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'A Beautiful Mind:' American Pi The beauty of mathematics, says Harvard- and
Oxford-trained mathematician Jonathan David Farley, can never be
fully captured on film By
JONATHAN DAVID FARLEY
Crowe on the set of 'A Beautiful Mind'
Saturday, Jan. 05, 2002 A few months
ago, I was at a party when somebody said, "Listen to this joke: Let
epsilon be a large negative number..." Those of us who were
mathematicians cracked up laughing; everybody else stood around
I would have never laughed at that same joke fourteen years ago.
That was the year before I entered college, and I visited the Math
Department at Harvard University along with a few other students
who, like me, intended to major in math. I remember two things from
that visit: First, a very strange and sheepish boy — a senior with a
perpetual five o'clock shadow and wide, staring eyes, someone whom
we might uncharitably call a "geek" or a "nerd." It was clear that
mathematics was his entire life, and he was undoubtedly good at it.
I prayed I would not become like him. The second thing I remember is
a word we used: "beauty." There were no girls present, so we weren't
referring to them. There were no Monets or Rembrandts around either.
We were talking about the pure, unadulterated beauty of mathematics
itself. And I remember thinking, I'll be damned if I'm ever so lost
as to think of math as beautiful.
Fourteen years later, I am wonderfully, happily Lost — lost in a
surreal world of the imagination, a world not merely of numbers but
of shapes, of structure, of order. I even laugh at math jokes. But
unfortunately, when people ask me what I do, I don't know what to
say. "I study compact disconnected topological spaces." No, that
wouldn't do. When a physicist talks, at least, about atoms and
stars, his audience will nod meaningfully. An artist can show us her
canvas; an economist, money and markets. We mathematicians have
nothing to show. That's why the new movies about math hold such
promise. They're opportunities for others to tell our stories better
than we could hope to.
"A Beautiful Mind," starring Russell Crowe, is the latest film to
make this daring attempt. It's the true story of John Nash, the man
who set the mathematical world ablaze at twenty-one, but went mad at
age thirty; a genius who believed he could speak with
extraterrestrials and who still won the Nobel Prize (in economics —
there is no prize for mathematics). Nash, a diffident, socially
awkward boy from West Virginia, dreamt up the idea that would make
him famous when he was an undergraduate at Carnegie Institute. He
had only ever taken one economics course. Later, at Princeton, he
produced a twenty-seven page thesis which laid the foundations for
the Theory of Games. His theory showed how the rules we use to play
poker can be applied to everything, from Cold War politics, to
evolutionary biology, to economics. Nash's insight was to say that,
whenever two parties have differing interests, they're like
"players" in a "non-cooperative game." The merits or demerits of
their strategies for winning the game can be numerically calculated
and compared until one finds the "Nash equilibrium," the best
strategy for both players. (The Americans and the Soviets both hired
mathematicians during the Cold War to keep it from turning hot.) But
a genius (it's been said) is someone who has two good ideas. Nash,
who dazzled his contemporaries with his quickness, went on to make
seminal contributions to several "pure" fields, areas of mathematics
with no current or future applicability to the real world. Until his
own world fell apart.
Nash is the universal archetype of the mathematician: an erratic
wunderkind on the verge of great discoveries, or madness. We see him
(and occasionally her) in acclaimed films like "Good Will Hunting,"
"Pi," and "Enigma," in award-winning plays like "Proof" and
"Arcadia," even in the sci-fi thriller "Jurassic Park." But why are
we seeing more math on film? Because our lives are increasingly
governed by numbers — PIN numbers, credit card numbers, social
security numbers. All of this information is kept safe thanks to
advances in cryptography — that is, thanks to mathematics. And just
as the threats of the nuclear age thrust physics into the popular
consciousness, the importance of information — and the importance of
protecting it — have done the same for math. If a mathematician were
to prove a theorem called "P=NP" tomorrow, the world's banking
systems might very well collapse, and our nation's military secrets
would be laid bare. (Safe encryption depends on the fact that it's
hard to factor big numbers, numbers with 200 digits or more; "P=NP"
would imply that there's a way to factor numbers — and hence crack
codes — quickly.) Mathematics is what keeps us safe.
While it is gratifying to see Hollywood hunks like Crowe playing
Mathematicians — a sort of "Gladiator" meets "Calculator" — the
beauty of math is too wild to be captured on camera. The real action
takes place in the caverns of the mind, and the enterprise of
mathematics cannot be reduced, for public consumption, to the
formula "boy meets girl." Make no mistake, the romance is there —
the Hungarian mathematician Paul Erdos said he preferred mathematics
to sex, and the Indian genius Ramanujan regarded numbers among his
best friends — but it is a people-less passion. Like Saint Paul, we
mathematicians do not care so much for this world as we do for a
world invisible, a world in which we — however ordinary our lives,
however failed our relationships with other human beings — are
knights-errant on a quest for that elusive beauty, Truth.
Ironically, "A Beautiful Mind," by focusing on that which can be
easily filmed, love affairs and dementia, fails to capture the
beauty of math itself, which is spiritual. It betrays the
prize-winning book of the same name on which it is based. And "A
Beautiful Mind" is a terrible thing to waste.
Dr. Jonathan David
Farley is a Fulbright Distinguished Scholar at Oxford