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Julia Hall Bowman Robinson (December 8, 1919 – July 30, 1985) was an American mathematician renowned for her contributions to the fields of computability theory and computational complexity theory–most notably in decision problems. Her work on Hilbert's 10th problem played a crucial role in its ultimate resolution.

Background and education
Robinson was born in St. Louis, Missouri, the daughter of Ralph Bowers Bowman and Helen (Hall) Bowman. Her older sister was the mathematical popularizer and biographer Constance Reid. When the girls were a few years old, the family settled in San Diego, where Julia attended San Diego High School. In 1936, she entered San Diego State University at the age of 16. In 1939, she transferred to University of California, Berkeley for her senior year and received her BA degree in 1940.

After graduating, Robinson continued in graduate studies at Berkeley. As a graduate student, Robinson was employed as a teaching assistant with the Department of Mathematics and later by Jerzy Neyman in the Berkeley Statistical Laboratory, where her work resulted in her first published paper. Robinson received her Ph.D. degree in 1948 under Alfred Tarski with a dissertation on "Definability and Decision Problems in Arithmetic".

Hilbert's tenth problem
Hilbert's tenth problem asks for an algorithm to determine whether a Diophantine equation has any solutions in integers. Robinson began exploring methods for this problem in 1948 while at the RAND Corporation. Her work regarding Diophantine representation for exponentiation and her method of using Pell's equation led to the J.R. hypothesis (named after Robinson) in 1950. Proving this hypothesis would be central in the final solution. Her research publications led to collaborations with Martin Davis, Hilary Putnam, and Yuri Matiyasevich. In 1970, the problem was resolved in the negative; that is, they showed that no such algorithm can exist. Through the 1970's, Robinson continued working with Matiyasevich on one of their solution's corollaries, which stated that"'there is a constant N such that, given a Diophantine equation with any number of parameters and in any number of unknowns, one can effectively transform this equation into another with the same parameters but in only N unknowns such that both equations are solvable or unsolvable for the same values of the parameters.'"At the time the solution was first published, the authors established N = 200. Robinson and Matiyasevich's joint work would produce further reduction to 9 unknowns.

George Csicsery produced and directed a one-hour documentary about Robinson titled Julia Robinson and Hilbert's Tenth Problem, that premiered at the Joint Mathematics Meeting in San Diego on January 7, 2008. Notices of the American Mathematical Society printed a film review and an interview with the director. College Mathematics Journal also published a film review.

Other decidability work
Robinson's Ph.D. thesis, "Definability and Decision Problems in Arithmetic," showed that the theory of the rational numbers was undecidable, by demonstrating that elementary number theory could be defined in terms of the rationals. (Elementary number theory was already known to be undecidable by Gödel's first Incompleteness Theorem.)

Other mathematical works
Robinson's work only strayed from decision problems twice. The first time was her first paper, published in 1948, on sequential analysis in statistics. The second was a paper in game theory where she proved that the fictitious play dynamics converges to the mixed strategy Nash equilibrium in two-player zero-sum games. This was posed by George W. Brown as a prize problem at RAND.

Career
After obtaining her Ph.D., Robinson spend a year working at the RAND Corporation. Robinson occasionally taught for Berkeley's Department of Mathematics and was appointed full professor in 1975. Later one, she served as President of American Mathematical Society from 1983–1984.

Political work
In the 1950s Robinson was active in local Democratic party activities. She was Alan Cranston's campaign manager in Contra Costa County when he ran for his first political office, state controller.

Personal life
She married Berkeley mathematics professor Raphael Robinson in 1941. In 1984, Robinson was diagnosed with leukemia and she passed away in Oakland, California, on July 30, 1985.

Honors

 * United States National Academy of Sciences elected 1976 (first woman mathematician elected );
 * Noether Lecturer 1982;
 * MacArthur Fellowship 1983;
 * President of American Mathematical Society 1983–1984 (first woman president );
 * Fellow of the American Academy of Arts and Sciences 1985;
 * The Julia Robinson Mathematics Festival sponsored by the Mathematical Sciences Research Institute, 2007–2013 and by the American Institute of Mathematics 2013–present, was named in her honor.