**Julia Bowman**'s parents were Ralph Bowers Bowman and Helen Hall. Julia was the younger of her parents two children, having an elder sister Constance who was two years older. Ralph Bowman owned a machine tool and equipment company while Helen had been a primary school teacher before her marriage. However Ralph seemed to lose interest in his business after his wife Helen died, partly because he had made enough money to support his family from investing it. Julia was two years old when her mother died and after this she and her sister Constance were sent to live in a community of about four houses in the Arizona desert. Ralph remarried Edenia Kridelbaugh a year later, retired from his business at this time, and moved with his new wife to Arizona to be with his children.

The family moved about a lot over the next few years, always being away from the desert in the summer time. Of course there was no school in the middle of the Arizona desert, so when Julia was five years old (and Constance was seven) her new mother Edenia insisted that the family settle permanently somewhere where the children could be sent to school. They chose Point Loma in San Diego which was very small, having around 50 families, with a primary school which had so few pupils that it combined children of different ages into the same classroom. The arrangement allowed both Julia and Constance to progress more rapidly through the levels than might otherwise have been possible. In 1928 Ralph and Edenia had a daughter Billie, so Julia now had a younger sister as well as an elder one. Her schooling was disrupted by a year off school with scarlet fever when she was nine years old.

Scarlet fever marked the beginning of a very difficult time for Julia. The whole family was put in quarantine for a month but soon after she had recovered from one disease Julia was struck down with another, namely rheumatic fever. This time she was sent to the home of a nurse and spent a year in bed before making a slow recovery. By the time she had fully regained her health, Julia had missed two years schooling. The family had already moved away from Point Loma so that Julia could restart school without having the problems of being far behind her friends. However the illness lasted longer than expected and two years seemed too much time for her to make up at the new school. A private tutor was employed and [8]:-

Bowman spent the year 1932-33 at the Theodore Roosevelt Junior High School before entering San Diego High School in 1933. By the time she reached the final years of her schooling she was the only girl in her mathematics class and in her physics class. She did exceptionally well, however, receiving awards in mathematics and sciences as well as the Bausch and Lomb medal for the best science pupil. Although her parents and teachers all expected her to go to college, there was no expectation that she should develop her obvious mathematics talents beyond working towards a teaching qualification.... in one year, working three mornings a week, she and I went through the state syllabuses for the fifth, sixth, seventh, and eighth grades. It makes me wonder how much time must be wasted in classrooms.

After graduating from San Diego High School she entered San Diego State College to study mathematics with the aim of being a high school teacher. Tragedy struck in September 1937 when Ralph Bowman, Julia's father, committed suicide. When he had retired in 1922 he was confident that he had savings which would support his family. However the Great Depression began in 1929 and by 1937 all Ralph Bowman's savings had been wiped out. The family moved to a small apartment and an aunt help provide the funds which allowed Julia and Constance to remain at College. The biggest influence on Bowman's mathematical development at this time came not through her College courses but through reading Bell's *Men of Mathematics*. She recounted [8]:-

Unhappy with the level of mathematics taught at San Diego State College, Bowman transferred to the University of California at Berkeley and after one year there she was awarded an A.B. During that year she took a number theory course from Raphael Robinson and began going for walks with him; on these he would teach her more mathematics which she found very exciting. When Bowman's job applications failed, Neyman found a small amount of money to allow her to stay on at Berkeley as his assistant. A year later, in 1941, she was awarded her M.A. then she turned down a civil service job to remain at Berkeley as a teaching assistant. After marrying Raphael Robinson on 22 December 1941 she was no longer allowed to teach in the mathematics department since her husband was on the mathematics staff. She was unhappy teaching statistics, which was allowed by the rules, but despite this her first publicationThe only idea of real mathematics that I had came from Men of Mathematics. ... I cannot overemphasise the importance of such books about mathematics in the intellectual life of a student like myself completely out of contact with research mathematicians.

*A note on exact sequential analysis*came out of her teaching in the statistics laboratory at Berkeley. Robinson left mathematics at this time.

In 1946 she visited Princeton, where her husband was a visiting professor, and took up mathematics again, working for a doctorate under Tarski's supervision. She wrote [8]:-

In her thesisTarski was a very inspiring teacher. He had a way of setting results into a framework so that they all fit nicely together, and he was always full of problems - he just bubbled over with problems.

*Definability and decision problems in arithmetic*Robinson proved that the arithmetic of rational numbers is undecidable by giving an arithmetical definition of the integers in the rationals. Robinson was awarded a doctorate in 1948 and that same year started work on Hilbert's Tenth Problem: find an effective way to determine whether a Diophantine equation is soluble. Along with Martin Davis and Hilary Putman she gave a fundamental result which contributed to the solution to Hilbert's Tenth Problem, making what became known as the Robinson hypothesis. She also did important work on that problem with Matijasevic after he gave the complete solution in 1970. Let us quote Robinson's own description of the problem which she wrote in an article intended for a general audience in 1975:-

Returning to the year 1949-50, Robinson spent that year at the RAND Corporation working on game theory. As a result of her work at RAND she publishedHilbert in1900posed the problem of finding a method for solving Diophantine equations as the10th problem on his famous list of23problems which he believed should be the major challenges for mathematical research this century. In1970, a22year old Lenigrad mathematician Yuri Matijasevic solved the problem by showing that no such method exists.

Now you are going to ask how could he be sure? He couldn't check each possible method and maybe there were very involved methods that didn't seem to have anything to do with Diophantine equations but still worked. The answer lies in a branch of mathematics called recursion theory which was developed during the1930s by several mathematicians: Church, Gödel, Kleene, Post in the United States, Herbrand in France, Turing in England, Markov in the USSR, etc. The method of proof is based on the fact that there is a Diophantine equation say P(x,y,z,...,w)=0such that the sets of all values of x in all solutions of P =0is too complicated a set to be calculated by any method whatever. If we had a method would tell us whether P(a,y,z,...,w)=0has a solution for a given value of a, then we would have a method of calculating whether a belongs to the set S, and this is impossible.

*An iterative method of solving a game*in the

*Annals of Mathematics*in 1951 in which she proved the convergence of an iterative process for approximating solutions for each player in a finite two-person zero-sum game. This result has been described as the most important theorem in elementary game theory.

In the 1950s Robinson continued to undertake research in mathematics, but also became involved with politics which occupied a lot of her time for around six years. In addition to work on Hilbert's Tenth Problem, Robinson also wrote other important mathematics papers: on general recursive functions (1950), on primitive recursive functions (1955), on the undecidability of algebraic rings and fields (1959) and on decision problems for algebraic rings in 1962 in which she showed that rings of integers of various fields of algebraic numbers are undecidable. Although she kept working on mathematics, Robinson suffered health problems in the 1960s having heart surgery.

In 1971 at a conference in Bucharest Robinson gave a lecture *Solving diophantine equations* in which she set the agenda for continuing to study Diophantine equations following the negative solution to Hilbert's Tenth Problem problem. In this lecture she said:-

In 1980 she gave the American Mathematical Society Colloquium Lectures on computability, Hilbert's Tenth Problem, decision problems for rings and fields, and non-standard models of arithmetic. She was the second woman to give the Colloquium Lectures, the first being Wheeler in 1927.Now it seems to me we should turn the problem around. Instead of asking whether a given Diophantine equation has a solution, ask "for what equations do known methods yield the answer?"

Julia Robinson received many honours. She was the first woman to be elected to the National Academy of Sciences in 1976, and in the same year was appointed to a professorship at the University of California in Berkeley. She was elected to the American Association for the Advancement of Science in 1978, became the first woman officer of the American Mathematical Society in the same year and the first woman president of the Society in 1982. She wrote [8]:-

She was American Mathematical Society Colloquium Lecturer in 1980, the Association for Women in Mathematics Emmy Noether Lecturer in 1982, and elected to the American Academy of Arts and Sciences in 1984. She was awarded a John D and Catherine D MacArthur Foundation Prize in 1983 in recognition of her contributions to mathematics.I found my service as president taxing but very, very satisfying.

Leon Henkin, writing in [5], describes her as follows:-

Let us end this biography by quoting Robinson's own words on how she would wish to be remembered:-The style of quiet decorum she generally adopted was in contrast to the flashes of lively spirit that could be discerned in a wide range of bright or strong feelings when she spoke. Especially strong was her stubborn insistence that opportunity ought to be freely accessible to all - whether economic opportunity or opportunity for access to a mathematical career.

A year after Robinson's death, her husband set up the Julia B Robinson Fellowship Fund to provide fellowships for graduate students in mathematics at Berkeley. When Raphael Robinson died in January 1995 almost all his estate went into the Fellowship Fund.What I really am is a mathematician. Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved.

**Article by:** *J J O'Connor* and *E F Robertson*

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