Stephen Cole Kleene

Stephen Cole Kleene ( born January 5, 1909 in Hartford, Connecticut; † January 25, 1994 in Madison, Wisconsin ) was an American mathematician and logician. He is considered one of the founders of theoretical computer science, especially the formal languages ​​and automata theory (see, for example, Kleene shell, lambda calculus, fixed point theorem of Kleene regular expression ).

Kleene grew up on the farm of his grandfather in Maine (which he also later) and studied at Amherst College ( completion 1930 " summa cum laude "). In 1934 he received his doctorate at Princeton University in Alonzo Church with " A Theory of Positive Integers in Formal Logic ." After a brief teaching career at Princeton, he went in 1934 to the University of Wisconsin in Madison, where he became assistant professor in 1937 and professor in 1948 and remained until his retirement in 1979. 1942 to 1946 he was an officer in the U.S. Navy.

Kleene was like his teacher Church to the development of the theory of recursive functions, which were formalized by Church in his lambda calculus (later used in the Lisp programming language ). Kleene examined in his dissertation in particular Church's assertion that his lambda calculus provides all " computable " functions, where he examined more general recursive functions for which he showed a normal form theorem. He found several stages of computation such as in partial recursive functions. He also introduced a " arithmetical hierarchy " and a " hyperarithmetische hierarchy " for predicates. In 1954, he wrote a work on degrees of unsolvability of mathematical problems with Emil Post.

Since staying at the Rand Corporation, 1951, he was also interested in machines and there wrote an influential report in which he combined ideas of John von Neumann on computing machines with those of neural networks of McCulloch and Pitts (1949 ).

Kleene in the U.S. was also a leader of intuitionistic mathematics, which grew out of ideas Brouwer. In 1950 he spent as a Guggenheim Fellow at Amsterdam in Brouwer and his students to study his ideas. Kleene wrote two widely used textbooks on mathematical logic and meta-mathematics, in which he was also a clear formulation of Gödel's theorem.

In 1983 he received the Leroy P. Steele Prize. In 1969 he became a member of the National Academy of Sciences. In 1990 he received the National Medal of Science. In 1958 he gave a plenary lecture at the International Congress of Mathematicians in Edinburgh ( Mathematical Logic: Constructive and non- constructive operations) and 1950 he was Invited Speaker on the ICM in Cambridge (Massachusetts ) ( Recursive functions and intuitionistic mathematics ).

Kleene was an experienced climber. He was married twice and had from his first marriage (from 1942) four children.

Writings

• Introduction to Metamathematics, North Holland, Amsterdam, 1952
• Mathematical logic, Wiley, New York, 1967
• With R.Vesley The Foundations of Intuitionistic Mathematics - Especially in Relation to Recursive Functions, North Holland 1965
• Kleene recursive functions of natural numbers General, Mathematische Annalen, Bd.112, 1936, S.727 -742