How Julia Robinson helped define the limits of mathematical knowledge

Every December 8 for years, Julia Robinson blew out the candles on her birthday cake and made the same wish: that someday she would know the answer to Hilbert’s 10th problem. Though she worked on the problem, she did not care about crossing the finish line herself. “I felt that I couldn’t bear to die without knowing the answer,” she told her sister.

Diagnosed with scarlet fever and then rheumatic fever at age 9, Julia lived away from home with a nurse. In the image above, she has returned home for a visit.Penicillin had just been discovered and was not yet available as a treatment. Instead, she lived at the home of a nurse for a year, missing two years of school.

If an equation does have integer solutions, you do not need to be particularly clever to find them — you just need to be patient. A brute-force search will eventually give you numbers that work. But if you do not know whether the equation can be solved in integers, you will never know whether your failure to find a solution is because none exists or because you have not been patient enough.=k, where k is a positive integer .

Shortly after getting her bachelor’s degree from UC Berkeley, Julia married mathematician Raphael Robinson. They are shown here beside their first home.When she was elected to the National Academy of Sciences in 1976, the university press office had to call the mathematics department to ask who Julia Robinson was. UC Berkeley quickly made her a full professor.

He was asked to review it — a mere five pages about the relative growth of solutions to certain Diophantine equations in two variables. Her ideas immediately sparked new ideas for him, and he was able to produce the needed “Goldilocks.”

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