What is Kurt Gödel?
[[File:1925 kurt gödel.png|right|thumb|Kurt Gödel]] '''Kurt Gödel''' (28 April 1906 [[Brno]], then [[Austria-Hungary]], now [[Czech Republic]] – 14 January 1978 [[Princeton, New Jersey]]) was a [[logician]], [[mathematician]], and [[philosopher]]. == Impact == Some people believe Gödel was one of the most significant logicians of all time. Gödel's work has had a big impact on scientific and philosophical thinking in the [[20th century]]. Many people, such as [[Bertrand Russell]], [[Alfred North Whitehead|A. N. Whitehead]], and [[David Hilbert]], tried to use [[logic]] and [[set theory]] at that time. They wanted to understand the foundations of [[mathematics]]. == Fame == Gödel is best known for his two [[Gödel's incompleteness theorems|incompleteness theorems]]. The theorems were published in 1931. He was 25 years of age, and had just finished his doctorate at the [[University of Vienna]] one year earlier. The more famous of the two theorems says that if there are consistent [[axiom]]atic systems that are powerful enough to describe themselves, there will be things that are true in those systems that can not be proved within the system itself. <!-- The more famous incompleteness theorem says that for any self-consistent [[Recursive set|recursive]] [[axiomatic system]] powerful enough to describe the arithmetic of the [[natural number]]s ([[Peano arithmetic]]), there are true propositions about the naturals that cannot be proved from the axioms. --> == Proof == To prove this theorem, Gödel developed a technique now known as [[Gödel number]]ing, which codes formal expressions as natural numbers. He also showed that the [[continuum hypothesis]] cannot be disproved from the accepted [[axiomatic set theory|axioms of set theory]], if those axioms are consistent. He made important contributions to [[proof theory]]. He did this by clarifying the connections between [[classical logic]], [[intuitionistic logic]], and [[modal logic]]. == Later life == Later in his life, Gödel probably suffered from [[paranoia]].