# Julia Robinson - Mathematician

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Julia Robinson was not expected to live beyond the age of 40 due to the ill health she experienced as a child. However, modern medical treatment enabled her to defy that prediction. After a distinguished career in academic research she became the best-known mathematician in the United States of America, thanks to her role as the first female President of the American Mathematical Society.

### Poor Health

Julia Bowman was born on 8 December, 1919 in St Louis, Missouri. She was the second child of Helen (née Hall) and Ralph Bowman. Helen died when Julia was just two years old. Julia and her older sister Constance lived with their grandmother for a year, then they were joined by Ralph and his new wife Edenia. When Julia was five, the family moved to San Diego, California. The sisters went to a small school where children of various ages were taught together (Constance was two years older than Julia). They were both able to learn quickly, and quickly moved on to studying topics for older age groups.

When Julia was nine, she caught Scarlet Fever. She was not well enough to attend school for a year, and then she developed Rheumatic Fever and had to spend a year in bed. When she was well enough again, she spent three mornings a week with a tutor, catching up on the schooling she had missed. The tutor introduced her to mathematics, and Julia was fascinated to learn that the square root of 2 could be written as a decimal number, but the numbers after the decimal point would never form a repeating pattern^{1}. Julia then spent half a day calculating the square root of 2 as a decimal to check the statement - although she was not able to prove it, her efforts did not disprove it either, so that sparked her interest in numbers.

At San Diego High School, although two of the mathematics teachers were women, by the time Julia was about 15 she was the only girl taking mathematics classes^{2}. She helped the boys with their homework and got good marks for her own work - she won the prize for mathematics at the end of her final year. To celebrate, Ralph and Edenia bought her a slipstick (slide rule) and she named it 'Slippy'.

### University Education

After leaving High School, Julia went to San Diego State College and expected to become a maths teacher. While she was there, her father committed suicide - he had retired in 1922 and had expected to be able to live off his savings for the rest of his life, but the stock market crash of 1929 and the Great Depression caused the money to run out in 1937. Julia's maternal aunt provided funds to enable her and Constance to continue with their education. Constance had completed general teacher training, but had not been able to get a job, so she went to University of California, Berkeley, to qualify to teach English. Julia decided to transfer to Berkeley to complete her mathematics degree. There she was taught Number Theory by Raphael Robinson, and went for walks with him to discuss the subject in more detail.

After obtaining her degree, Julia was offered a number of jobs as a typist, but found work as a laboratory assistant and teaching assistant in statistics at Berkeley. She published her first academic paper, 'A note on exact sequential analysis', during that time. She continued to study and was awarded her Master's Degree in 1941.

Julia and Raphael were married in December of the same year. Julia became pregnant, but lost the baby and then caught viral pneumonia. A doctor examined her and discovered that the Rheumatic Fever she had had as a child had damaged her heart. He advised her not to have a baby, and expected her heart to fail before she was 40.

### More Mathematics

Upset that she was unable to have the family she had wanted, Julia was 'deeply depressed' for a time, but returned to mathematics and started working towards a doctorate with the support of Raphael. Her thesis, entitled 'Definability and Decision Problems in Arithmetic', completed under the supervision of Alfred Tarski, involved concepts in mathematical logic that had been introduced by Kurt Gödel and also linked in with concepts such as the Turing Machine. Julia was awarded her PhD in 1948.

In 1900, David Hilbert proposed a list of 23 'Mathematical Problems' that he thought would influence the development of mathematics in the 20th Century^{3}. The Tenth Problem asked whether there was a method to determine whether a given Diophantine Equation could be solved. This question related to the work of Julia's thesis, so she started tackling it in 1948.

In 1949 Julia spent a year working on Game Theory and published a paper entitled 'An Iterative Method for Solving a Game'. She then spent some time working on hydrodynamics, but did not have any success in that field. During the (Republican) McCarthy Era in the 1950s she spent time supporting political campaigns for the Democratic Party.

In 1961, she and colleagues Martin Davis and Hilary Putnam published a paper relating to the Tenth Problem, and it included the JR Hypothesis, named after her. By then she was 41. Pioneering heart surgery was successful - just a month after the operation, she was able to take up cycling.

Julia came close to solving the Tenth Problem, but it was the 22-year-old Yuri Matijasevic who made the final breakthrough in 1970 - he found an equation that confirmed the JR Hypothesis was true and hence proved that there was no universal method to work out whether a Diophantine Equation could be solved. Julia corresponded with Yuri and met him twice. They collaborated on a number of papers exploring the applications of the Tenth Problem result.

### Honours

For her contribution to solving the Tenth Problem, in 1975 Julia Robinson became the first woman mathematician to be elected to the National Academy of Sciences and she was awarded a professorship at Berkeley. In 1982 she accepted the role of President of the American Mathematical Society - although it left her limited time for her own research, she was keen to encourage other women to become mathematicians.

In 1984, Julia was diagnosed with leukæmia. At first she responded to treatment, and was able to continue cycling. She also started writing her autobiography with the help of her sister (Constance Reid, as she was then, had become known as a biographer of mathematicians, including David Hilbert, thanks to Julia's encouragement). On 30 July, 1985, at the age of 65, Julia Robinson died.

*The Autobiography of Julia Robinson* is available online. Constance Reid's biography of her sister, written in collaboration with Raphael, is entitled 'Julia Bowman Robinson (1919–1985)' in *Women of Mathematics, a Bibliographic Source Book*, 1987. In 1986, Raphael established the Julia B Robinson Fellowship Fund to support mathematics graduates at Berkeley to continue with their studies. And in 1996 the book *Julia, a Life in Mathematics*, by Constance Reid in collaboration with Lisl Gaal, Martin Davis and Yuri Matijasevic, was published by the Mathematical Association of America. A share of the royalties from the book went to fund the Julia Bowman Robinson Prize for Mathematics at San Diego High School.

^{1}That is, the square root of 2 is an irrational number.

^{2}She was also the only girl taking physics.

^{3}The Problems did indeed lead to important new mathematics, such as optimum sphere packing methods, and some of the questions are still being explored in the 21st Century.