Kurt Gödel
1906–1978, Brünn, Austria-Hungary (now Brno, Czech Republic), Princeton, New Jersey, United States
Austrian-American logician whose incompleteness theorems showed that no consistent, effectively axiomatized system powerful enough for arithmetic can prove all truths about the numbers, or prove its own consistency.
Kurt Gödel entered the University of Vienna in 1923 and, drawn to the lectures of Philipp Furtwängler and Hans Hahn, turned from physics to mathematical logic. He completed his doctorate under Hahn in 1929 with a proof of the completeness of first-order logic — showing that every logically valid statement in that system has a formal proof.
In 1931 he published his incompleteness theorems, the single most consequential result in twentieth-century logic. The first theorem shows that in any consistent, effectively axiomatized system rich enough to express arithmetic, there are true statements the system cannot prove; the second shows that such a system cannot prove its own consistency. Together they ended a century of attempts, including Hilbert's formalist programme, to place all of mathematics on a single complete and self-justifying axiomatic foundation.
Gödel emigrated to the United States in 1940 and joined the Institute for Advanced Study in Princeton, where he became a close friend of Albert Einstein. In 1940 he proved the relative consistency over ZF of the axiom of choice and the generalized continuum hypothesis, using his constructible universe L — a result Paul Cohen would complete in 1963 by proving the reverse independence. Gödel became a professor at the Institute for Advanced Study in Princeton in 1953 and was professor emeritus from 1976 until his death in 1978.
Workplaces: University of Vienna, Institute for Advanced Study, Princeton
Austria, United States