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. An avid mountain climber, he had a strong interest in nature and the
environment, and was active in many
conservation causes. ==Legacy==