Paul Joseph Cohen

Paul Joseph Cohen, an emeritus professor of mathematics famed for work on set theory and 1966 winner of the world's top math prize, died March 23 at Stanford Hospital of a rare lung disease. He was 72. Cohen won two of the most prestigious awards in mathematics—in completely different fields. He won the American Mathematical Society's Bôcher Prize in 1964 for analysis and the Fields Medal, considered the "Nobel Prize" of mathematics, in 1966 for logic.In the late 1870s, German mathematician Georg Cantor put forth a hypothesis that said any infinite subset of the set of all real numbers can be put into one-to-one correspondence either with the set of integers or with the set of all real numbers. All attempts to prove or disprove this conjecture failed until 1938, when Kurt Gödel showed it was impossible to disprove the continuum hypothesis.Despite having never worked in set theory, Cohen proved the extremely surprising result that both the Continuum Hypothesis and the Axiom of Choice—two of the most basic ideas in mathematics—were actually undecidable using the axioms of set theory. This result, which meant that conventional mathematics could neither prove nor disprove concrete and well known mathematical assertions, caused healthy turbulence among philosophers, logicians and mathematicians concerned with the concept of truth.