Kurt Gödel: A godfather of computer science

Abstract

We argue that Kurt Gödel exercised a major influence on computer science. Although not immediately involved in building computers, he was a pioneer in defining central concepts of computer theory. Gödel was the first to show how the precision of the formal language systems of Frege, Peano and Russell could be put to work to prove important facts about those language systems themselves, with important consequences for mathematics. As Hilbert’s collaborator, Paul Bernays put it, in his famous Incompleteness Proof Gödel did the “homework” that the people in Göttingen working on Hilbert’s Program to prove the consistency of mathematics missed. (Hilbert’s Metamathematics assumed that all mathematical proofs could be treated as coding problems, and enciphering is applied arithmetic.) The core of Gödel’s Proof also gave exact definitions of the central concept of arithmetic, namely of the recursion involved in mathematical induction (with help from the great French logician Jacques Herbrand). This immediately led to whirlwind developments in Göttingen, Cambridge and Princeton, the working headquarters of major researchers: Paul Bernays and John von Neumann; Alan Turing; and Alonzo Church, respectively. Turing’s and von Neumann’s ideas on computer architecture can be traced to Gödel’s Proof. Especially interesting is the fact that Church and his lambda calculus was the main influence on John McCarthy’s LISP, which became the major language of Artificial Intelligence.