Alfred Foster (mathematician)

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Alfred Leon Foster (July 13, 1904 – December 24, 1994) was an American mathematician who taught at the University of California, Berkeley, from 1934 to 1971. He was born in New York City and earned a B.S. at Caltech in 1926 and a Ph.D. at Princeton in 1931. His Ph.D. advisor was Alonzo Church, and he also studied with Eric Temple Bell. In 1932, he was an Invited Speaker at the International Congress of Mathematicians in Zürich.

At Berkeley, Foster helped build a strong mathematics department alongside Griffith Evans, and later Charles Morrey. He spent sabbaticals in Freiburg and Tübingen but otherwise remained at Berkeley until his retirement at age 67 in 1971.

Foster’s early work was in mathematical logic, but he soon moved into algebra, focusing on Boolean algebras and Boolean rings and exploring duality in Boolean theory. He developed a theory of n-ality for certain rings, providing a framework for n-valued logics that plays a role similar to Boolean rings for Boolean algebras. This work culminated in his influential 1946 paper The Theory of Boolean-like Rings. He collaborated with Benjamin Bernstein on some of these ideas.

He was married to Else Wagner, and they had four children and eight grandchildren. He passed away in Berkeley, California, in 1994.