Julia Hall Bowman Robinson

Julia Hall Bowman Robinson (December 8, 1919 – July 30, 1985) was an American mathematician noted for her contributions to the fields of computability theory and computational complexity theory—most notably in decision problems. 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.

Early years Robinson was born in St. Louis, Missouri, the daughter of Ralph Bowers Bowman and Helen (Hall) Bowman. 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. one being a number theory course taught by Raphael M. Robinson. She received her BA degree in 1940,

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 eventual solution. Her research publications would lead to collaborations with Martin Davis, Hilary Putnam, and Yuri Matiyasevich.

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. is the first publication to use the phrase "travelling salesman problem". Shortly thereafter she published a paper called "An Iterative Method of Solving a Game" in 1951. In her paper, 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 Corporation. Alfred Tarski and Jerzy Neyman also flew out to Washington, D.C. to further explain to the National Academy of Sciences why her work is so important and how it tremendously contributed to mathematics. 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." 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.

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.

"I don't remember exactly what happened, but the end result was that Julia involved herself during those years in the nitty-gritty of Democratic Party politics—she registered voters, stuffed envelopes, rang door- bells in neighborhoods where people expected to be paid for their vote. She even served as Alan Cranston's campaign manager for Contra Costa County when he successfully ran for state controller—his first political office."|sign=Constance Reid 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.