Paul Cohen

Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician renowned for his groundbreaking contributions to set theory, particularly for inventing the forcing technique that demonstrated the independence of the continuum hypothesis and the axiom of choice from the Zermelo–Fraenkel axioms of set theory. Born in Long Branch, New Jersey, to Jewish immigrant parents, Cohen displayed early mathematical talent, graduating from Stuyvesant High School in 1950 and attending Brooklyn College from 1950 to 1953 without earning a degree before pursuing graduate studies at the University of Chicago, where he obtained his master's degree in 1954 and PhD in 1958 under supervisor Antoni Zygmund. His doctoral thesis focused on topics in the theory of uniqueness of trigonometric series, but Cohen's career pivoted dramatically toward mathematical logic and set theory during a fellowship at the Institute for Advanced Study from 1959 to 1961.

In 1963, while at Stanford University—where he joined as an assistant professor in 1961 and became a full professor in 1964—Cohen published his seminal paper proving the independence of the continuum hypothesis, a long-standing problem posed by David Hilbert as the first of his 23 problems in 1900. This work, detailed in "The Independence of the Continuum Hypothesis" in the Proceedings of the National Academy of Sciences, employed the novel forcing method to construct models of set theory where the hypothesis both holds and fails, resolving its undecidability within standard axioms. Building on this, Cohen extended forcing in 1963–1964 to prove the independence of the axiom of choice, a foundational principle asserting the existence of choice functions for any set of nonempty sets; these results were fully elaborated in his 1966 book Set Theory and the Continuum Hypothesis.

Paul Cohen was born on April 2, 1934, in Long Branch, New Jersey, to Polish-Jewish immigrant parents Abraham and Minnie Cohen. Abraham worked various jobs to support the family, while Minnie was a dressmaker. As the youngest of four children, Cohen experienced a significant family change when his parents separated during his ninth year, after which he was raised primarily by his mother.