Paul Cohen (mathematician)
| Paul J. Cohen | |
|---|---|
| Born |
April 2, 1934 Long Branch, New Jersey |
| Died | March 23, 2007 (aged 72) Stanford, California, near Palo Alto |
| Fields | Mathematics |
| Institutions | Stanford University |
| Alma mater |
Stuyvesant High School Brooklyn College University of Chicago |
| Doctoral advisor | Antoni Zygmund |
| Doctoral students | Peter Sarnak |
| Known for |
Cohen forcing Continuum hypothesis |
| Influences | Georg Cantor, Kurt Gödel |
| Influenced | Alain Badiou |
| Notable awards |
Bôcher Prize (1964) Fields Medal (1966) National Medal of Science (1967) |
Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician. He is best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was awarded a Fields Medal.
Cohen was born in Long Branch, New Jersey, into a Jewish family that had immigrated to the United States from what is now Poland; he grew up in Brooklyn. He graduated in 1950, at age 16, from Stuyvesant High School in New York City.
Cohen next studied at the Brooklyn College from 1950 to 1953, but he left before earning his bachelor's degree when he learned that he could start his graduate studies at the University of Chicago with just two years of college. At Chicago, Cohen completed his master's degree in mathematics in 1954 and his Doctor of Philosophy degree in 1958, under supervision of the Professor of Mathematics, Antoni Zygmund. The title of his doctoral thesis was Topics in the Theory of Uniqueness of Trigonometrical Series.
In 1957, before the award of his doctorate, Cohen was appointed as an Instructor in Mathematics at the University of Rochester for a year. He then spent the academic year 1958–59 at the Massachusetts Institute of Technology before spending 1959–61 as a fellow at the Institute for Advanced Study at Princeton. These were years in which Cohen made a number of significant mathematical breakthroughs. In Factorization in group algebras (1959) he showed that any integrable function on a locally compact group is the convolution of two such functions, solving a problem posed by Walter Rudin. In On a conjecture of Littlewood and idempotent measures (1960) Cohen made a significant breakthrough in solving the Littlewood Conjecture.
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