Hilbert Asks, Is Mathematics Complete, is it Consistent, and is it Decidable?

At the International Congress of Mathematicians held in Bologna, Italy, in 1928 mathematician and physicist David Hilbert returned to the second of the twenty-three problems posed in his 1900 paper Mathematische Probleme, asking “is mathematics complete, is it consistent, and is it decidable?”

Three years later, the first two of these questions were answered in the negative by Kurt Gödel. Working independently, Alonzo Church, Alan Turing, and Emil Post published answers to the third question in 1936.

Hilbert's paper, Probleme der Grundlegung del Mathematik, was first published in Atti del Congresso Internazionale dei Matematici, Bologna 3-10 settembre 1928 (VI) I (1929) 135-41.

Hook & Norman, Origins of Cyberspace (2002) no. 320.