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Julia Robinson and Hilbert's Tenth Problem features a heroine driven by the quest to solve one of the central problems of modern mathematics. She rises above formidable obstacles to assume a leading role in her field. Julia Robinson was the first woman elected to the mathematical section of the National Academy of Sciences, and the first woman to become president of the American Mathematical Society. While tracing Robinson's contribution to the solution of Hilbert's tenth problem, the film illuminates how her work led to an unusual friendship between Russian and American colleagues at the height of the Cold War.