The basic story of "Good Will Hunting" is that of a Boston townie, a 20-year-old blue collar guy too cutely named Will Hunting (or is the movie too cutely titled?), who, while sweeping the corridors of MIT, happens to solve graduate-level math problems when no one is looking. He's apparently better than the MIT professors, including the resident Fields Medalist (read: Nobel Prize in mathematics). He plays a sort of mathematician's elf, who builds intricate and subtle theorems at night.
Will Hunting is not an idiot-savant. He's actually an autodidact who happens to be brilliant at sciences, at math in particular. He also has an asshole personality, you know, the type that's been made heroic in movies over the years. The young brilliant rebel thing, who has social problems and a long rap sheet.
He's eventually discovered by the Fields Medalist, and, in a deal with the court to get Will out of jail time for assaulting a cop, the MIT professor takes him under his wing. They'll solve math problems together. Our prodigy also has to seek counsoling. The counsoling psychiatrist turns out to be Robin Williams, in a role somewhat reminiscent of the Oliver Sacks one in "Awakenings" and the Fisher King in that Holy Grail movie. Williams is good in this, by the way.
In any case, the movie annoyed the hell out of me until we began the psychiatric sessions and the meat of the story, mainly because this story of the unrecognized genius solving math problems that professional mathematicians can't do is an old urban legend, derived from the true story of how George Danzing came up with the simplex method as a grad student in Berkeley. It was also doing the math in an annoying way, even though I haven't really touched the subject in many, many years. Complex proofs apparently can be stated on a single blackboard panel, deep theorems and their proofs, beyond the understanding of a Fields Medalist, can be described on a single sheet of loose leaf, and so on. Movies, to be effective, have to make you suspend belief, and, sometimes, little things will shatter this suspension for some people. For New Yorkers, a scene of characters walking instantly from Zabar's to the Met will do this. For me, in the first part of this film, it was this reference to the urban legend, because I know how badly the legend is phrased, and because I dropped out of math grad school with my inferior parietal lobe somewhat worse for wear. [1]
Actually, another thing I find interesting is the movie's portrayal of intellectuals. This falls back to the old American distrust of intellectuals -- the two most prominent ones in the film, the somewhat effete, scarf-wearing Fields Medalist and this Harvard history grad student in some bar hitting on Minnie Driver -- are both thoroughly trounced, both subtly and obviously, by the Southie Will Hunting. He's better than them, morally, intellectually, physically. As said, it pushes those buttons in the American psyche. As a side note, one of my math professors wore a scarf just like the Field Medalist's, but he was French, and, as an American, I just classified that habit as a French thing.
Anyway, after this first part was out of the way, I actually liked the film a lot. The interactions between Robin Williams and the boy are well written, well acted. The same between the boy and his love interest. It's good movie making. The general story is what you'd expect in this sort of situation -- redemption, forgiveness, and so on until a tear-filled catharsis followed by going after the girl -- but the film handles it well. It's a good movie, highly recommended.
One nice thing, showing the screenwriters' Harvard heritage: the neat, non-explicit Bostonisms, mainly the ubiquitous presence of Dunkin' Donut coffee cups and Au Bon Pain. The townies also have a strong Boston accent which I actually find harder to understand than, say, Mimmie Driver's British accent, and they talk about the Red Sox like it's an old-time religion.
While math is not the primary focus of the film, I found the way it was used interesting, though perhaps not unexpected. Basically, we see only a dense wall of symbols and notation, a veritable foreign language without a Rosetta Stone for the audience, followed by a QED. For all intents and purposes, Will Hunting could have been writing in Sanskrit with little difference. Math, however, can inspire the fear of god in people, while Sanskrit probably doesn't.
So, with the various genius movies in the past few years, the majority have been with music ("Shine", "Amadeus", and maybe one or two others), chess ("Searching for Bobby Fisher"), and just general genius ("Little Man Tate"). As said, there's surprisingly not a single math genius in there (with the possible exception of "Relativity", the Richard Feynman film, though that had more to do with Feynman and his wife, and not Feynman's brilliant physics), despite math's higher intimidation factor, its particular mysteriousness. The only other thing I remember that used a math genius was the Tom Stoppard play, "Arcadia" (and it was used evocatively).
But this isn't that relevant. The movie, in the end, is about a troubled youth that just happens to be a prodigy. It's that genre, rather than the genius genre. Well, geniuses, I think, tend to be depicted as troubled in one way or another, and the movies tend to focus on them reconciling these troubles, so that doesn't say much -- I'm not sure if there is a "genius" genre. Except for "Amadeus", actually, which was about a lesser light reacting to genius. Now, that was a good film. Actually, same for "Arcadia", the Stoppard play, which is about other people's reaction to genius. Actually, I'm not sure what my point is here. Ignore me.
I recently finished a little book on Fermat's Last Theorem. That book, far more than this film, almost made me pull down my old Herstein's "Topics in Algebra" from my bookshelf (Lang's "Algebra" is too intimidating). There's a vague desire to see Galois Theory again, in the old, very particular sense of "see". But this is perhaps just nostalgia, brought on by the book's chatter on fields and abelian groups.
[1] That's the substance of the UL that seems to be based in George Danzig:
A professor talks about "impossible" math problems in class, and puts a few up on the board as examples. Undergrad gets into class late, thinks the problems on the board is homework, goes home, complains that they were really hard but solves them.
The moral of the UL is the usual one about not thinking things are "impossible", and that sometimes the student is smarter than the teacher. There's a positive thinking thing going on, as well as the Biblical one, the "from the mouths of babes" thing.
The real story about Danzig is that he was a grad student -- and so a different kettle of fish altogether -- and the professor was putting some open problems on the board. Open problems are very different from "impossible" problems.
Actually (falling into math folklore), there's a legend apparently told by Danzig that I heard second or third hand from professors. It's a von Neumann story, actually, and perhaps belongs in that subgenre. This is after Danzig got his PhD, and is doing postdoc work at Princeton. Von Neumann is there, and Danzig goes up to him to describe the simplex method. So Danzig is up at the board, writing things down, and after a really short amount of time (the length apparently decreases with each retelling by Danzig), von Neumann gets up and says, "oh, that", sits Danzig down, and proceeds to describe a number of implications of the method. The moral is that von Neumann, after working on game theory for all those years, basically had the ideas of the simplex method swimming around the back of his head, not quite formalized. A simpler moral: von Neumann is god.
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