Gödel, Kurt (1906-1978), an Austrian-born American mathematician, proved a famous rule of mathematics. That rule was published in 1931, and it is now known as Gödel’s theorem. According to the theorem, within any formal logical system are results that can be neither proved nor disproved. Such results are said to be undecidable. A consequence of the theorem is that any logically defined system, even one as familiar as arithmetic, might give rise to contradictory results.
Gödel was born on April 28, 1906, in Brunn, Austria-Hungary (now Brno, Czech Republic). He studied and taught at the University of Vienna, Austria, before moving to the United States in 1940. He became a U.S. citizen in 1948. Gödel worked at the Institute for Advanced Study in Princeton, New Jersey, where he was a professor from 1953. In 1974, he received the U.S. National Medal of Science, the nation’s highest science award. He died in Princeton on Jan. 14, 1978.
Gödel’s work in mathematical logic examined attempts that had been made to show that all mathematics could be based on a set of axioms (fundamental statements assumed to be true) and strictly logical reasoning. An important work in this area had been Principia Mathematica (1910-1913), written by the British philosophers and mathematicians Bertrand Russell and Alfred North Whitehead. Gödel’s proof of undecidability put an end to those attempts. Gödel’s theorem has had a major influence on modern mathematics.
See also Axiom; Mathematics (Philosophies of mathematics.).
