Julia Bowman's mother died when she was two years old and her father, retiring a year later, moved to Arizona and then later to San Diego. Her schooling was disrupted by a year off school with scarlet fever at age 9. After graduating from San Diego High School she entered San Diego State College. Later she transferred to the University of California at Berkeley. There she became Neyman's assistant but after marrying an assistant professor of mathematics there, she was no longer allowed to teach in the mathematics department. She left mathematics at this time.

In 1946 she visited Princeton and took up mathematics again, working for a doctorate under Tarski's supervision. In her thesis she 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. She also did important work on that problem with Matijasevic after he gave the solution in 1970.

In addition to this work on Hilbert's Tenth Problem, Robinson also wrote on general recursive functions and on primitive recursive functions. 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.

Julia Robinson received many honours. She was the first woman to be elected to the National Academy of Sciences in 1975, the first woman officer of the American Mathematical Society in 1978, and the first woman president of the Society in 1982. She was elected to the American Academy of Arts and Sciences on 1984. She was awarded a MacArthur Fellowship in 1983 in recognition of her contributions to mathematics.