Gödel, Kurt (1906–1978)

Kurt Gödel was a mathematical logician who is best known for his incompleteness theorem. He also developed a theory of time travel based on Einstein's theory of relativity.

Gödel was born on April 28, 1906, in Brunn, Austria (now known as Brno, Czech Republic), and was baptized as a Lutheran. He began studying physics at the University of Vienna in 1924, but in 1926 he switched to mathematics, in which he excelled. Eventually he settled into the field of mathematical logic, which originated in the work of Gottlob Frege and was more fully developed by David Hubert, Bertrand Russell, and Alfred North Whitehead.

In 1926, Gödel began participating in the Vienna Circle, a group of mathematicians and philosophers headed by Moritz Schlick. The group's members devoted themselves to propagating logical positivism, the philosophy that all that can be known about nature or reality must be deduced from immediate sensory experience. In spite of his participation, Gödel, like Albert Einstein, would become a lifelong opponent of positivism, arguing that intuition has a proper role to play in science and mathematics. Both he and Einstein rejected the Kantian notion that one can know only the appearances of things and not the things themselves. Because of Gödel's preference for the idealistic philosophies of Plato and Husserl, the philosophical establishment, dominated by the philosophy of Wittgenstein, either ignored or scorned much of his philosophical work.

In 1930, Gödel obtained his Ph.D. In 1931, Gödel published a response to David Hubert's formalist attempt to develop a system of first principles (or axioms) from which one could apply rules of syntax to derive all the theorems of a mathematical domain. He undermined Hubert's program by showing that no set of formalist axioms can ever fully capture the complete set of mathematical truths. There will always be some truths about integers, grasped intuitively, that cannot be proved true or false by any fixed set of axioms. He also showed that a system of axioms for arithmetic could not prove its own consistency. His incompleteness theorem (also known as Gödel's proof) ranks with Einstein's theory of relativity and Heisenberg's uncertainty principle as one of the three most revolutionary scientific findings in the 20th century. The recursive functions that he developed as part of this work were later used by Alan Turing and others in the development of the computer.

from 1933 to 1938, he alternated teaching stints between the University of Vienna and the Institute for Advanced Study (IAS) in Princeton, New Jersey. In 1938, he married Adele Porkert, a divorced nightclub performer. They had no children. After being declared fit for German military service, he and his wife emigrated to America in the winter of 1939–1940 by way of Siberia, Japan, and San Francisco, arriving in March at Princeton where he became a temporary member of the IAS. This status was renewed annually until he became a permanent member in 1946. In 1948, he became a citizen of the United States.

Gödel and Einstein became close friends in 1942 and remained so until Einstein's death in 1955. They joined each other in daily half-hour walks to and from the institute, during which they [Page 610]discussed politics, philosophy, and physics. During this time, Gödel's work focused on proving that Georg Cantor's continuum hypothesis (which dealt with the number of points on a line) was consistent with set theory and therefore could not be disproved.

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