STEPHEN COLE KLEENE

January 5, 1909–January 25, 1994

BY SAUNDERS MAC LANE

STEVE KLEENE, A YANKEE from Maine, became a pioneer mathematical logician. His clear, precise ideas developed the modern study of computable functions and of automata. He was also a devoted mountaineer.

Kleene was born in 1909 in Hartford, Connecticut, but his real home was his paternal grandfather's farm in Union, Maine. In 1930 Kleene graduated summa cum laude from Amherst College. He had become fascinated with mathematics, and he went to Princeton University for graduate study in that subject.

At Princeton, the mathematician Oswald Veblen had understood that the development of logic required careful analysis by mathematicians. His student Alonzo Church joined the Princeton faculty and initiated the mathematical and logical study of those functions that are computable.” For this purpose Church devised his so-called lambda calculus, which provided the names for all functions. For example, the notation λ x • (x2 + 1) with the Greek letter lambda names the function that sends each number x to its square plus 1, and likewise with other functions. Church developed this calculus as a new formal foundation for all of mathematics. Kleene and his fellow student Barkley Rosser



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