Stephen Cole Kleene (1909-1994) was a mathematician who greatly helped to advance the study of finite automata, which would eventually grow into the logical underpining of computer science. He was one of the founding fathers of recursion theory along with Alonzo Church, Kurt Gödel, and Alan Turing.

Stephen Kleene was born in Hartford, Connecticut, in 1909. He was the son of poet Alice Lena Cole and economics professor Gustav Kleene. He attended Amherst College and went on to receive his Ph.D. from Princeton while working under famed logician Alonzo Church. His doctoral thesis, entitled A Theory of Positive Integers in Formal Logic, helped lay some of the groundwork of the study of finite automata.

Kleene went on to the University of Wisconsin in 1935, where he remained until 1979, except for several leaves. Among those leaves included stays at the Institute for Advanced Study at Princeton and an extended leave during World War II, where he helped to teach navigation at the Naval Reserve's school for midshipmen and service as the directo of the Naval Research Laboratory.

During his time at Wisconsin, Kleene made significant contributions to the theory of recursive functions, investigated questions of computability and decidability, and proved one of the central results of automata theory, known today as the Kleene closure. In it, he mathematically proved that provided any set as an alphabet, there is a definable closure for that set in terms of words.

Kleene also was responsible for the idea of a regular expression, the notation of which he introduced in a 1956 paper. He went on to prove that the languages specified by regular expressions and the languages generated by finite automata constituted the same class, and thus that any regular expression has a matching automata and vice versa. This basic idea is today known as Kleene's Theorem.

Kleene, throughout the 1960s and 1970s, served as the acting director of the Mathematics Research Center and as Dean of the College of Letters and Sciences at the University of Wisconsin. This didn't take away from his active research, as he published a well-known logic text called Mathematical Logic in 1967 and continued to publish papers right up until his retirement.

Besides his mathematical research, Kleene was also an avid follower of natural history. He thoroughly enjoyed nature and was an active hiker and climber. In the mid-1950's, he discovered a previously undescribed variety of butterfly, which is today named after him, the Kleene butterfly. He also was a noted teller of anecdotes, with a powerful, booming voice.

Kleene passed away in 1994, leaving behind a legacy that helped to shape modern logic, finite automata theory, set theory, and computer science.

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