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The novelist E. M. Forster in his essay, "What I Believe," says "The people I admire the most are those who are sensitive and want to create something or discover something and do not see life in terms of power." Using this criterion it would be difficult indeed to find a more admirable man than Alfred Foster, professor emeritus of mathematics at Berkeley, who died on December 24, 1994 at the age of 90, of complications following surgery the previous spring. Up to the last year of his life he continued to work intensely, as he had all of his life, on mathematical problems that he found personally fascinating, motivated solely by his deep desire to create and to understand, quite independent of whether or not his interests coincided with what was in contemporary fashion. In fact, however, in following his independent quest, during his career he initiated and vitalized an area of modern algebra that subsequently flourished abundantly.
Foster was born in New York City on July 13, 1904. He earned a B.S. degree at Caltech in 1926 as well as an M.S. the following year. Further graduate work was done at Princeton, where he obtained the Ph.D. in 1931. His dissertation director was Alonzo Church who is still alive as of this writing, and who was then only one year older than Foster, his first Ph.D. student. In 1930 Foster married Else Wagner. Together they spent a postdoctoral year in Gottingen and then traveled across the United States by automobile to Berkeley for more study and part-time teaching. In 1934 he accepted a regular position at Berkeley. At that time Griffith Evans was Head of the Mathematics Department and was charged by President Sproul with building a first-class mathematics center, which he did. Alfred Foster and Charles Morrey (who became the first department chairman after Evans' retirement) were Evans' first two appointments. Except for subsequent sabbatical leaves, spent most notably in Freiburg and Tubingen, Foster served continuously at Berkeley until his retirement at the then-mandatory age of 67 in 1971.
Foster's Ph.D. dissertation and his first few papers were in the area of mathematical logic. Starting from this point, he soon focused his interest on the related theory of Boolean algebras and Boolean rings, and was thus led from logic to algebra. He extensively studied the role of duality in Boolean theory and subsequently developed a theory of n-ality for certain rings which played for n-valued logics the role of Boolean rings vis-a-vis Boolean algebras. The late Benjamin Bernstein of the Berkeley mathematics faculty was his collaborator in some of this research. This work culminated in his seminal paper ""The theory of Boolean like rings"" appearing in 1946.
In the course of this work Foster realized that the more general setting of the new area of universal algebra was more appropriate for continued development of his ideas, and in this context he developed the theory of primal algebras and in 1953 showed that the variety generated by a primal algebra has the same essential structure as the variety of Boolean algebras. The mathematician Bjarni Jonsson, in a recent paper dedicated to the memory of Alfred Foster, states: "This result is an acorn from which a mighty oak has grown," and Foster himself devoted the rest of his life to the development of this important work. Through his students and other mathematicians throughout the world, this mission continues.
When Foster first began his study of varieties in universal algebra, the subject was often regarded as somewhat sterile, perhaps because little more than the very basic abstract theory had been developed and also because its relevance to mainstream ideas then current was not yet clearly established. Probably for this reason, the value of his early work on primal algebra theory was not immediately recognized. Before long, however, it became clear to Foster and his students that this theory truly was relevant, and the subsequent four decades of explosive growth of universal algebra is testimony to the validity of Foster's persistent belief in the intrinsic value of his work. If Foster had had more interest in achieving personal recognition it is easy to imagine that he might have abandoned this work in favor of a more popular research area.
Alfred Foster, though somewhat formal and socially shy, will be remembered as warm-hearted, good-humored, and unconditionally generous, by all who knew him. Several of his former students, in recalling him, have pointedly used the word "gentleman" in describing his character. His teaching style was rather old-fashioned, in a very good sense, and was probably influenced by his admiration for the universities of Germany, which developed during his visits there. His former students were often surprised and flattered that he remembered them years after classroom contact, and that he had a continuing interest in their lives.
While cordial with all of his faculty colleagues, among Foster's closest personal friends at Berkeley, along with Benjamin Bernstein, were the mathematician Hans Lewy and Ronald Shepherd of Engineering. These men were rather like Foster in temperament and enjoyed each others' conversation in areas outside mathematics. Music and politics were of particular interest to him, and in the latter field he held deep and morally grounded convictions. On the other hand, and consistent with his personality, he did not engage in highly visible political action. Along with mathematics, Foster took the current great issues of science and human culture very seriously indeed. An important key to his character was that he never took himself nearly so seriously.
Together with his work, the great love of his life was his family. Alfred and Else Foster were deeply devoted to each other and to their two sons and two daughters, their eight grandchildren, and three great granddaughters. Always, and particularly in his last years, whenever possible he took a personal interest in their growth and education.
Following his express wish his ashes were scattered over the ocean on January 5, 1995.
Leon Henkin
John Kelley
Alden Pixley
Foster was born in New York City on July 13, 1904. He earned a B.S. degree at Caltech in 1926 as well as an M.S. the following year. Further graduate work was done at Princeton, where he obtained the Ph.D. in 1931. His dissertation director was Alonzo Church who is still alive as of this writing, and who was then only one year older than Foster, his first Ph.D. student. In 1930 Foster married Else Wagner. Together they spent a postdoctoral year in Gottingen and then traveled across the United States by automobile to Berkeley for more study and part-time teaching. In 1934 he accepted a regular position at Berkeley. At that time Griffith Evans was Head of the Mathematics Department and was charged by President Sproul with building a first-class mathematics center, which he did. Alfred Foster and Charles Morrey (who became the first department chairman after Evans' retirement) were Evans' first two appointments. Except for subsequent sabbatical leaves, spent most notably in Freiburg and Tubingen, Foster served continuously at Berkeley until his retirement at the then-mandatory age of 67 in 1971.
Foster's Ph.D. dissertation and his first few papers were in the area of mathematical logic. Starting from this point, he soon focused his interest on the related theory of Boolean algebras and Boolean rings, and was thus led from logic to algebra. He extensively studied the role of duality in Boolean theory and subsequently developed a theory of n-ality for certain rings which played for n-valued logics the role of Boolean rings vis-a-vis Boolean algebras. The late Benjamin Bernstein of the Berkeley mathematics faculty was his collaborator in some of this research. This work culminated in his seminal paper ""The theory of Boolean like rings"" appearing in 1946.
In the course of this work Foster realized that the more general setting of the new area of universal algebra was more appropriate for continued development of his ideas, and in this context he developed the theory of primal algebras and in 1953 showed that the variety generated by a primal algebra has the same essential structure as the variety of Boolean algebras. The mathematician Bjarni Jonsson, in a recent paper dedicated to the memory of Alfred Foster, states: "This result is an acorn from which a mighty oak has grown," and Foster himself devoted the rest of his life to the development of this important work. Through his students and other mathematicians throughout the world, this mission continues.
When Foster first began his study of varieties in universal algebra, the subject was often regarded as somewhat sterile, perhaps because little more than the very basic abstract theory had been developed and also because its relevance to mainstream ideas then current was not yet clearly established. Probably for this reason, the value of his early work on primal algebra theory was not immediately recognized. Before long, however, it became clear to Foster and his students that this theory truly was relevant, and the subsequent four decades of explosive growth of universal algebra is testimony to the validity of Foster's persistent belief in the intrinsic value of his work. If Foster had had more interest in achieving personal recognition it is easy to imagine that he might have abandoned this work in favor of a more popular research area.
Alfred Foster, though somewhat formal and socially shy, will be remembered as warm-hearted, good-humored, and unconditionally generous, by all who knew him. Several of his former students, in recalling him, have pointedly used the word "gentleman" in describing his character. His teaching style was rather old-fashioned, in a very good sense, and was probably influenced by his admiration for the universities of Germany, which developed during his visits there. His former students were often surprised and flattered that he remembered them years after classroom contact, and that he had a continuing interest in their lives.
While cordial with all of his faculty colleagues, among Foster's closest personal friends at Berkeley, along with Benjamin Bernstein, were the mathematician Hans Lewy and Ronald Shepherd of Engineering. These men were rather like Foster in temperament and enjoyed each others' conversation in areas outside mathematics. Music and politics were of particular interest to him, and in the latter field he held deep and morally grounded convictions. On the other hand, and consistent with his personality, he did not engage in highly visible political action. Along with mathematics, Foster took the current great issues of science and human culture very seriously indeed. An important key to his character was that he never took himself nearly so seriously.
Together with his work, the great love of his life was his family. Alfred and Else Foster were deeply devoted to each other and to their two sons and two daughters, their eight grandchildren, and three great granddaughters. Always, and particularly in his last years, whenever possible he took a personal interest in their growth and education.
Following his express wish his ashes were scattered over the ocean on January 5, 1995.
Leon Henkin
John Kelley
Alden Pixley
This University of California obituary is available at THIS LINK