NationMaster - Encyclopedia: Stephen Cole Kleene

Stephen Cole Kleene (January 5, 1909 – January 25, 1994) was an American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for theoretical computer science. Kleene was best known for founding the branch of mathematical logic known as recursion theory together with Alonzo Church, Kurt Gödel, Alan Turing , Emil Post, and others; and for inventing regular expressions. By providing methods of determining which problems are solvable, Kleene's work led to the study of which functions are computable. Among other things, Kleene algebra, the Kleene star, Kleene's recursion theorem and the Kleene fixpoint theorem are named after him. He also contributed to mathematical intuitionism as founded by Luitzen Egbertus Jan Brouwer. January 5 is the 5th day of the year in the Gregorian calendar. ... 1909 (MCMIX) was a common year starting on Friday (see link for calendar). ... January 25 is the 25th day of the year in the Gregorian calendar. ... 1994 (MCMXCIV) was a common year starting on Saturday of the Gregorian calendar, and was designated as the International Year of the Family and the International Year of the Sport and the Olympic Ideal by United Nations. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The University of Wisconsinâ€“Madison is a public research university located in Madison, Wisconsin. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Recursion theory, or computability theory, is a branch of mathematical logic dealing with generalizations of the notion of computable function, and with related notions such as Turing degrees and effective descriptive set theory. ... Alonzo Church (June 14, 1903 â€“ August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science. ... Kurt GÃ¶del Kurt GÃ¶del (IPA: ) (April 28, 1906 Brno, then Austria-Hungary, now Czech Republic â€“ January 14, 1978 Princeton, New Jersey) was a logician, mathematician, and philosopher of mathematics. ... Alan Turing is often considered the father of modern computer science. ... Emil Leon Post (February 11, 1897 - April 21, 1954) was a Polish-American mathematician and logician. ... A regular expression (abbreviated as regexp, regex or regxp) is a string that describes or matches a set of strings, according to certain syntax rules. ... It has been suggested that recursive function be merged into this article or section. ... In mathematics, a Kleene algebra (named after Stephen Cole Kleene, pronounced clay-knee) is either of two different things: A bounded distributive lattice with an involution satisfying De Morgans laws, and the inequality x∧−x ≤ y∨−y. ... In mathematical logic and computer science, the Kleene star (or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. ... In computability theory Kleenes recursion theorem, first proved by Stephen Kleene in 1938, is a fundamental result about the application of computable functions to their own descriptions. ... In mathematics, the Kleene fixpoint theorem in order theory states that given any complete lattice L, and a monotone function then the least fixed point (lfp) of F is where is the bottom element of . ... In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach to mathematics as the constructive mental activity of humans. ... Luitzen Egbertus Jan Brouwer (February 27, 1881 - December 2, 1966), usually cited as L. E. J. Brouwer, was a Dutch mathematician, a graduate of the University of Amsterdam, who worked in topology, set theory, measure theory and complex analysis. ...

Kleene pronounced his last name ['klej.ni] (IPA). ['kli.ni] and [klin] are extremely common mispronunciations. This is a concise version of the International Phonetic Alphabet for English sounds. ...

Kleene's standing in mathematical logic is reflected in the proverb "Kleeneliness is next to Gödeliness" among logicians (a pun on "Cleanliness is next to godliness"). To meet Wikipedias quality standards, this article or section may require cleanup. ... Look up proverb in Wiktionary, the free dictionary. ... Kurt GÃ¶del Kurt GÃ¶del [kurt gÃ¸Ëdl], (April 28, 1906 â€“ January 14, 1978) was a logician, mathematician, and philosopher of mathematics. ... It has been suggested that dajare be merged into this article or section. ... Cleanliness is the absence of dirt, including dust, stains and bad smells. ...

Biography

Kleene was born in Hartford, Connecticut, USA. He received his bachelor of arts degree from Amherst College in 1930. From 1930 to 1935, he was a graduate student and research assistant at Princeton University, where he received his doctorate in mathematics in 1934, supervised by Alonzo Church, for a thesis entitled A Theory of Positive Integers in Formal Logic. In 1935, he joined the UW-Madison mathematics department as an instructor. He became an assistant professor in 1937. This article or section does not cite its references or sources. ... It has been suggested that this article be split into multiple articles. ... Amherst College is an elite independent liberal arts college in Amherst, Massachusetts, USA. It is the third oldest college in Massachusetts. ... 1930 (MCMXXX) was a common year starting on Wednesday (link is to a full 1930 calendar). ... 1935 (MCMXXXV) was a common year starting on Tuesday (link will take you to calendar). ... Princeton University is a coeducational private university located in Princeton, New Jersey in the United States of America. ... 1934 (MCMXXXIV) was a common year starting on Monday (link will take you to calendar). ... Alonzo Church (June 14, 1903 â€“ August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science. ... 1937 (MCMXXXVII) was a common year starting on Friday (link will take you to calendar). ...

From 1939 to 1940, he was a visiting scholar at Princeton's Institute for Advanced Study, where he laid the foundation for recursion theory, an area that would be his lifelong research interest. In 1941 he returned to Amherst as an associate professor of mathematics. 1939 (MCMXXXIX) was a common year starting on Sunday (link will take you to calendar). ... Year 1940 (MCMXL) was a leap year starting on Monday (the link is to a full 1940 calendar). ... Fuld Hall The Institute for Advanced Study is a private institution in Princeton Township, New Jersey, U.S.A. (although it is not part of Princeton University), designed to foster pure cutting-edge research by scientists in a variety of fields without the complications of teaching or funding, or the... Recursion theory, or computability theory, is a branch of mathematical logic dealing with generalizations of the notion of computable function, and with related notions such as Turing degrees and effective descriptive set theory. ... This article is about the year. ...

During World War II, Kleene was a lieutenant commander in the United States Navy. He was an instructor of navigation at the U.S. Naval Reserve's Midshipmen's School in New York, and then a project director at the Naval Research Laboratory in Washington, D.C. Combatants Major Allied powers: United Kingdom Soviet Union United States Republic of China and others Major Axis powers: Nazi Germany Italy Japan and others Commanders Winston Churchill Joseph Stalin Franklin Roosevelt Harry Truman Chiang Kai-Shek Adolf Hitler Benito Mussolini Hideki Tojo Casualties Military dead: 17,000,000 Civilian dead... USN redirects here. ... Official language(s) English de facto Capital Albany Largest city New York City Area Ranked 27th - Total 54,520 sq mi (141,205 kmÂ²) - Width 285 miles (455 km) - Length 330 miles (530 km) - % water 13. ... Nickname: DC, The District Motto: Justitia Omnibus (Justice for All) Location of Washington, D.C., in relation to the states Maryland and Virginia. ...

In 1946, he returned to Wisconsin, becoming a full professor in 1948. He was chair of mathematics and computer sciences in 1962 and 1963, and dean of the College of Letters and Science from 1969 to 1974. In 1964 he was named the Cyrus C. MacDuffee professor of mathematics. He retired in 1979. 1946 (MCMXLVI) was a common year starting on Tuesday. ... Official language(s) None Capital Madison Largest city Milwaukee Area Ranked 23rd - Total 65,498 sq mi (169,790 kmÂ²) - Width 260 miles (420 km) - Length 310 miles (500 km) - % water 17 - Latitude 42Â°30N to 47Â°3N - Longitude 86Â°49W to 92Â°54W Population Ranked... To meet Wikipedias quality standards, this article or section may require cleanup. ... 1962 (MCMLXII) was a common year starting on Monday (the link is to a full 1962 calendar). ... 1963 (MCMLXIII) was a common year starting on Tuesday (the link is to a full 1963 calendar). ... 1969 (MCMLXIX) was a common year starting on Wednesday (the link is to a full 1969 calendar). ... 1974 (MCMLXXIV) was a common year starting on Tuesday. ... 1964 (MCMLXIV) was a leap year starting on Wednesday (the link is to a full 1964 calendar). ... This page refers to the year 1979. ...

An avid mountain climber, Kleene had a strong interest in nature and the environment and was active in many conservation causes. He led several professional organisations, serving as president of the Association of Symbolic Logic from 1956 to 1958. In 1961, he served as president of the International Union of the History and the Philosophy of Science. He died in Madison, Wisconsin. Galunggung in 1982, showing a combination of natural events. ... The conservation movement is a political and social movement that seeks to protect natural resources including plant and animal species as well as their habitat for the future. ... 1956 (MCMLVI) was a leap year starting on Sunday of the Gregorian calendar. ... 1958 (MCMLVIII) was a common year starting on Wednesday of the Gregorian calendar. ... 1961 (MCMLXI) was a common year starting on Sunday (the link is to a full 1961 calendar). ... Nickname: Mad Town or Mad City Location of Madison in Dane County, Wisconsin Municipality City Incorporated 1848 Mayor Dave Cieslewicz Area - City 136. ...

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Biography

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Important publications

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Biography