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Kurt Gödel [ kurˈt gřdl ], ( April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher of mathematics, whose biography lists quite a few nations, although he is usually associated with Austria. He was born in Brünn in Austria-Hungary (now Brno in the Czech Republic) became a Czechoslovak citizen at age 12 when the Austro-Hungarian empire broke up, and an Austrian citizen at age 23. When Hitler annexed Austria, Gödel automatically became a German citizen at age 32. After WWII, then 42 years old, he obtained the US citizenship. He was a deep logician whose most famous work was the incompleteness theorem stating that any self-consistent axiomatic systemIn mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems. An axiomatic system that is powerful enough to describe integer arithmetic will allow for propositions about integers that can neither be proven nor disproven from the axioms. He also produced celebrated work on the Continuum hypothesisIn mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. Georg Cantor introduced the concept of cardinality to compare the sizes of infinite sets, and he showed that the set of integers is strictly smaller than t, showing that it cannot be disproven from the accepted set theorySet theory is the mathematical theory of sets, which represent collections of abstract objects. It has a central role in modern mathematical theory, providing the basic language in which most of mathematics is expressed. For more information on set theory axioms, assuming that those axioms are consistent.
Gödel made important contributions to proof theoryLogic Proof theory Proof theory studied as a branch of mathematical logic, represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures, suc; he clarified the connections between classical logic, intuitionistic logicLogic Logic in computer science Mathematical logic Intuitionistic logic or constructivist logic is the logic used in mathematical intuitionism and other forms of mathematical constructivism. Roughly speaking, "intuitionism" holds that logic and mathematic and
modal logicModal logic, or (less commonly) intensional logic is the branch of logic that deals with sentences that are qualified by modalities such as can could might may must possibly and necessarily and others. Any logical system making use of modal operators, suc by defining translations between them.
Kurt Gödel is arguably the greatest logician of the 20th century19th century 20th century 21st century more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901- 2000 in the sense of the Gre and one of the three greatest logicians of all time, with the other two of this historical triumvirate being Aristotle and Frege. He published his most important result in 1931 at age 25 when he worked at Vienna University, Austria.
1 Short biography
1.1 Childhood
Kurt Gödel was born April 28, 1906, in Brno, Austria-Hungary (now Czech Republic) as the son of Rudolf Gödel, the manager of a textile factory, and Marianne Gödel (née Handschuh). In his German language family little Kurt was known as Der Herr Warum (Mr. Why). He attended German-language primary and secondary school in Brno and completed them with honors in 1923. Although Kurt had first excelled in learning languages he later became more fond of history and mathematics. His interest in mathematics increased when in 1920 his older brother Rudolf (born 1902) left for Vienna to go to Medical School at the University of Vienna (UV). Already during his teens Kurt studied Gabelsberger shorthand, Goethe's theory of colors and criticisms of Isaac Newton, and the writings of Kant.
