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Raphael M. Robinson contributed to astonishingly diverse areas of mathematics. He was born on November 2, 1911, in National City, California, and was the youngest of the four children of Bertram H. Robinson, an atypically peripatetic lawyer who wrote poetry, gave his sons romantic names, and ultimately drifted away. His mother, Bessie Stevenson Robinson, supported the family as an elementary school teacher. Robinson attended the University of California at Berkeley, where he took a B.A. in 1932, an M.A. in 1933, and a Ph.D. in December 1934. His dissertation was in the field of complex analysis.
During the Depression he considered himself lucky to obtain a half-time instructorship at Brown University, but his stay there was plagued by poverty and resultant tuberculosis. In 1937, he returned happily to Berkeley as an instructor, becoming a full professor in 1949 and emeritus in 1973. He was an excellent teacher, having a thorough knowledge of much of classical and modern mathematics so well organized in his mind that he could explain it with exceptional clarity.
In a number theory class in 1939 he had among his students Julia Bowman. Their courtship took place on long walks during which he educated her in modern mathematics. They were married in December 1941. At the end of her life, when she had become the first woman mathematician elected to the National Academy of Sciences and the first woman president of the American Mathematical Society, she said she doubted that she would have become a mathematician if it had not been for him: "He taught me and has continued to teach me, has encouraged me, and has supported me in many ways."
Even among world-renowned mathematicians, Robinson was exceptional. In an age of specialization he contributed significantly to six fields: logic, set theory, geometry, complex analysis, number theory, and combinatorics; and in a subject often considered a young person's game, he continued to produce significant mathematics into his eighties. He also anticipated most of the mathematical community by a good 20 years in making use of computers to obtain results in pure mathematics. In 1951, never having seen one of the new computing machines and working only from a manual, he coded the first successful program to test very large numbers for primality. "That the code was without error was (and still is) a remarkable feat," according to the recently published history of the Institute for Numerical Analysis on the UCLA campus. "In an age where most of our journals are filled with papers which (even if good) exploit theories for their own sake... it is refreshing and stimulating to encounter one of Robinson's papers," one of the foremost number theorists of the century has written. "In each of them he takes a problem, old or new, which can be stated in simple and intelligible terms, and either solves it, or at least adds much that is new. His scholarship is impeccable; it is plain that he never writes until he has thought deeply, and until he has sought out every relevant piece of existing knowledge."
Approximately a quarter of Robinson's publications are distributed among seven different topics in logic and the foundations of mathematics. The one to which he gave most attention was that of undecidable theories, an interest that he shared with his wife, Julia. By way of illustration, the mathematical structure consisting of the integers with their operation of addition is said to have a decidable theory. This means it is possible to program a computer so that, given any sentence about the structure in a logically defined language, the computer will make a finite computation that determines whether the sentence is true or false. Another mathematical structure with a decidable theory is that of all real numbers with their operations of addition and multiplication. (This was shown by Alfred Tarski, also of Berkeley.) But a major mathematical discovery of this century was the fact that that the structure of integers with both operations of addition and multiplication has an undecidable structure, because there is no computer program that can decide the truth or falsity of every sentence of its language. In several papers Robinson was able to show that a number of other mathematical theories are also undecidable. His most valuable contribution, however, was devising a theory with a finite number of axioms that is "essentially undecidable"--a concept introduced by Tarski. The book Undecidable Theories (Mostowski, Robinson and Tarski) has provided a tool for researchers to identify undecidable theories in all parts of mathematics.
In an area that combines logic, geometry, and combinatorics, Robinson did early work on tilings of the plane by tiles of such a shape that they can cover the plane but not in the familiar "periodic" manner of squares and hexagons. The general subject has turned out to have unexpected applications in crystallography, where the tiles correspond to so-called "quasi-crystals." A famous set-theory result of Robinson's is related to the so-called Banach-Tarski Paradox, a surprising theorem that the set of points making up a solid sphere can be decomposed into a finite number of parts that can be reassembled into two solid spheres, each having the same radius as the original sphere! Robinson was able to show that the number of parts required for such an operation is five and that decomposition with less than five is impossible. He also showed that the surface of a sphere can be decomposed into four parts and reassembled into two spherical surfaces of the same radius and that four is the minimum number.
Robinson was not generally active in university affairs; but during the controversy over the Loyalty Oath, he served as treasurer of a group from the mathematics faculty who gave up 10 percent of their salaries to support the five non-signers in the department. At the age of 61, when "early retirement" was not yet a popular option, Raphael chose to retire--at considerable financial sacrifice--so that he could devote more time to mathematics.
Even in retirement Robinson owned no casual clothes. His pleasures were sedentary. He enjoyed challenging table games, novels as well as nonfiction, old movies, and the verse of Ogden Nash (on occasion turning out efforts of his own in that genre). He was a generous donor to many causes and a thorough reader of the Chronicle, the New Yorker, and the Nation as well as Martin Gardner's columns and selected comic strips. He was also a faithful contributor to the Problems Section of the American Mathematical Monthly. What the section editor described as "a beautiful short paper" of his was accepted for publication just days before his death.
In the 10 years following his wife's death, he continued to live in their modest home, taking care of himself and never speaking of his loneliness. In 1986 he established the Julia Bowman Robinson Fund for fellowships for graduate students in mathematics at Berkeley. It will receive the bulk of his substantial estate.
Robinson suffered a stroke on December 4 and died on January 27, 1995. Although unable to speak, he was able to indicate by "yes" and "no" motions that his fine mind and memory were still operating. Contrary to the expectation of his doctors, he did not become depressed in his new situation but continued as the remarkably self-contained individual he had always been.
John Addison
David Gale
Leon Henkin
Constance Reid
During the Depression he considered himself lucky to obtain a half-time instructorship at Brown University, but his stay there was plagued by poverty and resultant tuberculosis. In 1937, he returned happily to Berkeley as an instructor, becoming a full professor in 1949 and emeritus in 1973. He was an excellent teacher, having a thorough knowledge of much of classical and modern mathematics so well organized in his mind that he could explain it with exceptional clarity.
In a number theory class in 1939 he had among his students Julia Bowman. Their courtship took place on long walks during which he educated her in modern mathematics. They were married in December 1941. At the end of her life, when she had become the first woman mathematician elected to the National Academy of Sciences and the first woman president of the American Mathematical Society, she said she doubted that she would have become a mathematician if it had not been for him: "He taught me and has continued to teach me, has encouraged me, and has supported me in many ways."
Even among world-renowned mathematicians, Robinson was exceptional. In an age of specialization he contributed significantly to six fields: logic, set theory, geometry, complex analysis, number theory, and combinatorics; and in a subject often considered a young person's game, he continued to produce significant mathematics into his eighties. He also anticipated most of the mathematical community by a good 20 years in making use of computers to obtain results in pure mathematics. In 1951, never having seen one of the new computing machines and working only from a manual, he coded the first successful program to test very large numbers for primality. "That the code was without error was (and still is) a remarkable feat," according to the recently published history of the Institute for Numerical Analysis on the UCLA campus. "In an age where most of our journals are filled with papers which (even if good) exploit theories for their own sake... it is refreshing and stimulating to encounter one of Robinson's papers," one of the foremost number theorists of the century has written. "In each of them he takes a problem, old or new, which can be stated in simple and intelligible terms, and either solves it, or at least adds much that is new. His scholarship is impeccable; it is plain that he never writes until he has thought deeply, and until he has sought out every relevant piece of existing knowledge."
Approximately a quarter of Robinson's publications are distributed among seven different topics in logic and the foundations of mathematics. The one to which he gave most attention was that of undecidable theories, an interest that he shared with his wife, Julia. By way of illustration, the mathematical structure consisting of the integers with their operation of addition is said to have a decidable theory. This means it is possible to program a computer so that, given any sentence about the structure in a logically defined language, the computer will make a finite computation that determines whether the sentence is true or false. Another mathematical structure with a decidable theory is that of all real numbers with their operations of addition and multiplication. (This was shown by Alfred Tarski, also of Berkeley.) But a major mathematical discovery of this century was the fact that that the structure of integers with both operations of addition and multiplication has an undecidable structure, because there is no computer program that can decide the truth or falsity of every sentence of its language. In several papers Robinson was able to show that a number of other mathematical theories are also undecidable. His most valuable contribution, however, was devising a theory with a finite number of axioms that is "essentially undecidable"--a concept introduced by Tarski. The book Undecidable Theories (Mostowski, Robinson and Tarski) has provided a tool for researchers to identify undecidable theories in all parts of mathematics.
In an area that combines logic, geometry, and combinatorics, Robinson did early work on tilings of the plane by tiles of such a shape that they can cover the plane but not in the familiar "periodic" manner of squares and hexagons. The general subject has turned out to have unexpected applications in crystallography, where the tiles correspond to so-called "quasi-crystals." A famous set-theory result of Robinson's is related to the so-called Banach-Tarski Paradox, a surprising theorem that the set of points making up a solid sphere can be decomposed into a finite number of parts that can be reassembled into two solid spheres, each having the same radius as the original sphere! Robinson was able to show that the number of parts required for such an operation is five and that decomposition with less than five is impossible. He also showed that the surface of a sphere can be decomposed into four parts and reassembled into two spherical surfaces of the same radius and that four is the minimum number.
Robinson was not generally active in university affairs; but during the controversy over the Loyalty Oath, he served as treasurer of a group from the mathematics faculty who gave up 10 percent of their salaries to support the five non-signers in the department. At the age of 61, when "early retirement" was not yet a popular option, Raphael chose to retire--at considerable financial sacrifice--so that he could devote more time to mathematics.
Even in retirement Robinson owned no casual clothes. His pleasures were sedentary. He enjoyed challenging table games, novels as well as nonfiction, old movies, and the verse of Ogden Nash (on occasion turning out efforts of his own in that genre). He was a generous donor to many causes and a thorough reader of the Chronicle, the New Yorker, and the Nation as well as Martin Gardner's columns and selected comic strips. He was also a faithful contributor to the Problems Section of the American Mathematical Monthly. What the section editor described as "a beautiful short paper" of his was accepted for publication just days before his death.
In the 10 years following his wife's death, he continued to live in their modest home, taking care of himself and never speaking of his loneliness. In 1986 he established the Julia Bowman Robinson Fund for fellowships for graduate students in mathematics at Berkeley. It will receive the bulk of his substantial estate.
Robinson suffered a stroke on December 4 and died on January 27, 1995. Although unable to speak, he was able to indicate by "yes" and "no" motions that his fine mind and memory were still operating. Contrary to the expectation of his doctors, he did not become depressed in his new situation but continued as the remarkably self-contained individual he had always been.
John Addison
David Gale
Leon Henkin
Constance Reid
This University of California obituary is available at THIS LINK