American mathematician and logician whose work on recursion theory helped lay the foundations of theoretical computer science.

Kleene was educated at Amherst College (A.B., 1930) and earned a Ph.D. in mathematics at Princeton University in 1934. After teaching briefly at Princeton, he joined the University of Wisconsin at Madison as an instructor in 1935 and became a full professor there in 1948. He retired in 1979.

Kleene's research was devoted to the theory of algorithms and recursive functions (i.e., functions defined in a finite sequence of combinatorial steps). Kleene, together with Alonzo Church, Kurt Gödel, Alan Turing, and others, developed the field of recursion theory, which made it possible to prove whether certain classes of mathematical problems are solvable or unsolvable. Recursion theory in turn led to the theory of computable functions, which governs those functions that can be calculated by a digital computer. Kleene was the author of Introduction to Metamathematics (1952) and Mathematical Logic (1967).