Cohen , Paul Joseph

Cohen , Paul Joseph
(1934–) American mathematician
Cohen, who was born at Long Branch, New Jersey, was educated at Brooklyn College and at the University of Chicago, where he obtained his PhD in 1958. He spent a year at the Massachusetts Institute of Technology and two years at the Institute for Advanced Studies, Princeton, before moving to Stanford in 1961. He was appointed professor of mathematics in 1964.
Mathematicians had been introduced to transfinite arithmetic by Georg Cantor from the 1870s onwards. Cantor had identified two distinct infinite sets, namely the set of natural numbers and the set of real numbers, represented by א0 and c respectively. He had also proved that there were an infinite number of infinite numbers, that following א0, there came א1, א2, א3… indefinitely. Where did c fit into this sequence? Cantor answered by proposing that c= א1, a supposition since known as the ‘continuum hypothesis’. It was the first member on David Hilbert's 1900 list of outstanding unsolved mathematical problems.
Little progress was made upon the problem before 1938 when Kurt Gödel demonstrated that set theory remains consistent if the continuum hypothesis is added as an axiom. This did not, however, constitute a proof of the hypothesis, for set theory's own absolute consistency has never been proved. Nonetheless, Gödel's work did show that the continuum hypothesis could not be shown to be false within set theory.
In 1963 Cohen proposed to develop a non-Cantorian set theory that contained not the continuum hypothesis but its negation. He showed that no contradiction ensued and it seemed to follow that the continuum hypothesis was quite independent of set theory and that it could be neither proved nor disproved within any standard system of set theory.

Scientists. . 2011.

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  • COHEN, PAUL JOSEPH — (1934– ), U.S. mathematician. Born in New Jersey, Cohen was a student at Brooklyn College from 1950 to 1953 and he received his M.Sc. in 1954 and his Ph.D in 1958 from the University of Chicago. From 1959 to 1961 he was a fellow at the Institute… …   Encyclopedia of Judaism

  • Cohen, Paul Joseph — ▪ 2008       American mathematician born April 2, 1934, Long Branch, N.J. died March 23, 2007 , Stanford, Calif. was awarded the Fields Medal in 1966 for his proof of the independence of the continuum hypothesis from the other axioms of set… …   Universalium

  • Cohen, Paul Joseph — ► (n. 1934) Matemático estadounidense. Demostró la independencia de la hipótesis del continuo, respecto a los otros axiomas de la teoría de conjuntos …   Enciclopedia Universal

  • Paul Joseph Cohen — (* 2. April 1934 in Long Branch, New Jersey, USA; † 23. März 2007 in Stanford (Kalifornien)) war ein US amerikanischer Logiker und Mathematiker. Er war Träger der Fields Medaille. Leben und Werk Cohen besuchte bis 1950 die Stuyvesant High School… …   Deutsch Wikipedia

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  • Paul Joseph Cohen — Saltar a navegación, búsqueda Paul Joseph Cohen, nacido el 2 de abril de 1934 en Long Branch, New Jersey EE. UU., estudió en la Universidad de Brooklyn en un periodo de 1950 a 1953. Posteriormente estudió su maestría en la Universidad de Chicago …   Wikipedia Español

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