Textbook of AI

1906–1978, Logician, mathematician

Also known as: Kurt Friedrich Gödel

Kurt Gödel was an Austrian-born logician whose 1931 paper Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I proved the incompleteness theorems: any consistent formal system rich enough to express elementary arithmetic must contain true statements it cannot prove (first incompleteness theorem), and such a system cannot prove its own consistency (second incompleteness theorem). The result demolished David Hilbert's programme of providing complete and provably consistent foundations for mathematics, and it remains the most celebrated theorem in mathematical logic.

Gödel's technique, Gödel numbering, in which formulas of a formal system are encoded as natural numbers so that statements about the system can be expressed inside the system itself, anticipated the universal-machine constructions of Turing and Church and is the conceptual ancestor of every interpreter, every reflection mechanism, and every self-reference in computer science.

He emigrated to the Institute for Advanced Study in Princeton in 1940, becoming a close friend of Albert Einstein. Later work included his 1938 proof of the consistency of the axiom of choice and the generalised continuum hypothesis with the rest of Zermelo–Fraenkel set theory, and his 1949 rotating-universe solution to Einstein's field equations.

In his final years he developed an obsessive fear of being poisoned and would only eat food prepared by his wife Adele. When she was hospitalised in late 1977 he stopped eating altogether and died of starvation in January 1978, weighing 29 kilograms.