Julia Robinson and Hilbert's Tenth Problem

The film Julia Robinson and Hilbert’s Tenth Problem had its world premier on January 7, 2008 at the Joint Mathematics Meetings in San Diego . George Paul Csicsery, the producer and director, has also produced N Is a Number: A Portrait of Paul Erdös, and Hard Problems: The Road to the World’s Toughest Math Contest, a documentary about the U.S. students at the 2006 International Mathematical Olympiad. So, while mathematics is not necessarily a big item in the world of film, there does seem to be at least a niche.

Julia Robinson and Hilbert’s Tenth Problem is biographical documentary. 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.

Role model she might be, but Julia Robinson was foremost — heart and soul — a mathematician. This film tells the story of her life, in large part through interviews with her sister, Constance Reid. Much of the film focuses on Julia Robinson as a mathematician, and in particular on her work on Hilbert’s tenth problem. (Hilbert’s tenth problem, in brief, asks whether there is a general algorithm that will determine if a polynomial equation in several variables with integer coefficients has a solution in integers.)

The negative answer to Hilbert’s question was finally given in 1970 by 22-year-old Yuri Matiyasevich, but his work built on years of effort and partial results from Julia Robinson, Martin Davis, and Hilary Putnam. A remarkable aspect of the story for me was the graciousness with which Matiyasevich’s solution was met by the others. They were all ambitious and competitive mathematicians, but they showed nothing but pride and admiration (and perhaps relief) at Matiyasevich’s solution. In their own words, Hilbert’s tenth problem had “captured” them and “would not let them go.”

Interviews with Davis and Putnam are an important part of the film. They succeed in giving this rather abstract problem a very human context, and illustrate furthermore both the frustrations and rewards of mathematical work. Supporting interviews with Anita and Solomon Feferman and Lenore Bloom address Julia Robinson’s struggles as a woman to work in a field dominated by men.

The interviews with Yuri Matiyasevich are probably the most powerful part of the film. He and Julia Robinson developed a unique relationship via correspondence in spite of all the obstacles created by the cold war. Matiyasevich describes how he too became obsessed with Hilbert’s tenth problem, was ridiculed for it, forced himself to put his work aside, and then returned to it when a new paper by Julia Robinson appeared. He becomes visibly emotional when he recalls her influence on his life. He says, “I tried to convey the impact of Julia Robinson’s paper on my work by a rather poetic Russian word, which seems to have no direct counterpart in English; roughly it means, ‘as if blown by the wind.’”

Robinson and Matiyasevich finally met at a conference in Bucharest in 1971. Matiyasevich had his home movie camera, and the footage he shot there contains the only known film images of Julia Robinson, with her husband Raphael and Alfred Tarski. That footage is incorporated into Csicsery’s film.

This is a marvelous film and deserves a wide audience.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.