Good Will Hunting--A Movie Review

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Movie Review

Good Will Hunting Reviewed by Mark Saul

Good Will Hunting who works as a janitor at MIT and cannot resist Miramax Films displaying anonymously his solutions to (suppos- Starring Robin Williams, Matt Damon, Ben Affleck, edly) baffling mathematical problems. The identity Stellan Skarsgard, and Minnie Driver of the solver is discovered just about the time that Screenplay by Ben Affleck and Matt Damon Will (Matt Damon) is arraigned for his part in a Directed by Gus Van Sant street brawl. His subsequent court-ordered su- pervision by a professor of mathematics and Fields The place of mathematics in general culture, and Medalist (Professor Lambeau, played by Stellan particularly in the arts, has varied only a little Skarsgard) includes psychological counseling. This since Plato set the basic tone. He saw mathemat- sets the plot in motion. Will’s feelings about him- ics as pure rationality, but also as a glimpse of di- self, about a woman he courts, about his gift and vine reality contained within even the lowest slave- his background are explored and developed boy. In more recent times this rationality came to through his interaction with the psychologist (mas- be a metaphor for a lack of emotion (Whitman’s terfully portrayed by Robin Williams) whose back- Astronomer) or transcendent but inhuman beauty ground turns out to be similar. (Millay’s Euclid). More recently, Stoppard’s play So what role does mathematics play in all this? Arcadia sets mathematics as rationality against ro- Alfred Hitchcock’s metaphor of the “MacGuffin” manticism but views both as extremes. Luckily, comes to mind: an object or idea that drives the mathematics (but not the physical sciences) has plot and with which everyone in the film, but not been spared the symbolism of forbidden knowl- the audience, is preoccupied. In Hitchcock’s films edge, fraught with ethical dilemmas (Faust, the MacGuffin might be a military secret, a hidden Frankenstein, Rappacini). In contrast, the film Good treasure, or someone’s identity. This film’s Will Hunting is more balanced, and its math- MacGuffins are Will’s talent and the mathematical ematicians are portrayed as more complex than problems that he solves so easily. Will could have those in the works referred to above. been gifted in biology, in physics, in languages Good Will Hunting is in fact not about math- and faced similar issues in his life. In fact, his in- ematics. It is the touching story of a young man’s tellect is drawn larger than life, so that he can talk struggle to transcend his Dickensian childhood, to about economics, learn organic chemistry, and discover his place in the world, and to achieve in- even defend himself in court, citing precedents with timacy with others. The main character, Will (the facility. So why mathematics? title is a play on his name), is a tough and preter- One reason is that mathematics is perceived as naturally gifted orphan from Boston’s South Side so obscure that few can do it. Indeed, this is among Mark Saul teaches mathematics in the Bronxville, NY, the few comments about mathematics that this film school district. His e-mail address is MSaul@ makes with which a mathematical audience will not compuserve.com. agree. The first frames of the film, under the open-

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ing credits, are of a mathematical text out of focus site. O’Donnell says that he built on references in and blurred, as if beheld by a general reader who the script to select mathematical content for film- cannot construe it. The mathematics referred to ing. These references included eigenvectors, com- later on ranges from basic linear algebra, through plex analysis, graph theory, and combinatorics, simple graph theory, to Parseval’s theorem (mis- and the writers’ choices were probably not guided pronounced in the film), Fourier analysis, and on by mathematical coherence. In a telephone inter- to what seem to be some deeper graph theoreti- view O’Donnell revealed that he used a paper on cal results. Mathematics is referred to constantly, graph theory (the reference from Mathematical but in no scene is it presented coherently. Will’s Reviews appears at the end of this article). Those gift, it seems, is valuable partly because it is so rare. curious about this particular MacGuffin are wel- Mathematics also highlights the class distinction come to look. between Will and the academics. Will is a tough So the mathematical reader will enjoy stringing street kid. His gift is admired but not envied by his together the bits of proof and calculation that friends. Had he been gifted in sports or rock music, flash on the screen. Likewise, the Boston denizen the plot could not turn on the choice Will has to will have fun trying to discern which actors grew make between his background and his destiny. up in Boston and which have been coached for their The culture of mathematics does not fit well with accent. MIT alumni and Cambridge hands will that of blue-collar South Boston. amuse themselves identifying the locations (in And it is not particularly “our fault”. Professor fact, most of the film was shot in Toronto, at- Lambeau takes great pains to keep Will out of jail, tracted there by tax breaks and the Canadian dol- to find him a job which uses his talents, and to get lar). All these details have about the same impor- him appropriate counseling. It is Will, out of loy- tance to the total effect of the film. alty to his background, who thwarts Lambeau’s ef- Yet the film does contribute to the public image forts, until a poorly motivated breakthrough in of mathematics. The Fields Medal gets some ex- his therapy (the weakest detail of the film) allows posure, including an incident in a bar where it him to begin a reconciliation between the two emerges that Unabomber Ted Kaczinsky is better worlds he has come to know. known than any Fields Medalist. Some of the most The people that create mathematics fare some- memorable scenes in the film concern a series of what better in the film than the subject itself. Lam- job interviews that Lambeau sets up for Will. Pre- beau is a hard-working guy who drinks and talks dictably Will disdains these offers, but the se- tough with the Robin Williams character. He is quence shows us a glimpse of the import that much more patient with Will’s foibles than one mathematical research has for the emerging world might expect, but not so sensitive to another grad- economy. uate student, a background character who is shown The film can also contribute to the self-knowl- up by Will’s talents, is clearly miffed, but is still edge of the mathematical community. One lesson able to support and admire Will. A third math- we can learn is about social class. It is Will’s back- ematician, an established professor, is crestfallen ground, and not just his abuse as a child, that pre- and humiliated when Will points out an error in a vents his talents from surfacing. We would do well proof and offers the correct alternative on the to remember, in our efforts to include members spot. Each character has a different adaptation to of underrepresented groups in mathematics, that working with the intractable material of math- there can be as much resistance to our efforts ematics, and the viewer will find each in some from the students we work with as from the sys- measure familiar. The least familiar situation is tem we work in. Will’s own. He is not portrayed as ever struggling But social reality is not everything, and Will’s per- with anything mathematical. Without the presence sonal struggle is at the center of the film. Perhaps of such a struggle, the achievement of making a the most important point in this for mathemati- mathematical discovery easily loses its attraction, cians is made by Lambeau’s graduate student, the and so the film misses an essential emotional el- one who finds himself outshone by Will. When ement of the experience of doing mathematics (I Will bridles at some of Lambeau’s suggestions, the am indebted to Hyman Bass for this insight). In- graduate student tells him, in a scene which brings deed, no one in the film is portrayed as taking par- life to this minor character, how lucky he is to ticular pleasure in doing mathematics. have a teacher who cares about him. The film did have “coaches” for the mathemat- And I think we should take this to heart. We ics. One was Daniel Kleitman, of MIT, who tells his don’t nurture our young mathematicians nearly own story in a sidebar. Listed in the credits as enough. Even those who have every advantage of “math consultant” was Patrick O’Donnell, a physi- family, education, and resources have an uphill bat- cist at the University of Toronto, who was originally tle establishing their careers. We would do well to hired as an extra. His authentic Irish brogue is examine our treatment as a community of these heard in a bar scene late in the film, and he can be gifted young people. Mathematical talent is where recognized from a photograph posted on his Web you find it, but remains lodged in us useless un-

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less there is a reason, a personal reward, for de- Reference veloping it. Some are lucky enough to acquire this [1] FRANK HARARY and GEERT PRINS, The number of home- reason on their own, but others need a helping omorphically irreducible trees, and other species, hand. It is not enough for us to spend time hunt- Acta Math. 101 (1959), 141–162, MR 21 #653. ing our good Wills. We must extend our own good will to them as well.

My Career in the Movies One day this spring I got a phone call from some- evening being in two scenes. One was huge, one asking if I would talk to two young men who with perhaps a hundred extras and involved the were writing a screenplay for a movie. I made an hero and heroine walking through Brattle Square appointment with them, and they appeared in my where there were magicians, jugglers, etc., and office. They told me the movie was about a young crowds of extras watching all this amusement. guy they had originally envisioned being a genius This shooting lasted a long time but never ap- in physics, but after talking with Sheldon Glashow peared in the movie. In any case, I was way out of Harvard they had decided his being a math- in left field and never would have been seen. ematician was more plausible. Glashow, who is Afterward a few of us were retained to walk married to my wife’s sister, suggested they come up and down outside the Tasty, a now defunct talk with me. They wanted to hear mathemati- sandwich shop in Harvard Square, while the hero cians talk about mathematics, so that the lines and heroine smooch a bit at the counter with the about mathematics in the film would not be em- window as a backdrop. Strangely enough, in the barrassingly foolish. I felt a bit silly mumbling ran- take that appears in the movie I walk by the win- dom mathematics to nonmathematicians, so I got dow and then do it again in the opposite direc- ahold of Tom Bohman, a postdoc here, and we tion. I guess I was lost. Two more strange things: talked a bit about problems in combinatorics the scene in the Tasty with me visible outside is and graph theory, which are among our fields of in one of the cuts used to advertise the movie; interest. I even gave a short lecture (on Fred also—and this is a first—the review of the movie Galvin’s proof that the stable marriage theorem in the Boston Globe was full of praise for it and implies the k-list colorability of a certain k by k even praised the extras. graph). They also asked for an important un- As another thank you I was invited to the Cam- solved problem that the hero could claim to have bridge premiere of the movie and to the party af- solved. We suggested P = NP and had a discus- terward, where I got to shake hands with the two sion as to which way the hero might resolve this authors and Minnie Driver. They apologized for question. I recall that Ben Affleck suggested that any botching of the math, and I congratulated after the hero announces his solution the MIT them on the movie, which seemed to me to be mathematician should say, “I better tell Mike prize winning, though I rarely go to the movies. Sipser about this.” Unfortunately or fortunately The movie is really about a troubled, intelli- the movie was vague about mathematics and gent young man, and the mathematics is only a did not resolve such serious questions even fic- gimmick to get him a sponsor who will make him tionally. see a psychiatrist. The mathematician seemed a To be honest, I was a bit skeptical at this point bit of a wimp to me, but he could have been much as to whether a movie would actually emerge worse, and he does indeed take an interest in the from all of this, but I was happy to help in any hero and is responsible for anything good that case. happens to him. They left after an hour or two, and we wished Well, my short movie career has brought me them good luck. a credit for advising on a screenplay that has won During the summer I received another call, this a Golden Globe Award and a bit part that actu- time from the man in charge of hiring extras for ally appeared visibly on national television. I can the movie. He offered me, as a sort of reward for now retire from it with satisfaction. my help, a part as an extra. My wife decided I —Daniel J. Kleitman, should agree to do this. So one day in the late Massachusetts Institute of Technology summer I went to Harvard Square and spent an

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