Cohen, Paul Joseph

▪ 2008American mathematicianborn 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 theory. Cohen attended the University of Chicago (M.S., 1954; Ph.D., 1958). He held appointments at the University of Rochester, N.Y. (1957–58), and the Massachusetts Institute of Technology (1958–59) before joining the Institute for Advanced Study, Princeton, N.J. (1959–61). In 1961 he moved to Stanford University; he became professor emeritus in 2004. Cohen solved a problem (first on David Hilbert's influential 1900 list of important unsolved problems) concerning the truth of the continuum hypothesis. Georg Cantor's continuum hypothesis states that there is no cardinal number between ℵ_{0} and 2^{ℵ0}. In 1940 Kurt Gödel had shown that if one accepts the ZermeloFraenkel system of axioms for set theory, then the continuum hypothesis is not disprovable. Cohen, in 1963, showed that it is not provable under those hypotheses and hence is independent of the other axioms. To do this he introduced a new technique known as forcing, a technique that has since had significant applications throughout set theory. The question still remains whether with some axiom system for set theory, the continuum hypothesis is true. Alonzo Church, in his comments to the Congress in Moscow, suggested that the “GödelCohen results and subsequent extensions of them have the consequence that there is not one set theory but many, with the difference arising in connection with a problem which intuition still seems to tell us must ‘really' have only one true solution.” After proving his startling result about the continuum hypothesis, Cohen returned to research in analysis. Cohen's publications included Set Theory and the Continuum Hypothesis (1966).
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▪ American mathematicianborn April 2, 1934, Long Branch, N.J., U.S.died March 23, 2007, Stanford, Calif.American mathematician, who was awarded the Fields Medal in 1966 for his proof of the independence of the continuum hypothesis from the other axioms of set theory.Cohen attended the University of Chicago (M.S., 1954; Ph.D., 1958). He held appointments at the University of Rochester, N.Y. (1957–58), and the Massachusetts Institute of Technology (1958–59) before joining the Institute for Advanced Study, Princeton, N.J. (1959–61). In 1961 he moved to Stanford University in California; he became professor emeritus in 2004.Cohen was awarded the Fields Medal at the International Congress of Mathematicians in Moscow in 1966. Cohen solved a problem (first on David Hilbert's influential 1900 list of important unsolved problems) concerning the truth of the continuum hypothesis. Georg Cantor's continuum hypothesis (Cantor, Georg) states that there is no cardinal number between ℵ_{0} and 2^{ℵ0}. In 1940 Kurt Gödel had shown that, if one accepts the ZermeloFraenkel system of axioms for set theory, then the continuum hypothesis is not disprovable. Cohen, in 1963, showed that it is not provable under these hypotheses and hence is independent of the other axioms. To do this he introduced a new technique known as forcing, a technique that has since had significant applications throughout set theory. The question still remains whether, with some axiom system for set theory, the continuum hypothesis is true. Alonzo Church, in his comments to the Congress in Moscow, suggested that the “GödelCohen results and subsequent extensions of them have the consequence that there is not one set theory but many, with the difference arising in connection with a problem which intuition still seems to tell us must ‘really' have only one true solution.” After proving his startling result about the continuum hypothesis, Cohen returned to research in analysis.Cohen's publications include Set Theory and the Continuum Hypothesis (1966).* * *
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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 — (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… … Scientists
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
Paul Joseph Cohen — Paul Cohen Pour les articles homonymes, voir Cohen. Paul Joseph Cohen, (né 2 avril 1934 à Long Branch (New Jersey) et mort le 23 mars 2007), est un mathématicien américain. Il est surto … Wikipédia en Français
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
Paul Joseph Weitz — Paul Weitz Land (Organisation): USA (NASA) Datum der Auswahl: 4. April 1966 (5. NASA Gruppe) Anzahl der Raumflüge: 2 Start erster Raumflug … Deutsch Wikipedia
Cohen — Paul Joseph … Scientists
Cohen — Cohen, Herman Cohen, Leonard Cohen, Marcel Cohen, Paul Joseph Cohen, Stanley * * * I (as used in expressions) Brandes, Georg (Morris Cohen) Samuel Cohen Judy Cohen Elizabeth Cohen II o kohen ( … Enciclopedia Universal
COHEN (P. J.) — COHEN PAUL JOSEPH (1934 ) Mathématicien et logicien américain. En 1963, Cohen a découvert une nouvelle construction de modèles, appelée forcing, qui joue désormais un rôle fondamental dans la théorie des ensembles et dans la théorie des modèles;… … Encyclopédie Universelle