Paul Cohen  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 without 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 Antoni Zygmund. The title of his doctoral thesis was "Topics in the Theory of Uniqueness of Trigonometrical Series". On June 2, 1995 Cohen received an honorary doctorate from the Faculty of Science and Technology at Uppsala University, Sweden. Cohen is noted for developing a mathematical technique called forcing, which he used to prove that neither the continuum hypothesis (CH) nor the axiom of choice can be proved from the standard Zermelo–Fraenkel axioms (ZF) of set theory. In conjunction with the earlier work of Gödel, this showed that both of these statements are logically independent of the ZF axioms: these statements can be neither proved nor disproved from these axioms. In this sense, the continuum hypothesis is undecidable, and it is the most widely known example of a natural statement that is independent from the standard ZF axioms of set theory. For his result on the continuum hypothesis, Cohen won the Fields Medal in mathematics in 1966, and also the National Medal of Science in 1967. The Fields Medal that Cohen won continues to be the only Fields Medal to be awarded for a work in mathematical logic, as of 2018. Apart from his work in set theory, Cohen also made many valuable contributions to analysis. He was awarded the Bôcher Memorial Prize in mathematical analysis in 1964 for his paper "On a conjecture by Littlewood and idempotent measures", and lends his name to the Cohen–Hewitt factorization theorem. Cohen was a full professor of mathematics at Stanford University. He was an Invited Speaker at the ICM in 1962 in Stockholm and in 1966 in Moscow.