Significant figures: Julia Robinson

Ashleigh Ratcliffe

17 November 2025

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It is no secret that throughout the history of mathematics women have been hidden. As someone with a passion for gender equality and a supporter of initiatives to promote women and underrepresented genders in mathematics, I was surprised to be made aware of a woman who was key to one of the results I had mentioned briefly in a talk (I also regarded this as Matiyasevich’s result in a previous Chalkdust article). Of course, mathematics is a hierarchical subject with new results building upon previous results, usually by different people. While this is good for the progress of the field, it does mean that in many cases the people whose results are a fundamental step are not as recognised as the final step. A key result to the resolution of Hilbert’s tenth problem was made by Julia Robinson, and this is her story.

Early life

Julia Hall Bowman Robinson was born in Missouri, United States on 8 December 1919. When Julia was two, her mother passed away. Her father, a business owner, remarried and raised their children, including Julia, an older sister, Constance Reid, and a younger sister, Billie Comstock. Her biological mother’s passing was not the only major event in Julia’s childhood, as when she was nine she suffered a number of serious illnesses leading to her being out of school for two years, and this is when her attraction to mathematics began.

Julia Robinson was born in St Louis, Missouri. Jefferson National Expansion Memorial, NPS, CC BY 2.0.

Julia’s results

Initially, Julia studied mathematics at university with the intention of being a high-school teacher. Instead, she continued her studies and was awarded a PhD, titled Definability and decision problems in arithmetic at the University of California, Berkeley. Her PhD supervisor was Alfred Tarski, a logician—she was one of his first students! Julia’s work in mathematics was predominantly on decidability, in the context of logic: this is determining whether an algorithm exists to solve a problem in a finite amount of time. One such problem she looked at was Hilbert’s tenth problem: to decide whether an algorithm exists to determine whether a given Diophantine equation has any integer solutions.

Julia’s hypothesis

A Diophantine equation can be written as $P(x_1,\dots,x_n)=m$ where $m$ is a parameter and $x_1,\dots,x_n$ are variables. A Diophantine set, we will call it $S$, is then a subset of integers $m$ for which there exist integers $x_1,\dots,x_n$ such that $P(x_1,\dots,x_n)=m$. For example, the set of natural numbers given by

$\{x \in \mathbb{N} : x = a^2+2b^2, a,b \in \mathbb{Z} \}  = \{1,2,3,4,6,9,\dots\}$

is a Diophantine set. Martin Davis and Hilary Putnam also worked on Hilbert’s tenth problem but from a different direction to Julia. They approached it from a number theory perspective, whereas she approached it as a logician. Julia took a hiatus to pursue politics, during which Davis and Putnam posed a result dependent on two hypotheses. Julia returned to mathematics and removed one of these, but the other remained and Davis and Putnam coined it the JR hypothesis.

University of California, Berkeley. Jefferson National Expansion Memorial, NPS, CC BY 2.0.

The implication of Julia’s result was that, if it were possible to construct a Diophantine set which grows exponentially, this would imply the undecidability of exponential Diophantine equations which would then imply the undecidability of Diophantine equations. To conclude, to show that no such algorithm could exist, it would be necessary to find a Diophantine set that grows exponentially, and this was what Yuri Matiyasevich did!

Being a woman

While studying for her PhD, women were not permitted in the main dining room of the faculty. This meant that Julia could not participate in many mathematical conversations. Fortunately, her husband, Raphael Robinson, was present in these conversations and reported back things he thought she would find interesting, one of which being Hilbert’s tenth problem. While Julia made many mathematical accomplishments, including a plethora of awards such as the MacArthur fellowship and giving the Noether lecture, being a woman in maths came with its own challenges. Despite both being mathematicians in their own right, Julia was not able to get a job in the same department as her husband and although she wanted to teach calculus, ended up working in the statistics department. It took over three years of her husband being retired for her to be made a full-time professor in the mathematics department.

Impact on mathematics

Julia was the first woman elected president of the American Mathematical Society and the first woman mathematician elected to the National Academy of Sciences, but she didn’t want to be remembered just as the first woman to do this. As a mathematician, she wanted to be remembered for the theorems she proved. As well as a big impact towards the final solution of Hilbert’s tenth problem, she also solved one of the Rand Corporation’s prize problems in game theory, but due to being an employee of the company, she never received the prize fund.

Final words

In 1984, Julia Robinson was diagnosed with leukaemia and she died shortly after. Growing up, she was inspired by reading stories about other mathematicians and her sister Constance Reid convinced her to let her write Julia’s biography in the short time before she died.

Ashleigh Ratcliffe

Ashleigh is a PhD student and graduate teaching assistant at the University of Leicester. Her main mathematical interests are in number theory. She is passionate about outreach and inclusion in mathematics, volunteers as a STEM ambassador and is a representative for the Piscopia Initiative.

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