Kurt Gödel

Born into a wealthy German-speaking family in Brno on April 28, 1906, Gödel earned his doctorate at the University of Vienna with a proof of the completeness theorem in 1929. Two years later, in 1931, he published the incompleteness theorems — showing that formal axiomatic systems meeting certain conditions cannot decide the truth of all statements about natural numbers and cannot prove their own consistency. He developed Gödel numbering to encode formal expressions as numbers, a technique that made the proof possible. He also demonstrated that neither the axiom of choice nor the continuum hyp…