**Stephen Cole Kleene** (/ˈkleɪni/ *KLAY-nee*;^{[a]} January 5, 1909 – January 25, 1994) was an American mathematician. 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. He also invented regular expressions in 1951 to describe McCulloch-Pitts neural networks, and made significant contributions to the foundations of 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,^{[5]} 1961. The importance of Kleene's work led to Daniel Clement Dennett coining the saying, published in 1978, that "Kleeneness is next to Gödelness."^{[6]} 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.

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.^{[7]}

- 1935. Stephen Cole Kleene (Jan 1935). "A Theory of Positive Integers in Formal Logic. Part I".
*American Journal of Mathematics*.**57**(1): 153–173. doi:10.2307/2372027. JSTOR 2372027.