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. Her father owned a machine equipment company while her mother was a school teacher before marriage. Her mother died when Robinson was 2 years old and her father remarried. Her older sister was the mathematical popularizer and biographer Constance Reid and her younger sister is Billie Comstock. 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.
Mathematical contributions 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 as a statistics lab assistant by Jerzy Neyman in the Berkeley Statistical Laboratory, where her work resulted in her first published paper, titled "A Note on Exact Sequential Analysis". 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 rational numbers 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=BN is definable in the arithmetic of rationals."
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.
Game theory During the late 1940s, Robinson spent a year or so at the RAND Corporation in Santa Monica researching game theory. Her 1949 technical report, "On the Hamiltonian game (a traveling salesman problem)," 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.
Professorship at UC Berkeley Robinson was not allowed to teach in the Mathematics Department at Berkeley after marrying Raphael M. Robinson in 1941, as there was a rule that prevented family members from working together in the same department. Robinson then instead stayed in the statistics department despite wanting to teach calculus. Although Raphael retired in 1973, it was not until 1976 she was offered a full-time professorship position at Berkeley after the department heard of her nomination to the National Academy of Sciences.
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