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Chapter 1 Good Math Hunting Will Hunting, played by Matt Damon, is a mathematical wunderkind. Will has no formal mathematical education, and when we first encounter him as a twenty-year-old in Good Will Hunting (1997), he is working as a janitor at the Massachusetts Institute of Technology (MIT). Will solves a couple of (supposedly) difficult problems left on a blackboard by the math professor Lambeau (Stellan Starsgård). Lambeau is suitably impressed and tries to help Will sort out his somewhat messed up life. To this end, Lambeau enlists the help of his psychologist colleague, Sean (Robin Williams). This is not really a movie about mathematics or mathematicians, but there is plenty of math to be spotted. In fact, having talked to Patrick O’Donnell, a professor of physics at the University of Toronto and the man responsible for most of the mathematics in the movie, we think it would have been great to have included a “math consultant’s commentary” on the DVD. One of our goals here is to provide this missing commentary, a fascinating peek behind the scenes of the mathematical making of Good Will Hunting. This commentary is based on our telephone interview with Patrick O’Donnell, who turns out to be a raconteur. In order to capture the spirit and the fun of O’Donnell’s anecdotes, the following is a fairly literal transcript of the relevant parts of the interview. A second goal of this chapter is to explain the mathematics behind the problems that Will solves. These problems turn out to be quite accessible to anybody unintimidated by matrices. However, any reader should feel free to skip our forays into “higher” mathematics: none of the mathematics is required to appreciate either the movie or Patrick O’Donnell’s engaging commentary . 1.1 How to Become a Math Consultant O’DONNELL: “First of all, the really funny thing is how I became the consultant . A bunch of graduate students and some of our faculty here went out for lunch near the university. We were sitting in this little Vietnamese 3 4 1 Good Math Hunting restaurant and this man and these two women came in and sat near us. The man kept looking at me and I thought: ‘He must know me or something or I know him.’ “Anyway, we left the restaurant and were walking up the street. About twenty feet up the street or so, one of these two women came running up to me and said, ‘We’re making a movie and the director would like to have you as an extra. Would you agree?’ I said, ‘Oh sure that sounds good,’ and so we went back, they took a photograph, and they asked me what I did. “About an hour later they turned up at my office. They had tracked me down, it turned out. When they came in, my board was full of jottings and wave functions and things like that, and the director was very impressed by this, I think, and asked me, ‘Would you be a consultant?’ “So, the next day Gus Van Sant, the director came back with the script, told me the story, and said he wanted the math to be technically correct but he didn’t have to understand it. He didn’t want made up things. “At that stage they had only one math scene written out completely, and that turned out to be totally wrong. It looked like something in number theory, but it had to do with counting patterns and squares of something, and it didn’t make sense. So I had to think of something else. However, in the end the replacement we did for that scene didn’t get into the movie.” 1.2 Actors Versus Blackboards O’DONNELL: “One thing I found about Hollywood is that none of the actors could write on a blackboard. Not at all [laughs]. Essentially all the writing you see, maybe one wasn’t quite, is mine. I did some of it where it really was not appropriate because it was too much of mine. “In fact, we were invited to New York to the premiere. My wife had seen the dailies in the scenes I am the actor in, but had never seen the rest of the movie. She said to me at one point, ‘This is terrible, I see your handwriting everywhere but somebody else is finishing it off!’ “There is one scene (based on a visit...


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