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.

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.

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.