Kurt Godel

Kurt Godel was an Austrian-American logician and mathematician best known for his incompleteness theorems, published in 1931, which proved fundamental limits on what any sufficiently powerful formal mathematical system can achieve. His first incompleteness theorem showed that in any consistent formal system capable of expressing basic arithmetic, there will always exist true statements that cannot be proved within that system, and his second theorem showed that such a system cannot prove its own consistency from within itself. These results resolved, in a largely negative direction, a major open question in the foundations of mathematics concerning whether a complete and self-verifying formal system could ever be constructed. Godel emigrated from Austria to the United States in 1940 and spent the remainder of his career at the Institute for Advanced Study in Princeton, where he became a close friend of Albert Einstein and also made significant contributions to mathematical logic, set theory and the philosophy of mathematics.