PAUL JOSEPH COHEN

Paul Joseph Cohen, Emeritus Professor of Mathematics at Stanford and a 1966 Fields Medallist, died unexpectedly on 23 March 2007 of interstitial lung disease. He was elected Honorary member of the LMS in 1973. He was a member of the US National Academy, and a recipient of the US National Medal of Science (1967).

Cohen became world famous in 1963, when he was 29, with his proof that Cantor's continuum hypothesis CH cannot be proved in the standard axiomatic set theory ZFC of Zermelo-Fraenkel (unless ZFC is inconsistent). This complemented Godel's result of 1938 that CH cannot be refuted in ZFC (unless ZFC is inconsistent). Cohen's method of forcing, for constructing models by adding elements 'generically' to a (countable) model of set theory, has proved enormously flexible and powerful. Over 40 years the method has clarified the status, over ZFC, of many significant principles of set theory, topology, analysis and algebra. Moreover, it has proved valuable quite outside independence theory.

A dramatic aspect of the CH work is that Cohen was a self-taught outsider in logic. His work on set theory and p-adic fields has a very characteristic style, combinatorial and rather free of general theory.

Prior to 1963, Cohen had established a major reputation in harmonic analysis. His 1960 work on idempotent measures won the 1964 Bôcher Prize. In 1969 Cohen published a highly original paper on p-adic cell decomposition, giving a constructive version of the famous results of Ax-Kochen-Ersov. It is now fundamental for logical analysis of motivic integration. From 1969 on Cohen devoted himself to some of the most challenging and unyielding problems, such as the Riemann Hypothesis. He was a passionate and inspiring mathematician. The September 2006 celebration at Stanford brought together (as his former student Peter Sarnak said) people from subjects that rarely interact. On this occasion they came together naturally, to honour a truly unique mathematician, whose work had inspired them all.

Cohen's origins were humble. He was born in Long Branch, New Jersey on 2 April 1934, into a Polish immigrant family. He was an early developer in mathematics. He left Brooklyn College after three years, without a degree, going directly to graduate study at Chicago, under Zygmund. He graduated PhD in 1958 with a thesis on trigonometric series. He was part of a particularly illustrious group of graduate students at Chicago, among them John Thompson, another Fields Medallist. He had positions at Rochester, MIT and IAS before going in 1961 to Stanford, where he spent the rest of his life.

Cohen married Christina Karls from Sweden in 1963. He is survived by Christina and their three sons, Eric, Steven and Charles.

A.J. Macintyre
Queen Mary, University of London