From Connect® magazine
January/February, 2003
Volume 16 Issue 3

Seeing the Star in Math

by Dan Rockmore

We asked Dan Rockmore, professor of math and filmmaker, to give us a sense of the place of mathematics in the modern world. He also reflects on the lives of mathematicians as well as the math experiences of children. --EDITOR

I like to tell people that one of the great things about mathematics is that with a background in math you can do just about anything. Do you want to design the first great anti-cancer drug? Well, its the mathematics of shape, in the form of geometry and topology that helps you unravel the twists and turns of the DNA molecule, while knowing something about combinatorics helps you sort through the billions of possible messages in the genetic sequence. Need a way to keep your credit card number secret while internet shopping? This time it's the mathematics of number theory that has made possible the secure communication codes that hide your account number from evil electronic eavesdroppers. Or maybe you want to make the next great CD player or digital camera? Then you'll want to know a little bit about the math of bits n' bytes, called signal processing.

For medicine, communications, even the arts--math can open doors. Oh, there's one more: I've recently discovered that math can also provide a road to movie-making!

"The Math Life"

Inspired by another recent movie, one with a slightly larger budget, "Good Will Hunting," I've completed a two-year collaboration with filmmakers Wendy Conquest and Bob Drake. With the support of the National Science Foundation (NSF), we've been making a documentary film on the people, problems, and process of mathematical research.

We have been interviewing mathematicians all around the country, trying to get to the heart of what makes mathematicians tick. We've called the resulting film "The Math Life." It is now available for distribution through Films in the Humanities and Sciences, and will soon be appearing on a public television station near you.

Young mathematicians at work You may remember that in "Good Will Hunting," Matt Damon plays a wrong-side-of-the-tracks kid, Will Hunting. While working as a janitor at MIT, he happens upon a mathematics problem left on a blackboard. Unbeknownst to Will this is an incredibly difficult problem, but in a flash of insight (in spite of seemingly having no background in mathematics) he solves the problem. He is thus propelled into what is portrayed as the high-powered and cutthroat world of academic mathematics, and slowly comes to grips with the new opportunities afforded by the revelation of his genius. Of course there is also a beautiful right-side-of-the-tracks Harvard girlfriend (Minnie Driver) to help him along, as well as a kindly (albeit damaged) therapist (Robin Williams) who learns a thing or two about life from helping Will work through his anger management problems.

Friends kept asking me what I thought of this "math movie." I felt the same as many people did; I liked it. It is a good Hollywood love story--but is definitely not a movie about math! From the tried and (less than true) stereotype of, "born to be mathematician or not," to an arrogant genius deriding an apocryphal assistant, it's just not like that.

So, I began to think about making a film that showed what research mathematics was really like. I wanted to give some insight into what it means to "do" mathematics, and then to reveal it for the diverse world that it is, both in terms of the people who do it, and the intellects that are attracted to it. In short, I wanted to show that mathematics is more than just numbers and mathematicians are more than just the extreme personalities that periodically make it to the big, or little, screen.

The meandering road to mathematics

In "The Math Life," we trace the arc of a career as mathematician. We start at the beginning, touching upon some of the different and surprising ways in which some people have been brought to mathematics. There are naïve, wonder-inspired beginnings, as well as frustration-laden false starts. Stanford's Persi Diaconis tells of being led to mathematics from mysteries of magic and card shuffling. Princeton's Ingrid Daubecheis remembers discovering the wonder of pi after measuring the diameters and circumferences of all the platters in the house. Dartmouth's Dorothy Wallace, (recipient of the 2000 New Hampshire Professor of the Year), recalls that as a schoolchild, she was labeled as slow due to her lack of facility with fractions. The road to a career in math can be, and often is, a meandering one. Along the way we discuss some of the things that attract people to mathematics.

Exploring problems of scale As Wallace's story shows, mathematics is done by all kinds of people with all sorts of different skills and aptitudes--not just the quiet kid in the back who got all the multiplication problems right. Those with a talent for picturing things find their way to subjects like geometry and topology. A love of numbers leads others to become number theorists. A fascination with randomness is the first step on a road to probability and statistics. A desire to understand the workings of the world can be the hook to becoming an applied mathematician.

Indeed, Wallace's story is but one of several cautionary tales for educators embedded in "The Math Life." Cornell's Steven Strogatz recalls almost, "being derailed," by a classroom experience. Microsoft's Michael Freedman (winner of the Fields Medal, mathematics Nobel Prize equivalent) reminds us that an aptitude for mathematics is reflected less in, "getting A's on all the tests," than in having a "quirky" mind, able to produce a different reason to explain why something is true. Many of the mathematicians we interviewed told horror stories of being browbeaten for not getting the right answer in the "right" way.

Implications for the classroom

When teaching, we need to be continually vigilant against shoehorning students' intellect into a one-size-fits-all template as well as being continually supportive of creative and nonstandard problem-solving techniques. It is important, especially in the early years, to remember that different children do have different ways of learning. There are a variety of ways in which one can acquire the basic understandings and skills necessary to solve, and enjoy solving mathematics. Many an educator has told me that in spite of most people's recollection of that last "killer" math course that caused them to abandon ship, the early mathematical experiences are by and large enjoyable and intoxicating. Children relish the chance to think about a problem on their own as well as the right/wrong nature of their answers.

If being a mathematician is in someone's future, well then, they are entering a discipline that is a funny mixture of art and science. It is on the one hand, freer than the natural sciences in that mathematicians really are at liberty to create abstract worlds bound only by imagination, often divorced from reality. We can, and do, study worlds of infinite dimensions, investigate abstract symbolic universes that obey only the weakest of algebraic laws, and in general, often just dream things up for the fun of it. This is math as poetry, but a poetry that provides a language mysteriously well-suited to describing the world around us.

On the other hand, whatever strange new worlds we do create, our conclusions and derivations are always bound to the strictest of logical laws. Science posits theories, conclusions that are only as good as their most recent empirical validation. Fire, water, air, and earth eventually gave way to the elements, which in turn stepped aside for the atom, which then had to admit the electron, proton, and neutron, only to genuflect to the quark. But, mathematics is about theorems, and a theorem is forever.

In the film, we touch on the process of choosing a problem and then working on it. Along the way, we describe some of the main areas comprising modern mathematical research, each of which is illustrated by artistic metaphor, as well as graphic animations. I can't resist pointing out that these cool graphics have all been enabled by a multitude of mathematical advances. Mathematicians experience the ups and downs that accompany any creative endeavor. We relive some of the individual concomitant frustrations that are perhaps particular to mathematical research as well as the excitement of discovery that is rare, but not impossible.

In spite of what recent Hollywood movies (such as "A Beautiful Mind") might have you believe, the inside of the head of a mathematician is not such a scary place--a good sense of humor is just as important as the ability to focus the intellect. Mathematicians are more than just the cartoon mix of genius and arrogance that we usually see on the big screen.

Dan Rockmore is Professor of Mathematics and Computer Science at Dartmouth College, Hanover, New Hampshire, where he is also Vice-Chair of Mathematics. His research interests focus on the mathematics of signal and image processing. He can be reached by email at or through his webpage;