Gödel, Kurt (1906–1978)

Austrian-born US mathematician and philosopher. He proved that a mathematical system always contains statements that can be neither proved nor disproved within the system; in other words, as a science, mathematics can never be totally consistent and totally complete. He worked on relativity, constructing a mathematical model of the universe that made travel back through time theoretically possible.

Gödel was born in Brünn, Moravia (now Brno in the Czech Republic) and educated at the University of Vienna, where he worked until 1938. When Austria was annexed by Nazi Germany, he emigrated to the USA. He settled at Princeton, where he was appointed professor in 1953.

In 1930, Gödel showed that a particular logical system (predicate calculus of the first order) was such that every valid formula could be proved within the system; in other words, the system was what mathematicians call complete. He then investigated a much larger logical system – that constructed by English philosophers Bertrand Russell and Alfred Whitehead as the logical basis of mathematics. The resultant paper, ‘On formally undecidable propositions of Principia Mathematica and related systems’ (1931), is the one in which Gödel dashed the hopes of philosophers and mathematicians alike.