Kurt Gödel was a twentieth century pre-eminent Austrian mathematician. He was also philosopher and logician as well. After Gottlob Frege and Aristotle, he was one of the foremost logicians in the history. He influenced twentieth century scientific and philosophical school of thoughts. In 1931, he published his incompleteness theorems. He developed a technique which is now called Gödel numbering. He had proven that the continuum hypothesis and the axiom of choice can be disproved. Besides, he helped considerably in the development of the proof theory.
Kurt Friedrich Gödel was born on April 28, 1906, in Brünn, Austria-Hungary to an ethnic German family. His father, Rudolf Gödel, was a Catholic and manager in a textile factory. He had close ties with his Protestant mother and remained in a constant correspondence with her. There is a long list of citizenships that Gödel took up. At the age of 12 he received the Czechoslovak citizenship when the Austro-Hungarian Empire broke up. He always felt excommunicated in Czechoslovak so when he became an adult he chose Austrian citizenship. Subsequently, Germany annexed Austria and in consequence Austrian citizens became German, so did Gödel in 1938. Post World War II, he moved to America where he applied for American citizenship.
Gödel was nicknamed by his family as ‘Mr. Why’ for his ever insatiable curiosity to known the unknown. In his childhood he suffered from rheumatic fever and poor health episodes for the remainder of his life. He received his early education from a Lutheran school in Brünn. He then went to Deutsches Staats-Realgymnasium majoring in religious studies, languages and mathematics. Initially, he was interested in languages and later became taken with mathematics in 1920s. In his adolescence he studied criticisms of Isaac Newton, Immanuel Kant’s work and Theory of Colours by Goethe.
Following his brother’s footsteps Gödel joined the University of Vienna. Theoretical Physics was his initial choice to study as major but later he showed inclination toward philosophy and mathematics. While reading Kant’s Metaphysische Anfangsgründe der Naturwissenschaft, Gödel tried adopting the concept of mathematical realism. He was a participant in the Vienna Circle along with Hans Hahn and Moritz Schlick. His interest in mathematical logic was stimulated by Russell’s Introduction to Mathematical Philosophy which was discussed in a seminar by Moritz. Godel believed that mathematical logic is the foundation of all disciplines of science, comprising all the ideas and principles to support science.
All those seminars and books may have piqued Gödel’s interest but what truly inspired him to dedicate all his life to mathematics was a lecture conducted by David Hilbert in Bologna. He completed his doctoral studies in 1930, which was based on the query whether axioms are sufficient to derive every statement in a formal system. Vienna Academy of Science published his dissertation and other significant researches. Gödel had his incompleteness theorems published in 1931. He became a Privatdozent, now termed as intern, in 1933. The same year he first traveled to United States following the Adolf Hitler’s take over and assassination of a former student of his. He met the genius Albert Einstein in America and befriended each other.
Furthermore, during his stay in America he developed the ideas of computability and recursive functions. He even delivered a lecture on the subject. In Princeton, the Institute for Advanced Study invited him to conduct a series of lectures in 1934 and they were later published. Kurt Gödel married a divorced dancer, an older woman, Adele Nimbursky, after much opposition by his parents.