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Paul Joseph Cohen

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2 April 1934

Long Branch, New Jersey, USA

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Paul Cohen was a student at Brooklyn College from 1950 until 1953. He then studied for his master's degree at the University of Chicago, being awarded the degree in 1954. Continuing to study at Chicago for his doctorate he was awarded his PhD in 1958. His doctoral thesis Topics in the Theory of Uniqueness of Trigonometric Series was written under the supervision of Antoni Zygmund .

In 1957, before the award of his doctorate, Cohen was appointed an instructor 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.

In 1961 Cohen was appointed to the faculty at Stanford University, being promoted to professor there in 1964. In 1966 Cohen was awarded a Fields Medal at the International Congress of Mathematicians in Moscow for his fundamental work on the foundations of set theory.

Cohen used a technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalised continuum hypothesis . The continuum hypothesis problem was the first of Hilbert 's famous 23 problems delivered to the Second International Congress of Mathematicians in Paris in 1900. Hilbert 's famous speech The Problems of Mathematics challenged (and today still challenges) mathematicians to solve these fundamental questions and Cohen has the distinction of solving Problem 1.

The Fields Medal was not the first award that Cohen received. In 1964 he was awarded the Bôcher Memorial Prize from the American Mathematical Society :

...for his paper, On a conjecture of Littlewood and idempotent measures, American Journal of Mathematics 82 (1960), 191-212.

Three years later, in 1967, Cohen received the National Medal of Science. He has also been elected to the National Academy of Sciences .

In addition to his work on set theory, Cohen has worked on differential equations and harmonic analysis .

Source:School of Mathematics and Statistics University of St Andrews, Scotland