Paul Cohen (mathematician)

Paul Joseph Cohen (born April 2, 1934 in Long Branch , New Jersey , USA , † March 23, 2007 in Stanford (California) ) was an American logician and mathematician . He was the recipient of the Fields Medal .

life and work

Cohen attended Stuyvesant High School in New York City until 1950 , then Brooklyn College in New York until 1953, and then studied at the University of Chicago , where he studied with Antoni Zygmund in 1958 on a topic on trigonometric series (uniqueness theorems for Fourier series) PhD. In 1958/59 he was a Moore Instructor at the Massachusetts Institute of Technology (MIT) and from 1959 to 1961 at the Institute for Advanced Study in Princeton . In 1961 he went to Stanford University in California , where he became a professor in 1964. In 1962 he became a Sloan Research Fellow .

In 1963 he developed the so-called “ forcing ” method, with the help of which he was able to prove that the continuum hypothesis cannot be proven with the usual axioms of mathematics, the set-theoretical ZFC axioms (see Zermelo-Fraenkel set theory ) . Together with Kurt Gödel , who had shown with his constructible universe that the continuum hypothesis from the ZFC axioms cannot be refuted, Cohen found an answer to Hilbert's first problem .

Cohen was also able to show that the axiom of choice does not follow from the Zermelo-Fraenkel axioms.

The forcing method is still today in set theory the most important basis for independence results (ie for proofs that show the unprovability of mathematical statements).

He also worked on partial differential equations and measure theory .

For his work Cohen received the Fields Medal in 1966 , as well as the Bôcher Memorial Prize in 1964 . In 1964 he was elected to the American Academy of Arts and Sciences , 1967 to the National Academy of Sciences and 1972 to the American Philosophical Society .

Peter Sarnak is one of his doctoral students .

literature

• Paul Cohen Set Theory and the Continuum Hypothesis , New York, Benjamin, 1963
• Kanamori The mathematical development of set theory from Cantor to Cohen , Bulletin of Symbolic Logic, Vol. 2, 1996, pp. 1–71, online as a Postscript file in: [1]
• Cohen The discovery of forcing , Rocky Mountain Journal of Mathematics, Vol. 32, 2002, p. 1071
• Paul Cohen How I Discovered Forcing , Lemgo, e-enterprise, 2017
• Donald J. Albers, GL Alexanderson, Constance Reid More Mathematical People - Contemporary Conversations , Academic Press 1994

Web links

• John J. O'Connor, Edmund F. Robertson :  Paul Cohen (mathematician). In: MacTutor History of Mathematics archive .
• obituary
• PaulCohen.org

Some of Cohen's works (including on the continuum hypothesis) can be found on the pages of the Proceedings of the National Academy of Sciences .

Individual evidence

1. ↑ Paul Cohen in the Mathematics Genealogy Project (English)