Stephen Cole Kleene

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. 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.

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. Gustav's parents were immigrants from Germany.

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. In the 1930s, he did important work on Church's lambda calculus. 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.

He was a visiting scholar at the Institute for Advanced Study in Princeton in 1939–1940. 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.

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.

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, 1961. The importance of Kleene's work led to Daniel Dennett coining the saying, published in 1978, that "Kleeneness is next to Gödelness." In 1990, he was awarded the National Medal of Science.

Kleene and his wife Nancy Elliott had four children. He had a lifelong devotion to the family farm in Maine.

Selected publications