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Hilbert asked for a general method of ascertaining whether a polynomial equation with whole number coefficients has a solution. Three American mathematicians—Martin Davis, Hilary Putnam, and Julia Robinson—were "captured" very early in their respective careers by Hilbert's tenth. In their own words, "it would not let them go." Julia Robinson told her sister, Constance Reid, that she did not want to die without knowing the answer, even if she herself did not solve the problem. Then, in 1970, a 22-year-old Russian mathematician named Yuri Matiyasevich put in place the last, necessary piece for the solution. The negative answer to Hilbert's question turned out to be a solution with significant implications for the development of computer science. Three of the four mathematicians involved in solving H10 are in the film. Fortunately, Julia Robinson's place in the film is filled by her biographer and sister, Constance Reid, who also wrote highly acclaimed biographies of David Hilbert and of other modern mathematicians, including E. T. Bell. Treatment and Style We meet Julia Robinson through shots of a three-year-old girl (Eva Liddle) as she squats under a giant saguaro cactus in the Arizona desert. A closer look reveals that she is lining up stones in neat rows, creating sequences of numbers. This reenacted moment is recalled by Robinson's sister, closest friend, and biographer, Constance Reid, who plays a central role in Julia's story, and in the film.
The thread of these comments returns to the film's main theme of Julia's interest in unsolved problems, and to her decades-long obsession with Hilbert's tenth problem (H10). Throughout the film, the three living mathematicians who were involved in its solution, describe their work in the context of her contribution. Robinson's own words, taken from papers, speeches, letters, and from the autobiography, Julia, a Life in Mathematics—dictated to Constance Reid before her death in 1985—are brought to life using the voice of an actress who is never seen in the film. Where did Julia Robinson's passion for mathematics come from, and how was it nurtured? Robinson's childhood is presented through her father Ralph Bowman's beautiful black and white photographs of the Bowman family's life, and scenes filmed with Constance Reid in present-day San Diego. Locations include early years in the desert near Phoenix, Arizona, the home on Point Loma where Robinson suffered the illness that changed her life and drastically affected her mathematical career. Following a series of childhood illnesses that kept her out of school during her early teens, Julia developed an early fascination with numbers. This led to a pursuit of mathematics at San Diego High School. One question raised by the film: did disease and isolation prepare her for being the only girl in her mathematics class, and for a life of being different? During the 1930s, Julia was clearly an exception. Girls in the United States did not pursue scientific studies. "What are we going to do with a girl like that?" asked her stepmother in a comment about Julia's unflagging interest in science and mathematics. It is a line Constance Reid likes to quote. She recounts the story on stage at the 1999 San Diego High School graduation ceremony. Throughout the film, Reid's presence provides an echo of Julia Robinson herself, describing Robinson's decisions, feelings, and motives, as Robinson confided these to her sister. Reid's collection of papers and photographs further enrich the film with authentic archival materials. Robinson's own words, taken from papers, speeches, letters, and from the autobiography, Julia, a Life in Mathematics—dictated to Constance Reid before Robinson's death in 1985—are brought to life through two surviving clips of Julia Robinson's own voice, and readings by narrator Danica McKellar.
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In Paris, on the morning of Wednesday, August 8, 1900, David Hilbert, the most scientifically charismatic mathematician of his time, proposed to his fellow mathematicians a list of problems, the solving of which he felt would make for great mathematical progress during the coming century. The story of H10 and its solution is nested within this biographical film about Julia Robinson.
The introductory sequence segues into a series of statements by prominent mathematicians and collaborators appraising Julia's skill as a research mathematician, and her accomplishments late in life as a pioneer and role model for women in American mathematics. A key person in this section is Carnegie-Mellon Professor Lenore Blum, a leading mathematician who has written about Julia Robinson and her work. Blum conveys some of the film's most important themes concerning the struggles of American women in mathematics. One of the tensions in the film is a debate over whether or not Julia Robinson suffered discrimination because she was a woman in a field dominated by men. On some questions there are contradictory statements from different sources. For example: 1.) Julia was prevented from holding a tenured position until late in life primarily because the mathematics department at the University of California, Berkeley, discriminated against women; and 2.) freedom from academic responsibility gave her the time she needed to pursue what really interested her—pure research instead of teaching.