Stephen Cole Kleene was an American mathematician. One of many distinguished students of Alonzo Church, Kleene, along with 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 which functions are computable. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star, Kleene's recursion theorem and the Kleene fixpoint theorem. He also invented regular expressions, and made significant contributions to the foundations of mathematical intuitionism.
Kleene pronounced his last name KLAY-nee. Commonplace mispronunciations include and.