Proofs, women, and
youth: a new movie and some old clichés
(October 14, 2005) -- College Park, MD Are genius and madness two sides
of the same coin? Are mathematicians crazy, or are they just eccentric folks
who pop speed to stay up all night proving theorems? What kind of people could
possibly drool over math anyway? And most importantly, is math still a young
man's game?
Like Good Will Hunting (1997) or A Beautiful
Mind (2001)
before it, Proof (rated PG-13) caters to the public's curiosity about
math -- or rather, about those who study it. Based on the award-winning play
by David Auburn, who also co-wrote this adaptation, Proof benefits from Auburn's
insights and extensive research into the math tribe. Auburn became intimate with
their social dynamics, their aspirations, and their idiosyncrasies, and to this
writer -- a former mathematician -- the results sound eerily realistic.
But Proof also plays with, and sometimes indulges in, some trite stereotypes.
To a young woman, the movie's main message could sound like: "You too could
become a great mathematician, but beware, it's a man's world out there." While
women certainly used to be all but shut out from math research, reality may now
be a bit rosier than in the movies, as recent
surveys have shown.
Proof's heroine, Catherine (Gwyneth Paltrow), is a mid-twenties woman mourning
the sudden loss of her father Robert (Anthony Hopkins). Robert, who appears in
Catherine's delusional flashbacks, had been a star mathematician at the University
of Chicago, but in his late years his mind had been ravaged by mental illness.
Catherine, who also had displayed a gift for math earlier in her life, chose
to forgo her graduate studies, and the potential for a career, to spend years
caring for her father. Meanwhile, her sister Claire (Hope Davis) moved to New
York and grew increasingly detached.
Catherine reluctantly allows a former student of Robert's, named Hal (Jake
Gyllenhaal), to go through the papers of her late father, hoping to uncover some
worthy unpublished work. Meanwhile Hal, who has long had an interest in Catherine,
manages to breach the wall of her emotional defensiveness, and a romance begins.
Hal sifts through hundreds of notebooks bearing sad evidence of Robert's hallucinations
-- like the real John Nash, the man portrayed in A Beautiful
Mind, Robert believed
that the aliens were sending him ciphered messages -- until he finds what seems
to be a manuscript of historic importance. It is the proof of an important conjecture,
one that many before had tried, unsuccessfully, to crack. Could it be, as Catherine
insists, that the proof's author was not Robert, but herself -- a loner with
little formal schooling in advanced math, who moreover seems to display early
symptoms of her father's delusions?
When Hal doubts her, she feels betrayed and she is tempted to follow Claire's
invitation to move to New York, in the role of the unstable little sister who
needs to be taken care of.
We never find out what Catherine claims to have proved, although the story
may be hinting at a two-and-a-half-century-old number theory problem called the
Goldbach conjecture. The conjecture says that every even number greater than 3 is
the sum of two prime numbers. (Prime numbers are the whole numbers that are not
the product of whole numbers -- other than themselves and 1.)
The content of Catherine's theorem is left in narrative limbo, like a missing
character in a Samuel Beckett play. Imagine a movie about an artist's life that
offers viewers no glimpse of a single painting, or one about a musician in which
one hears no music. But that's beside the point, as the story is ultimately about
a different kind of proof: the proof Claire and Hal feel they need in order to
believe that the notebook is Catherine's work.
Hal eventually comes to believe Catherine. The math in the notes, he says,
involves concepts too new and "hip" for her father to have learned
during his illness. (Hal mentions noncommutative geometry and random matrices
-- truly new and hip stuff, at least in the 1990's.)
As Hal suggests, Catherine's claim to greatness comes from solving a problem
in one field of math by using ideas from other fields of math. This is, in fact,
one of the modern hallmarks of mathematical genius: As math has become increasingly
diverse and specialized, mathematicians have come to revere those among them
who are able to connect seemingly unrelated concepts -- as Robert puts it in
one scene, making people "talk to each other."
But another supposed feature of mathematical genius -- youth -- may be largely
a stereotype, one that even many mathematicians seem to buy. The characters in
the movie are no exception: "You better get cracking," Catherine recalls
hearing from Robert. "By the time I was your age, I had already done my
best work." Meanwhile Hal, having turned 28 without significant achievements,
already seems condemned to mediocrity.
Some -- though by no means all -- of the famous mathematicians of the past
have had their best ideas at a very young age, and we learn that Robert had already
revolutionized his field by age 22. But as Jordan Ellenberg wrote in Slate, modern
math has become so complex that, by that age, even the most precocious minds
can barely get up to speed with current research. "Today one doesn't find
mathematicians who revolutionize their field -- even once -- before the age of
22," Ellenberg wrote. He mentioned as examples the two most celebrated proofs
of the last decade: Fermat's last theorem, by Andrew Wiles, and the Poincaré
conjecture, by Grigori Perelman. Both mathematicians did their best work in their
mid-to-late 30s.
And while it is true that many mathematicians are intensely competitive, the
movie's suggestion that most use amphetamines to stay up and crank out theorems
is one that most mathematicians would disagree with. At the time Auburn's play
was on Broadway, he reportedly admitted that he was taking "dramatic liberties" here
(see this article about
a public conversation between Auburn and mathematician Robert Osserman).
But the real point of the story is that Catherine is a woman, in a field traditionally
dominated by men. Had she been Robert's son, perhaps she would have had an easier
time convincing people that she could do such great work. All other mathematicians
in the story are men, as Catherine explicitly points out.
In reality, the situation is not as extreme as Proof portrays it, perhaps
inadvertently discouraging young women from entering the field. According to
a recent article by Allyn Jackson, editor of the Notices of the American Mathematical
Society, women are still a minority at all levels of math research, especially
at the tenured professor level, but, "given that there are a lot of talented
young women in the pipeline, that is sure to change." At many universities
and colleges, Jackson wrote, there are signs that women in math may be reaching
a critical mass, the point where their presence is seen as ordinary.
The presence of other women can help recruit new students to the fields, and
it can help women in math be successful in subtle ways, Jackson pointed out. Traditionally,
she reminds us, mathematical street cred comes in part from the boldness in asserting
one's ideas in front of his peers. That's something a woman may be less inclined
to try, she says, especially if she is in a room filled with men.
But for now, Catherine only has Hal.
References:
Contact
Robert Osserman
Professor Emeritus, Stanford University, and
Special Projects Director
Mathematical Sciences Research Institute
510-643-6019
osserman@msri.org
Davide Castelvecchi
dcastelv@aip.org
301-209-3087
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