Wikinventia — Atlas of discoveries and inventions · Global Age

Independence of the continuum hypothesis — Paul Cohen

1963 AD · Transmission: Global
MathematicsTheoryNorth American

Paul Cohen proves in 1963, in Proceedings of the National Academy of Sciences, that the continuum hypothesis is independent of the Zermelo-Fraenkel axioms with the axiom of choice (ZFC): it can neither be proved nor disproved from them. To do so, Cohen develops the "forcing" technique, an entirely new method for constructing models of set theory that would become a standard tool of later mathematical logic. Together with Kurt Gödel's earlier result (1940, showing the hypothesis is consistent with ZFC), Cohen's work completes the determination of the logical status of one of the oldest problems in set theory, originally posed by Cantor in 1878. Cohen received the Fields Medal in 1966, still, as of this entry, the only mathematician awarded the prize for a work in mathematical logic.

InstitutionStanford University
Historical regionUSA
Primary sourceCohen, P. — "The Independence of the Continuum Hypothesis" (Proceedings of the National Academy of Sciences, 50, December 1963)
Secondary sourceInternational Mathematical Union — Fields Medal citation 1966
Original languageEnglish
View this entry in the interactive atlas → View in graph →