1930s, he did important work on Church's lambda calculus.[8] In 1935, he joined the mathematics department at the University of Wisconsin–Madison, where he spent nearly all of his career. After two years as an instructor, he was appointed assistant professor in 1937. In the 1930s, Kleene laid the foundation for recursion theory, an area that would be his lifelong research interest.[9]

He was a visiting scholar at the Institute for Advanced Study in Princeton in 1939–1940.[10] In 1941, he returned to Amherst College, where he spent one year as an associate professor of mathematics. In 1942, he married Nancy Elliott. In the same year he enlisted in the United States Navy Reserve as a lieutenant, attaining the rank of lieutenant commander by his discharge in 1946.[11]

In 1946, Kleene returned to the University of Wisconsin-Madison, becoming a full professor in 1948 and the Cyrus C. MacDuffee professor of mathematics in 1964. He served two terms as the Chair of the Department of Mathematics and one term as the Chair of the Department of Numerical Analysis (later renamed the Department of Computer Science). He also served as Dean of the College of Letters and Science in 1969–1974. During his years at the University of Wisconsin he was thesis advisor to 13 Ph.D. students. He retired from the University of Wisconsin in 1979. In 1999 the mathematics library at the University of Wisconsin was renamed in his honor.[12]

Kleene's teaching at Wisconsin resulted in three texts in mathematical logic, Kleene (1952), (1967), and Kleene and Vesley (1965). The first two are often cited and still in print. Kleene (1952) wrote alternative proofs to the Gödel's incompleteness theorems that enhanced their canonical status and made them easier to teach and understand. Kleene and Vesley (1965) is the classic American introduction to intuitionistic logic and mathematical intuitionism.

Kleene served as president of the Association for Symbolic Logic, 1956–1958, and of the International Union of History and Philosophy of Science,[13] 1961. The importance of Kleene's work led to Daniel Dennett coining the saying, published in 1978, that "Kleeneness is next to Gödelness."[14] In 1990, he was awarded the National Medal of Science.[15]

Kleene and his wife Nancy Elliott had four children. He had a lifelong devotion to the family farm in Maine. An avid mountain climber, he had a strong interest in nature and the environment, and was active in many conservation causes.

Legacy

At each conference of the Symposium on Logic in Computer Science the Kleene Award, in honour of Stephen Cole Kleene, is given for the best student paper.[16]

Selected publications

See also

External links

Notes and References

  1. Web site: Stephen Cole Kleene Mathematician, Logician, Recursion Britannica . October 12, 2025 . Britannica . en.
  2. Book: Jurafsky, Daniel . Dan Jurafsky . Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition . Martin . James H. . . 2009 . 9780131873216 . 2nd . 42.
  3. Moschovakis . Joan R. . Moschovakis . Yiannis N. . February 2018 . Intuitionism and effective descriptive set theory . Indagationes Mathematicae . 29 . 1 . 396–428 . 10.1016/j.indag.2017.06.004 . 0019-3577. subscription .
  4. Web site: February 10, 1994 . Obituary: Professor Stephen Kleene . October 6, 2025 . The Independent . en.
  5. Book: Marquis, Albert Nelson . Who's who in New England . 1916 . . Chicago . 639 . First published 1909.
  6. Web site: NARA . National Archives and Records Administration . Gustav Kleene; United States Census, 1910 . October 12, 2025 . FamilySearch.
  7. Web site: Mathematics Library: S.C. Kleene . October 12, 2025 . library.wisc.edu . en-US.
  8. Church . Alonzo . 1936 . An Unsolvable Problem of Elementary Number Theory . American Journal of Mathematics . 58 . 2 . 345–363 . 10.2307/2371045 . 0002-9327 . The notion of λ-definability is due jointly to the present author and S. C. Kleene.... subscription .
  9. Shoenfield . J. R. . Kleene . S. C. . 1995 . The Mathematical Work of S. C. Kleene . Bulletin of Symbolic Logic . 1 . 1 . 8–43 . 10.2307/420945.
  10. Web site: 1985 . STEPHEN C. KLEENE and J. BARKLEY ROSSER . October 12, 2025 . web.math.princeton.edu.
  11. Mac Lane . Saunders . 1998 . STEPHEN COLE KLEENE - Biographical Memoirs . Biographical Memoirs of the National Academy of Sciences . 75.
  12. Web site: S. C. Kleene . February 8, 2021.
  13. http://www.icsu.org/publicdb/frmDisplayMember?docid=97d44bb2b86ba6e145872f68db2d0d62 IUHPS website
  14. Daniel Dennett and Karel Lambert, "kleene", in The Philosophical Lexicon, 7th ed. (Newark, DE: American Philosophical Association, 1978), 5; and Hyperborea (blogger pseudonym), "Dennett's Logocentric Lexicon" (9 December 2007): http://aeconomics.blogspot.com/2007/12/dennetts-logocentric-lexicon.html
  15. Web site: Stephen C. Kleene . October 12, 2025 . National Science and Technology Medals Foundation . en-US.
  16. Web site: LICS – Archive. lics.siglog.org.
  17. Book: Kleene, Stephen Cole. Stephen Cole Kleene. 0. reprint. Ishi Press. 1952. 2009-03-13. 9780923891572.
  18. Bishop. Errett. Errett Bishop . Review: The foundations of intuitionistic mathematics. . 1965 . 71 . 6 . 850–852 . 10.1090/s0002-9904-1965-11412-4 . free.

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