- Stephen Cole Kleene
Infobox_Scientist

name = Stephen Kleene

caption =

birth_date = birth date|1909|1|5

birth_place =USA

death_date = death date and age|1994|1|25|1909|1|5

death_place =

residence =USA

nationality =USA

field =Mathematics

work_institutions =University of Wisconsin-Madison

alma_mater =Princeton University

doctoral_advisor =Alonzo Church

doctoral_students = John Addison Jr.

Paul Axt

Douglas Clarke

Robert Constable

David Kierstead

Shih-Chao Liu

Joan MoschovakisYiannis Moschovakis

Nels Nelson

Gene RoseClifford Spector

Richard VesleyDick de Jongh

known_for =

prizes =

religion =

footnotes =**Stephen Cole Kleene**(January 5 ,1909 ,Hartford, Connecticut , USA –January 25 ,1994 ,Madison, Wisconsin ) was an Americanmathematician who helped lay the foundations for theoreticalcomputer science . One of many distinguished students ofAlonzo Church , Kleene, along withAlan Turing ,Emil Post , and others, is best known as a founder of the branch ofmathematical logic known asrecursion theory . Kleene's work grounds the study of which functions are computable. A number of mathematical concepts are named after him:Kleene hierarchy ,Kleene algebra , theKleene star ,Kleene's recursion theorem and theKleene fixpoint theorem . He also inventedregular expressions , and was a leading American advocate ofmathematical intuitionism .Kleene pronounced his last name IPAEng|ˈkleɪni. IPA|/ˈkliːni/ and IPA|/ˈkliːn/ are common mispronunciations.

**Biography**Kleene was awarded the BA degree from

Amherst College in 1930. He was awarded the Ph.D. in mathematics fromPrinceton University in 1934. His thesis, entitled "A Theory of Positive Integers in Formal Logic", was supervised byAlonzo Church . In the 1930s, he did important work on Church'slambda calculus . In 1935, he joined the mathematics department at theUniversity of Wisconsin-Madison , where he spent nearly all of his career. After two years as an instructor, he was appointed assistant professor in 1937.While a visiting scholar at the

Institute for Advanced Study in Princeton, 1939-40, he laid the foundation forrecursion theory , an area that would be his lifelong research interest. In 1941, he returned to Amherst College in 1941, where he spent one year as an associate professor of mathematics.During

World War II , Kleene was a lieutenant commander in theUnited States Navy . He was an instructor of navigation at the U.S. Naval Reserve's Midshipmen's School inNew York , and then a project director at theNaval Research Laboratory inWashington, D.C. In 1946, Kleene returned to

Wisconsin , becoming a full professor in 1948 and the Cyrus C. MacDuffee professor of mathematics in 1964. He was chair of the Department of Mathematics and Computer Science, 1962-63, and Dean of the College of Letters and Science from 1969 to 1974. The latter appointment he took on despite the considerable student unrest of the day, stemming from theVietnam War . He retired from the University of Wisconsin in 1979. The mathematics library at the University of Wisconsin was renamed in his honour.Kleene's teaching at Wisconsin resulted in three texts in

mathematical logic , Kleene (1952, 1967) and Kleene and Vesley (1965), often cited and still in print. Kleene (1952) wrote alternative proofs to theGödel'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 tointuitionist logic and mathematics. Kleene's standing among logicians is suggested by the witticism "Kleeneliness is next to Gödeliness", apun on "Cleanliness is next to godliness".Fact|date=April 2007Kleene served as president of the

Association of Symbolic Logic , 1956-58, and of theInternational Union of the History and the Philosophy of Science , 1961. In 1990, he was awarded theNational Medal of Science .Kleene and his spouse Nancy Elliott had four children. He had a lifelong devotion to the family farm in Maine. An avid mountain climber and

canoe ist, he had a strong interest innature and the environment and was active in many conservation causes.**Important publications***1952. " [

*http://worldcat.org/oclc/523942 Introduction to Metamathematics.*] " North-Holland (originally published by D. Van Nostrand).

*1956. "Representation of Events in Nerve Nets and Finite Automata" in [*http://worldcat.org/oclc/564148 Automata Studies*] ".Claude Shannon andJohn McCarthy , eds.

*1965 (with Richard Eugene Vesley). "The Foundations of Intuitionistic Mathematics". North-Holland.

*1967. " [*http://worldcat.org/oclc/523472 Mathematical Logic.*] " John Wiley. Dover reprint, 2001. ISBN 0486425339.

*1981. "Origins of Recursive Function Theory" in " [*http://worldcat.org/oclc/4583089 Annals of the History of Computing 3,*] " No. 1.**See also***

Kleene closure (or Kleene star)

*Kleene hierarchy

*Kleene's s-m-n Theorem

*Realizability

*Intuitionism

*Kleene-Rosser paradox **References***

**External links***

*

* [*http://www.nap.edu/html/biomems/skleene.html Biographical memoir*] – bySaunders Mac Lane

* [*http://math.library.wisc.edu/bibliography.html Kleene bibliography.*]

* [*http://infoshare1.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/pmc23.htm Interview*] with Kleene andJohn Barkley Rosser about their experiences at Princeton

*Wikimedia Foundation.
2010.*

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**Stephen Cole Kleene**— Kleene en 1978 Stephen Cole Kleene – né le 5 janvier 1909 à Hartford (Connecticut) et mort le 25 janvier 1994 à Madison (Wisconsin) – est un mathématicien et logicien américain. Biographie et contribution scientifique Klee … Wikipédia en Français**Stephen Cole Kleene**— (* 5. Januar 1909 in Hartford, Connecticut; † 25. Januar 1994 in Madison, Wisconsin) war ein US amerikanischer Mathematiker und Logiker. Er gilt als einer der Begründer der theoretischen Informatik, besonders der formalen Sprachen und der… … Deutsch Wikipedia**Kleene, Stephen Cole**— ▪ American mathematician born Jan. 5, 1909, Hartford, Conn., U.S. died Jan. 25, 1994, Madison, Wis. American mathematician and logician whose work on recursion theory helped lay the foundations of theoretical computer science. Kleene… … Universalium**Stephen Kleene**— Stephen Cole Kleene (* 5. Januar 1909 in Hartford, Connecticut, USA; † 25. Januar 1994 in Madison, Wisconsin) war ein US amerikanischer Mathematiker und Logiker. Er gilt als einer der Begründer der theoretischen Informatik, besonders der formalen … Deutsch Wikipedia**Kleene**— Stephen Cole Kleene (* 5. Januar 1909 in Hartford, Connecticut, USA; † 25. Januar 1994 in Madison, Wisconsin) war ein US amerikanischer Mathematiker und Logiker. Er gilt als einer der Begründer der theoretischen Informatik, besonders der formalen … Deutsch Wikipedia**Kleene**— Stephen Cole Kleene Stephen Cole Kleene (né le 5 janvier 1909 à Hartford, mort le 25 janvier 1994) est un mathématicien et logicien américain. Biographie et contribution scientifique Kleene est connu pour avoir fondé la branche de la logique… … Wikipédia en Français**Kleene's T predicate**— In computability theory, the T predicate, first studied by mathematician Stephen Cole Kleene, is a particular set of triples of natural numbers that is used to represent computable functions within formal theories of arithmetic. Informally, the T … Wikipedia**Kleene'sche Hülle**— Die Kleenesche Hülle (auch endlicher Abschluss, Kleene * Abschluss oder Verkettungshülle genannt) eines Alphabets Σ oder einer formalen Sprache L ist die Menge aller Wörter, die durch beliebige Konkatenation (Verknüpfung) von Symbolen des… … Deutsch Wikipedia**Kleene-Abschluss**— Die Kleenesche Hülle (auch endlicher Abschluss, Kleene * Abschluss oder Verkettungshülle genannt) eines Alphabets Σ oder einer formalen Sprache L ist die Menge aller Wörter, die durch beliebige Konkatenation (Verknüpfung) von Symbolen des… … Deutsch Wikipedia**Kleene-Stern**— Die Kleenesche Hülle (auch endlicher Abschluss, Kleene * Abschluss oder Verkettungshülle genannt) eines Alphabets Σ oder einer formalen Sprache L ist die Menge aller Wörter, die durch beliebige Konkatenation (Verknüpfung) von Symbolen des… … Deutsch Wikipedia