Kurt Gö²del (Gedel Kurt)( Austrian mathematician.)
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Biography Kurt Gö²del (Gedel Kurt)
Born April 28, 1906 in Brno. In 1924 entered the University of Vienna, in 1930 a doctorate in mathematics. In 1933-1938 - assistant professor, University of Vienna, in 1940 he emigrated to the U.S.. From 1953 until the end of life - a professor at Princeton Institute for Advanced Studies.
Gö²del's thesis was devoted to the problem of completeness. In the 1930's were some results on the completeness of various axiomatic systems. For example, Gilbert is an artificial system, which covers part of arithmetic, proved its completeness and consistency. Gö²del in his dissertation proved the completeness of predicate calculus of the first stage, and this gave hope to mathematicians that they will be able to prove the consistency and completeness of all mathematics. However, in 1931 the same Godel proved a theorem about incompleteness, dealt a crushing blow to those hopes. According to this theorem, any procedure of proof of true statements of elementary number theory is doomed to incompleteness. Consequently, the internal consistency of any mathematical theory can not be proved otherwise than by reaching out to another theory, using stronger assumptions, and therefore less reliable.
The methods used in the proof of Gö²del's incompleteness theorems have played a further role in the theory of computing machines.
Gö²del made an important contribution to the theory of sets. Two principle - the axiom of choice and the continuum hypothesis - for decades, did not respond to the proof, but interest has not waned: too attractive were their logical consequences. Godel proved (1938) that adherence to these principles to the usual axioms of set theory does not lead to a contradiction.
Gö²del died in Princeton on Jan. 14, 1978.