Stephen Cole Kleene

Stephen Cole Kleene (/ˈkleɪni/ KLAY-nee;[a] January 5, 1909 – January 25, 1994) was an American mathematician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science. Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented regular expressions in 1951 to describe McCulloch-Pitts neural networks, and made significant contributions to the foundations of mathematical intuitionism. 

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 [link] (1967). 


(Bubliotheca Mathematica) Stephen Cole Kleene-Introduction to Metamathematics-Wolters-Noordhoff Publishing (1971).pdf