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Julia Hall Bowman Robinson (December 8, 1919July 30, 1985) was an American mathematician noted for her contributions to the fields of computability theory and computational complexity theory—most notably in . Her work on Hilbert's tenth problem (now known as Matiyasevich's theorem or the MRDP theorem) played a crucial role in its ultimate resolution. Robinson was a 1983 MacArthur Fellow.
When she was 9 years old, she was diagnosed with scarlet fever, which was shortly followed by rheumatic fever. This caused her to miss two years of school. When she was well again, she was privately tutored by a retired primary school teacher. In just one year, she was able to complete fifth, sixth, seventh and eighth year curriculum. While in junior high school, she was given an IQ test in which she scored a 98, a couple points below average, which she explains away as being "unaccustomed to taking tests". Nevertheless, Julia stood out in San Diego High School as the only female student taking advanced classes in mathematics and physics. She graduated high school with a Bausch-Lomb award for being overall outstanding in science.
In 1936, Robinson entered San Diego State University at the age of 16. Dissatisfied with the mathematics curriculum at San Diego State University, she transferred to University of California, Berkeley in 1939 for her senior year. Before she was able to transfer to UC Berkeley, her father committed suicide in 1937 due to financial insecurities. She took five mathematics courses in her first year at Berkeley, one being a number theory course taught by Raphael M. Robinson. She received her BA degree in 1940, and later married Raphael in 1941.
Robinson received her PhD degree in 1948 under Alfred Tarski with a dissertation on "Definability and Decision Problems in Arithmetic". Her dissertation showed that the theory of the was an undecidable problem, 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.)
Here is an excerpt from her thesis:
"This consequence of our discussion is interesting because of a result of Gödel which shows that the variety of relations between integers (and operations on integers) which are arithmetically definable in terms of addition and multiplication of integers is very great. For instance from Theorem 3.2 and Gödel's result, we can conclude that the relation which holds between three rationals A, B, and N if and only if N is a positive integer and A= B N is definable in the arithmetic of rationals."Robinson, J. (1949). Definability and decision problems in arithmetic. Journal of Symbolic Logic, 14(2), 98-114.
In 1950, Robinson first met Martin Davis, then an instructor at the University of Illinois at Urbana-Champaign, who was trying to show that all sets with listability property were Diophantine in contrast to Robinson's attempt to show that a few special sets—including prime numbers and the powers of 2—were Diophantine. Robinson and Davis started collaborating in 1959 and were later joined by Hilary Putnam, they then showed that the solutions to a "Goldilocks" equation was key to Hilbert's tenth problem.
In 1970, the problem was resolved in the negative; that is, they showed that no such algorithm can exist. Through the 1970s, Robinson continued working with Matiyasevich on one of their solution's corollaries, which she once 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.
In her paper, she proved that the fictitious play dynamics converges to the mixed strategy Nash equilibrium in two-player . This was posed by George W. Brown as a prize problem at RAND Corporation.
Robinson was chosen as the first female president of the American Mathematical Society (for the term of 1983–1984) but was unable to complete her term as she was suffering from leukemia. It took time for her to accept the nomination, as stated in her autobiography:
"In 1982 I was nominated for the presidency of the American Mathematical Society. I realized that I had been chosen because I was a woman and because I had the seal of approval, as it were, of the National Academy. After discussion with Raphael, who thought I should decline and save my energy for mathematics, and other members of my family, who differed with him, I decided that as a woman and a mathematician I had no alternative but to accept. I have always tried to do everything I could to encourage talented women to become research mathematicians. I found my service as president of the Society taxing but very, very satisfying."
In 1982, Robinson gave the Noether Lecture of the Association for Women in Mathematics; her lecture was called Functional Equations in Arithmetic. Around this time she also was given the MacArthur Fellowship prize of $60,000. In 1985, she also became a member of the American Academy of Arts and Sciences.
Robinson was also a volunteer for Adlai Stevenson's presidential campaigns.
One of her sisters, Constance Reid, won the Mathematical Association of America's George Pólya Award in 1987 for writing the article "The Autobiography of Julia Robinson".
The Julia Robinson Mathematics Festival, sponsored by the American Institute of Mathematics from 2013 to the present and by the Mathematical Sciences Research Institute from 2007 to 2013, was named in her honor.
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. Julia Robinson and Hilbert's Tenth Problem on IMdB Notices of the American Mathematical Society printed a film review and an interview with the director. The College Mathematics Journal also published a film review.
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