Let’s be real: Watching someone doing math is only slightly more exciting than watching metal corrode. That may be why we’ve never seen a naturalistic depiction of math in the movies; such a snoozer would show someone hunched over a desk or a computer for hours, maybe with a few coffee refills and bathroom breaks. Math is such a mental sport that its dramas, its twists and surprises, its gradual build to Unassailable Truth, are usually locked between the eyes and the fingertips.
But not at the movies! A good math movie can draw out those inner eddies of abstraction. Which is why the math music of movies is so great. Imagine the the task given to a film’s composers as they start to assemble a soundtrack for a math-heavy movie: “Okay folks, in this scene the genius is going to solve some equations, and you have to write music to make people care. Go!” And yet they do it.
Last year’s Hidden Figures, for example, included several scenes where Katherine Johnson (Taraji P. Henson), NASA math genius, obliterator of obstacles rooted in racism, does nothing more than solve equations. And we’re riveted, partly because Henson pulls it off, and also because the soundtrack — by Pharrell Williams, Hans Zimmer, and Benjamin Wallfisch — tells us we should be. (To hear what I’m writing about, and for enhanced experience of this post, play one of the HF math-doing tracks by clicking here. In fact, if you play the music, this post will be better.)
At its best, math movie music helps the rest of us experience the emotional payoff of mathematics: The elegance of a proof, for example, or the underlying beauty of group theory. For just a moment, the music connects us to the mathematician’s mental gymnastics, and while may not get the math itself, we share in her feeling of triumph as she approaches the truth.
Near the end of Hidden Figures, Johnson has to work out the numbers to predict where John Glenn will splash down after his spin as the first American in space. “Give her some space,” says her friend Dorothy Vaughn (Octavia Spencer), reminding us that Johnson’s gifted brain contains a lot of knowledge. The strings swell; we hear a staccato undercurrent faintly, resonant of a ticking clock, or turning gears. After a few tense seconds: Johnson circles a number! Again and again, and again! Dark circles! She did it! She is circling the number! Everybody is about to win everything! Which is why there’s lots of cheering, smiling, and joy in the remaining few minutes.
Unless you have a dead iPhone where your emotional center used to be, you, too, want to cheer. She’s victorious in math, just as she — together with Vaughn and their friend Mary Jackson (Janelle Monáe) — have been stepwise victorious over institutional and personal bigotries. (Monáe, as Jackson, nearly steals the whole movie with a speech about “firsts” in a courthouse.)
There’s a rich history of math in movies, and of math music. Film composers draw from a spectrum of musical tools to tap that weirdly cerebral, abstract experience of doing math. Math soundtracks— no, those weren’t a thing, not until right here, right now—often include a few standard elements. A gradual swelling in the music, like waves, carrying the math-doing character to some amazing application/ conclusion/world-saving insight. Steady, quick beats that shift from the background to the foreground, or get faster or more complicated. Faint voices, like secular angels leading us to The Truth. A grand, wide-eyed finish. Hidden Figures delivers on all these fronts, but it also pulls off a weird aural trick of sounding like it belongs to both times—ours, and that of the characters.
More examples: The movie Pi uses anxious electronica to paint the soundscape of a tortured protagonist who can’t escape seeing mathematical patterns everywhere, at least not until [spoiler!] he discovers trepanning [end spoiler!]. Here’s a link to one of those anxious themes—start at about 2:30. Feeling anxious yet? (How about this: Pi is 20 years old. Now do you feel unsettled?)
Purists gnash their teeth at Pi‘s mathematical nonsense, for good reason. The monologues rehash all the stuff your cool high school calculus teacher talked about, like golden spirals and Fibonacci numbers and fractals, but told to you with the important earnestness of a teen who just discovered On the Road. But with the music, those ideas seems exciting and important and irresistible and dangerous!
Some soundtracks speak to mathematics – even if the movie isn’t explicitly about the field. The German film Run Lola Run doesn’t include any scenes of Lola (Franka Potente) working out equations, but the movie’s engine is decidedly mathematical, driven by nonlinearity and initial conditions. So is its soundtrack, which doubles back on itself in surprising ways, repeating patterns and an underlying tick-tick-ticking. (The movie earns its happy ending, which starts here. You can hear the same musical math themes come into play, just before The Scream.)
Or consider Contact, based on the 1985 novel by Carl Sagan. In this clip, Jodie Foster’s astronomer figures out the pattern underlying a sequence of alien pulses from outer space. The soundscape, combines a growing musical urgency with screechy signals, and it’s monumental. With math, we find aliens! (BTW: The link above takes you to a website that includes lots of movie scenes involving math, compiled by Harvard mathematician Oliver Knill. It’s a fantastic rabbit hole.)
Math can even be funny: The math-doing scene—and math-doing music—that opens Rushmore combines high-school fantasy with trigonometry, with an underlying music that’s all Spanish guitar and brushes on a snare. Take two minutes and watch it here. You’ll have a better day.
Does the math always check out in Tinseltown? Nope, of course not. And you’ll find mathophiles who gleefully point out every fault on film. But I’d argue that it’s enough to get to that spirit of math, the common thrill we all get when all the pieces lock into place, and we glimpse the beauty of precision. Maybe it’s the triumph of mathiness over rigor, but for most of us and our movies, that’s enough. In Hidden Figures, I didn’t pay attention to Johnson’s calculations to see if the writers had done their homework, but I didn’t want to. It was enough to cheer.
Top: Taraji P. Henson as Katherine Goble in Hidden Figures.
The most effective use of math music I saw is somewhere in the documentary, Particle Fever. A theorist is writing on a blackboard, one equation after another, chalk hitting the board bam, bam, bam. Then a sharp little drumbeat comes in, bam bam bam, and you get this idea that it’s the theorist thinking,one thought after another, bam bam bam. Then the scene cuts to the theorist’s feet, now propped up on his desk, his foot tapping bam bam, those equations going step after step all the way to his feet, he’s thinking with his whole body.