Date of Birth: 04/28/1906
Place of birth: Bruno
Born April 28, 1906 in Brno. In 1924 he 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 United States. From 1953 to the end of life - a professor at Princeton Institute for Advanced Study. Godel died in Princeton January 14, 1978.
Dissertation Godel was devoted to the problem of completeness. Completeness of the system of axioms which are the basis of any field of mathematics, is the adequacy of the axioms of the area that with their help is given, ie, It is an opportunity to prove the truth or falsity of any meaningful statements containing concepts considered mathematics. The 1930s were obtained some results on the completeness of the various axiomatic systems. So, Gilbert has built an artificial system that covers a part of arithmetic, and proved its completeness and consistency. Godel in his thesis proved the completeness of the predicate calculus of the first stage, and it gave mathematicians hope that they will be able to prove the consistency and completeness of the whole of mathematics. However, in 1931 the same Godel proved the incompleteness theorem, which inflicted a crushing blow to these hopes. According to this theorem, any procedure for evidence of true statements elementary number theory is doomed to incompleteness. The elementary theory of numbers - a branch of mathematics dealing with the addition and multiplication of integers, and, as shown by Godel, in any meaningful and practically applicable systems, some evidence of the truth, even in a modest area of ??mathematics will remain unprovable. As a consequence, he found that the internal consistency of any mathematical theory can not be proved otherwise than by referring to another theory, using stronger assumptions, and therefore less reliable.
The methods used in the proof of Godel`s incompleteness theorem, later played an important role in the theory of computing machines.
Godel made an important contribution to the theory of sets. The two principles - the axiom of choice and the continuum hypothesis - for decades, did not respond to the proof, but the interest has not abated: they were the logical consequences of too attractive. Godel proved (1938) that the accession of these principles to the usual axioms of set theory does not lead to a contradiction. His reasoning is valuable not only the results that they provide; Godel developed a design that improves the understanding of the internal mechanisms of set theory itself.