Kurt Godel
| Kurt Gödel | |
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| Born | Kurt Friedrich Gödel April 28, 1906 Brünn, Austria-Hungary (now Brno, Czech Republic) |
| Died | January 14, 1978 (aged 71) Princeton, New Jersey, U.S. |
| Citizenship | Austria, United States |
| Fields | Mathematics, Mathematical logic |
| Institutions | Institute for Advanced Study |
| Alma mater | University of Vienna |
| Thesis | Über die Vollständigkeit des Logikkalküls (On the Completeness of the Calculus of Logic) (1929) |
| Doctoral advisor | Hans Hahn |
| Known for | Gödel's incompleteness theorems, Gödel's completeness theorem, the consistency of the Continuum hypothesis with ZFC, Gödel metric, Gödel's ontological proof, Gödel–Dummett logic |
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Kurt Friedrich Gödel (/ˈkɜːrt ˈɡɜːrdəl/;German: [ˈkʊɐ̯t ˈɡøːdl̩]; April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell,A. N. Whitehead, and David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor.
Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
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