Mathematician Kurt Gödel made his fame in 1931 with the publication of his Incompleteness Theorem, also known as Gödel's Theorem. Written while Gödel was a young faculty member at the University of Vienna, his paper demonstrated that any axiomatic system of arithmetic would have true but unprovable statements -- and that any formal system would therefore always be incomplete. This stomped all over the then-prevailing idea that the totality of mathematics could be neatly ordered with the correct set of axioms, or self-evident truths. Gödel's influence was also felt in science and in philosophy, which at the time was dominated by works such as Bertrand Russell and Alfred North Whitehead's Principia Mathematica (1913). Gödel left Austria and ended up joining the Institute for Advanced Study at Princeton University in 1940. There he spent time with his friend Albert Einstein and continued to work on number theory and on revisions of his classic work Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory. Gödel's work on recursive functions puts him in the company of Alan Turing as an influential figure in the history of computer science.
Gödel was a sensitive and fastidious man, and later in life he became so concerned with germs and food poisoning that he gave up eating and starved to death.
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