Within the past eighteen months, math has even made its way into the movies, with two feature films in which not only was the lead character a mathematician, but we even see mathematics portrayed on the silver screen: Good Will Hunting and Pi.
What's going on here? Math in the movies? Is this the start of a trend? How long before we go to a film and there's a quiz at the end?
I jest, of course. The popular association of math with quizzes is one that I have split much writer's ink -- and several hours in radio and television studios -- trying to overcome. But why did the writers of Good Will Hunting and Pi make their lead characters mathematicians?
Good Will Hunting, written by Matt Damon and Ben Affleck, who both starred in the film, is a Hollywood feel-good movie about the problems involved in moving from one social world to another, brought about by being born with an unusual ability. The hero, Will Hunting (played by Damon), has to have a precocious talent that can surface without any formal training and which the audience will regard as completely incomprehensible, which makes math the number one pick.
Pi, shot on a tiny budget by first-time director Darren Aronovsky in grainy black-and-white, much of it using a shaky hand-held camera, is a dark, brooding, Kafka-esque film about the human obsession to find order in the universe, especially scientific and religious order. Mathematics is the discipline above all that tries to find perfect order in the world. Hence the lead character -- he's hardly a hero in the conventional sense -- is a mathematician. (Much of the universe's order involves the mathematical constant pi, of course, which gives the movie its title.)
In each film, the director had to include sufficient mathematics to establish the characters. The mathematics shown on screen in Good Will Hunting, though correct, is deliberately chosen to be unfamiliar to the audience, and is not explained. Viewers are supposed to be baffled. In Pi, on the other hand, the mathematics shown has to connect to the audience's own (possibly distant) memories of mathematics, and remind them that mathematics involves finding formulas that describe order in the world, formulas that often involve pi. (The familiar formula for the area of a circle is given considerable prominence at one point.)
Math in the movies is unusual, but Good Will Hunting and Pi are not the first films to include some mathematics. In the 1980 romantic comedy It's My Turn, for instance, star Jill Clayburgh plays a college math professor, and the film opens with her lecturing to a graduate mathematics class. She proves a well known (to mathematicians!) theorem of homological algebra. It's all correct. The point of having Clayburgh's character be a mathematician is simply to establish Clayburgh as a highly intelligent intellectual. Math plays no other role in the film (unless you include the eternal triangle).
Going back to 1971, Dustin Hoffman's character in Straw Dogs was also a mathematician. Again, the mathematics shown on the blackboard at one point is the genuine article (gravitational equations on that occasion). And, as with It's My Turn, the aim is to establish Hoffman's credentials as an intellectual -- in his case, as an expert in a field generally regarded as having nothing to do with personal violence. (The director was Sam Peckinpah, so you can guess what kind of ending that film has.)
In the 1992 movie Sneakers, starring Robert Redford, a pair of freelance spies battle foreign agents for a powerful code-breaking chip. As the film makes clear, modern security codes depend on lots of heavy duty mathematics. At one point, we see the chip's inventor lecturing on the mathematics behind its design. Again, it looks right, as it should, given that one of the world's leading experts on the mathematics of cryptography was an advisor on the film.
In the movie Contact (1997), based on the novel by the late Carl Sagan, star Jodie Foster makes a good job of defining prime numbers for a bunch of Washington bigwigs, and explaining why primes provide a good way to communicate with intelligent aliens. (Pi would be better.)
The Mirror Has Two Faces (1996) shows math professor Jeff Bridges explaining the Twin Prime Conjecture (there are infinitely many pairs of primes only two apart, such as 3 and 5 or 11 and 13) to English professor Barbra Streisand.
In a little known 1995 film called Antonia's Line, a chronicle of five generations of women, we see Antonia's granddaughter Theresa grow from being a child prodigy to become a professional mathematician, who, with unfortunate stereotypical coldness, prefers to lecture on cohomology and read research papers on differential geometry rather than nurse her baby. (All the real-life mathematician mothers I know would do both.)
Finally, let's not forget Stand and Deliver, the excellent 1987 dramatization of the real-life story of the late Jaime Escalante, an inspired math teacher who managed to teach calculus to a class of socially deprived, Hispanic high school students in riot torn South Central Los Angeles. This is really about math teaching rather than math, though for most people (apart from mathematicians) the two are the same.
As the lead character says in Pi, mathematics is about identifying and analyzing patterns. What, if any, pattern can we see in the inclusion of mathematics in movies?
Apart from films such as Sneakers, where the plot brings in mathematics automatically, the most common attraction seems to be the very fact that, for most people, math is so incomprehensible. This immediately sets the mathematical character apart in terms of intellectual ability. The audience expects the mathematician to do clever things. The problem facing the director is to show the audience the mathematician at work in a credible way that intrigues at the same time as it baffles.
Do Good Will Hunting and Pi really indicate a new Hollywood trend, where all the leading stars will clamor to play the role of a mathematician? Will we see Clint Eastwood eyeball a young student along a stick of chalk and growl "Go on, prove my theorem." Somehow, I doubt it. Looking back over all those other films involving a mathematician, I suspect that what we witnessed of late was merely the familiar bunching of a random sequence. But who knows? In any event, I'll give my two thumbs up to the idea of having more mathematician movie heroes -- for the simple reason that mathematicians should not be the only group not represented in the movies.
Going back to my original question: Movies apart, why the sudden popular interest in mathematics? In true mathematics instructor fashion, I'll leave that as an exercise for the reader. I'll give my answer in next month's column. Let me know what you think, and I'll try to include some views that differ from mine. (Experience tells me there will be no shortage of those!)
- Keith Devlin