Gödel, Kurt Friedrich (1906–1978)
Kurt Gödel was an Austrian-American mathematician and logician who, in 1931, proved that within
a formal system questions exist that
are neither provable nor disprovable on the basis of the axioms that define the system. This is known as Gödel's undecidability
theorem. He also showed that in a sufficiently rich formal system
in which decidability of all questions is required, there will be contradictory
statements. This is called Gödel's
incompleteness theorem. In establishing these theorems Gödel showed
that there are problems that can't be solved by any set of rules or procedures;
instead, for these problems one must always extend the set of axioms. This
disproved a common belief at the time that the different branches of mathematics
could be integrated and placed on a single logical foundation.
Gödel was a close friend of Albert Einstein at the Institute for Advanced Studies, Princeton, from 1953 to his death,
and contributed to general relativity theory
and cosmology. The so-called Gödel universe is a rotating model of the universe in which it is theoretically possible
to travel into the past.