Paul Joseph Cohen, a leading mathematician known for his work on set theory, has died. He was 72.

The recipient of several of the world's leading math awards, Cohen died March 23 at Stanford Hospital in Palo Alto of a rare lung disease, according to Stanford University, where he taught for four decades.

"Paul Cohen was one of the most brilliant mathematicians of the 20th century," said Peter Sarnak, a Princeton professor who received his doctorate from Stanford in 1980 under Cohen. "He made mathematics look simple and unified."

Cohen's passion was studying extremely difficult, long-standing mathematical problems, including the continuum hypothesis, which is considered central to set theory and holds that sets of items are the fundamental objects defining all ideas in mathematics.

He shocked the math establishment by proving that the continuum hypothesis could not be decided. The notion that conventional mathematics couldn't prove or disprove concrete and well-known assertions caused an uproar among academics.

In 1964 he won the American Mathematical Society's Bocher Prize for analysis, and in 1966 he won the Fields Medal -- the math world's equivalent of the Nobel Prize -- for logic. Cohen won the 1967 National Medal of Science for his work in logic, and he was an honorary foreign member of the London Mathematical Society.

In awarding the National Medal of Science in a White House ceremony, President Johnson called Cohen "one of the most brilliant of mathematical logicians. His work has greatly influenced the foundation and development of mathematics."

Cohen was born April 2, 1934, in Long Branch, N.J., and grew up in Brooklyn, N.Y., the fourth and youngest child of immigrants from Poland. His sister, Sylvia, checked out a library book on calculus for him when he was 9.

He attended Brooklyn College from 1950 to 1953 but left before receiving a bachelor's degree, going directly to graduate school at the University of Chicago, where he received a master's degree in 1954 and a doctorate in 1958.

Cohen joined Stanford in 1961 as an assistant professor of mathematics. He became a full professor in 1964. He retired in 2004 but continued teaching until this quarter.

"He had a very special style, full of enthusiasm and very hands-on," said Angus MacIntyre, a professor of applied logic at Queen Mary, University of London. "He was dauntingly clever."

Cohen met his Swedish wife, Christina, on a cruise from Stockholm to Leningrad in 1962. He played piano and violin and sang in the Stanford chorus and in a Swedish folk group, family members said. He spoke Swedish, French, Spanish, German and Yiddish and traveled widely, taking sabbaticals in England, Sweden, France and Hawaii.

He is survived by his wife; sister Tobel Cosiol of San Jose, Costa Rica; brother Ruby Cassel of Brooklyn, N.Y.; twin sons Eric and Steven Cohen of Los Angeles; and son Charles Cohen of Boston.

Memorial services are pending.