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Julia Robinson was born in St. Louis, Missouri on December 8, 1919 to Ralph Bowers Bowman and Helen Hall Bowman. When she was two years old her mother died and the family was sent to Phoenix, Arizona to live with a grandmother. In the fall of 1925, the family moved again to Point Loma on San Diego Bay. Julia received her elementary and secondary education in the San Diego public schools. In 1936 she began her college career at San Diego State College, majoring in mathematics and transferring to Berkeley for her senior year. She received three degrees from Berkeley: A.B. 1940, M.A. 1941, and Ph.D. in 1948. In 1941 she married Raphael Robinson, who had taught her number theory at Berkeley.
Robinson's Ph.D. thesis was written under the supervision of Alfred Tarski. In it she settled a difficult problem that had attracted considerable attention for some years. This was the decision problem for the elementary theory of the system of rational numbers (with operations of addition and multiplication). Her solution showed that there cannot be an algorithm which, given any first-order sentence about the rational number system, decides in a finite number of steps whether the sentence is true or false; this result is expressed by saying that the theory is undecidable. Earlier work by Alonzo Church had shown that the elementary theory of the system of integers is undecidable. On the other hand, Tarski had produced an algorithm showing that the elementary theory of the system of real numbers is decidable. The question of the theory of rational numbers was then a very natural one to raise, but it had resisted solution for a long time. To solve it, Robinson brought to bear a deep theorem of number theory, dealing with ternary quadratic forms, that had been proved by Helmut Hasse in 1923.
In all, Robinson published 25 papers. Her first four papers dealt with probability theory, game theory, the subject of her dissertation, and the theory of recursive functions.
Robinson's fifth paper was her first step along a road that led her to fame, and she followed it with eight other papers that brought her very
― 260 ―far along the same road--although not quite to the end. These papers were successive efforts to solve "Hilbert's tenth problem"; this terminology refers to a list of 23 problems proposed at the International Congress of Mathematicians held in 1900 by David Hilbert, generally acknowledged to be the greatest mathematician of his time. Hilbert's list of problems provided a framework for a vast amount of the mathematical research of our century.
Hilbert's 10th problem deals with Diophantine equations, which are equations between two polynomials (in several variables) having integer coefficients. Given any such equation one can look for solutions-integers to be assigned to the variables that will make the equation true. However, it is easy to see that some Diophantine equations have no solutions. Hilbert proposed the problem of finding an algorithm which could determine, in an automatic way involving a finite computation, whether or not any given Diophantine equation has a solution. Robinson set out to prove that there is no such algorithm to be found.
In a series of leapfrogging papers, Robinson, Martin Davis, and Hilary Putmam reached an important milestone in 1960 when it was shown that there is no algorithm for deciding which exponential Diophantine equations have solutions--this is a wider class of equations in which polynomials with variable exponents are considered. Subsequent papers moved closer and closer to a solution of Hilbert's problem. Robinson showed in 1969 that if there is a polynomial equation in one variable whose solutions are all prime numbers and no others, then there could be no algorithm of the kind proposed by Hilbert. The following year a young Soviet mathematician, Yuri Matyjasevic, based on earlier work of Robinson, showed how to construct a Diophantine equation whose solution set is any of a large class of sets, including the set of prime numbers, thus completing the conquest of Hilbert's tenth problem.
During the Second World War, and some years after, Julia did research in Berkeley's Statistical Laboratory under Jerzy Neyman. From time to time, she was invited to teach in the Department of Mathematics, holding the title of lecturer. Then in 1976, after she was elected to the National Academy of Sciences, she was appointed professor of mathematics, a position from which she retired in 1985 just before her death.
In the summer of 1984 she was stricken with leukemia and, after a gallant battle, she finally succumbed on July 30, 1985.
Julia was the first woman to be elected to the Academy's mathematical section, and the first woman president of the American Mathematical Society. She was appointed a MacArthur Foundation Fellow in February of 1983. She was a leading figure among academic women's organizations and received the Achievement Award of the American Association of University Women.
Julia was loved and admired by her colleagues. Her gentle manner, quiet sense of humor, idealism and integrity, and her obvious and contagious love of mathematics won for her a wide circle of friends around the world.
Julia Robinson is survived by her husband and two sisters: Constance Reid, the well known San Francisco mathematical biographer, and Billie Comstock, a lawyer of Santa Cruz.
Elizabeth Scott
Marina Ratner
John Addison
Leon Henkin
Derrick Lehmer
Robinson's Ph.D. thesis was written under the supervision of Alfred Tarski. In it she settled a difficult problem that had attracted considerable attention for some years. This was the decision problem for the elementary theory of the system of rational numbers (with operations of addition and multiplication). Her solution showed that there cannot be an algorithm which, given any first-order sentence about the rational number system, decides in a finite number of steps whether the sentence is true or false; this result is expressed by saying that the theory is undecidable. Earlier work by Alonzo Church had shown that the elementary theory of the system of integers is undecidable. On the other hand, Tarski had produced an algorithm showing that the elementary theory of the system of real numbers is decidable. The question of the theory of rational numbers was then a very natural one to raise, but it had resisted solution for a long time. To solve it, Robinson brought to bear a deep theorem of number theory, dealing with ternary quadratic forms, that had been proved by Helmut Hasse in 1923.
In all, Robinson published 25 papers. Her first four papers dealt with probability theory, game theory, the subject of her dissertation, and the theory of recursive functions.
Robinson's fifth paper was her first step along a road that led her to fame, and she followed it with eight other papers that brought her very
― 260 ―far along the same road--although not quite to the end. These papers were successive efforts to solve "Hilbert's tenth problem"; this terminology refers to a list of 23 problems proposed at the International Congress of Mathematicians held in 1900 by David Hilbert, generally acknowledged to be the greatest mathematician of his time. Hilbert's list of problems provided a framework for a vast amount of the mathematical research of our century.
Hilbert's 10th problem deals with Diophantine equations, which are equations between two polynomials (in several variables) having integer coefficients. Given any such equation one can look for solutions-integers to be assigned to the variables that will make the equation true. However, it is easy to see that some Diophantine equations have no solutions. Hilbert proposed the problem of finding an algorithm which could determine, in an automatic way involving a finite computation, whether or not any given Diophantine equation has a solution. Robinson set out to prove that there is no such algorithm to be found.
In a series of leapfrogging papers, Robinson, Martin Davis, and Hilary Putmam reached an important milestone in 1960 when it was shown that there is no algorithm for deciding which exponential Diophantine equations have solutions--this is a wider class of equations in which polynomials with variable exponents are considered. Subsequent papers moved closer and closer to a solution of Hilbert's problem. Robinson showed in 1969 that if there is a polynomial equation in one variable whose solutions are all prime numbers and no others, then there could be no algorithm of the kind proposed by Hilbert. The following year a young Soviet mathematician, Yuri Matyjasevic, based on earlier work of Robinson, showed how to construct a Diophantine equation whose solution set is any of a large class of sets, including the set of prime numbers, thus completing the conquest of Hilbert's tenth problem.
During the Second World War, and some years after, Julia did research in Berkeley's Statistical Laboratory under Jerzy Neyman. From time to time, she was invited to teach in the Department of Mathematics, holding the title of lecturer. Then in 1976, after she was elected to the National Academy of Sciences, she was appointed professor of mathematics, a position from which she retired in 1985 just before her death.
In the summer of 1984 she was stricken with leukemia and, after a gallant battle, she finally succumbed on July 30, 1985.
Julia was the first woman to be elected to the Academy's mathematical section, and the first woman president of the American Mathematical Society. She was appointed a MacArthur Foundation Fellow in February of 1983. She was a leading figure among academic women's organizations and received the Achievement Award of the American Association of University Women.
Julia was loved and admired by her colleagues. Her gentle manner, quiet sense of humor, idealism and integrity, and her obvious and contagious love of mathematics won for her a wide circle of friends around the world.
Julia Robinson is survived by her husband and two sisters: Constance Reid, the well known San Francisco mathematical biographer, and Billie Comstock, a lawyer of Santa Cruz.
Elizabeth Scott
Marina Ratner
John Addison
Leon Henkin
Derrick Lehmer
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