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Stephen Cole Kleene

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5 Jan 1909

Hartford, Connecticut, USA

25 Jan 1994

Madison, Wisconsin, USA

Stephen C Kleene studied for his first degree at Amherst College. He went on to receive a doctorate from Princeton University in 1934, supervised by Church , for a thesis entitled A Theory of Positive Integers in Formal Logic. Then Kleene taught at Princeton until he joined the University of Wisconsin at Madison in 1935. He became a full professor at the University of Wisconsin at Madison in 1948 and remained on the staff there until he retired in 1979.

Kleene's research was on the theory of algorithms and recursive functions. He developed the field of recursion theory with Church , Gödel , Turing and others. He contributed to mathematical Intuitionism which had been founded by Brouwer .

His work on recursion theory helped to provide the foundations of theoretical computer science. By providing methods of determining which problems are soluble, Kleene's work led to the study of which functions can be computed.

At a lecture in the University of Chicago in 1995, Robert Soare described his work in these terms:

Kleene's formulation of computable function via six schemata is one of the most succinct and useful, and his previous work on lambda functions played a major role in supporting Church 's Thesis that these classes coincide with the intuitively calculable functions.

From 1930's on Kleene more than any other mathematician developed the notions of computability and effective process in all their forms both abstract and concrete, both mathematical and philosophical. He tended to lay the foundations for an area and then move on to the next, as each successive one blossomed into a major research area in his wake.

Kleene developed a diverse array of topics in computability: the arithmetical hierarchy, degrees of computability, computable ordinals and hyperarithmetic theory, finite automata and regular sets with enormous consequences for computer science, computability on higher types, recursive realizability for intuitionistic arithmetic with consequences for philosphy and for program correctness in computer science.

Kleene's best known books are Introduction to Metamathematics (1952) and Mathematical Logic (1967).

Source:School of Mathematics and Statistics University of St Andrews, Scotland