I recently saw "Proof", a wonderful play based very loosely on the life of mathematician John Nash. Nash, who after an extremely prolific early career (basically inventing mathematical game theory and making major contributions to elliptic differential equations, topology and geometry) literally went insane for most of the rest of his life, with only brief lapses back into clarity. The play focuses on the daughter of a deceased math professor of Nash's caliber, who seems to have inherited much of her father's genius, as well as (she worries) his propensity toward mental instability.

While the play is going on I am reminded of a lecture entitled "The Madwoman in the Attic" from an undergraduate English course. The course was taught by Elaine Showalter, but most of the ideas were Sandra Gilbert's. Gilbert now has a book out with the same title, subtitled "The Woman Writer and the Nineteenth-Century Literary Imagination". The madwoman reference, of course, is to Bertha in Jane Eyre, but the book makes a larger commentary on the figure of the madwoman in 19th C. literature, and how that image gets applied in a reflexive way to the women writers themselves. Fascinating stuff, actually.

As I left the theater I couldn't get the figurative language of that long-ago lecture out of my head. Something about that image kept lingering in the foreground. The madwoman in the attic.

The madman in the basement.

That was it: I had seen this idea, the mathematician as madman, many times before. And then I think: when have I not seen it? In my head I start to run through portrayals of mathematicians in movies, plays, the press. Hollywood likes to present characters in stereotypes, of course, but we in turn have to view those portrayals as some sort of telltale reflection of how we as a society imagine the targets of the stereotype, or perhaps how we would like to imagine them. And mathematicians, almost without exception, are portrayed as disturbed, antisocial, and sometimes actually insane.

My first thought was that this is merely a stereotypical depiction of high intelligence or brilliance, the "disturbed genius". But in that case you would expect the same kind of portrayal of folks like physicists, who instead tend to appear as eccentric, absent-minded and somewhat loveable, mostly in an isn't-it-cute-he-has-trouble-dressing-himself kind of way.

Part of the problem, I imagine, is that there are plenty of Physics "celebrities" in the popular press and imagination (Einstein, Hawking, Feynman, Penrose, Gell-Mann, etc.) whereas the average moviegoer cannot name even a single mathematician, much less a living one. (Quick...name two living mathematicians. Betcha can't.) A friend of mine who teaches math at the junior high school level asked his students to name as many famous mathematicians as they could, living or dead. Lots of hands apparently shot up, all of which with the intention to name "Einstein". When he pointed out that Einstein was actually a physicist, they were stumped in trying to name anyone further.

To make things worse, the one person associated with mathematics that the public does know is the Unabomber. And the Unabomber has emerged as a sort of prototypical figure that looms over the mathematician in the same way that Einstein looms over the physicist. The physicist is the amiable, frumpy guy in the labcoat making incomprehensible scribbles on the chalkboard. The mathematician is the scary-looking misanthrope building bombs in the basement.

It's difficult enough to find things with mathematicians in them at all, but here are some examples:

(WARNING: many of these contain spoilers, and most of them are good movies you might want to see someday. You've been warned.)

  • Pi (Darren Aronofsky; 1998): Perhaps the most convincing example. A disturbed, antisocial mathematician living in a hovel of a New York walkup filled with computers and paper stumbles upon a number-theoretic code that may unlock many of the secrets of pseudorandom and random numbers. Once this is discovered everyone is after him -- faceless Wall Street corporations, cabalistic religious organizations -- as such knowledge, the film suggests, could literally unravel the fabric of society. But by the end of the movie even he doesn't want to know what he knows, because the more he comes to understand the mathematics he has uncovered the more physical pain he experiences, in the form of extreme headaches and a loud ringing noise. In the end he chooses to literally drill into his head to free himself and restore his sanity. Symbolically he chooses ignorance over understanding--mathematics is reduced to the pain in our heads that drives us away from humanistic and societal concerns. To try to comprehend its deeper secrets is to blur the boundary between man and God, to overreach.
  • Good Will Hunting (Matt Damon; 1997): Damon plays a university janitor from wrong-side-of-the-tracks Boston who is a natural, untrained mathematical genius. He is discovered by a Fields medal-winning faculty member, who tries to mentor him, but has trouble because the boy (despite being the kind of person who's fun to go out and have a few beers with) has deeply-rooted emotional problems. What's most disturbing about this film is the total lack of intellectual and emotional joy that all parties seem to have with mathematics--Damon's character seems to do it because he is cursed with his ability and has to get it out of his system, while the MIT mathematicians seem to all be cold and egotistical, interested more in awards, fame and career advancement than the advancement of knowledge and joy in acquiring it.
  • Proof (David Auburn, playwright, currently on Broadway starring Mary-Louise Parker): As mentioned above, about a daughter of a world famous, recently deceased mathematician who lost his sanity for most of the latter part of his career. Again, as in Pi, doing mathematics, or at least really great mathematics, is associated with insanity and mental instability. His daughter, played by Parker, lives alone and is emotionally troubled.
  • Antonia's Line (1995). Examines five generations of women and the lives they lead, beginning with a Dutch matriarch named Antonia. Antonia's granddaughter Theresa becomes a mathematician, and is portrayed as detached and cold-hearted, at one point choosing to read a paper on differential geometry instead of nursing her child.
  • Breaking the Code (Derek Jacobi, 1996): Chronicles the life of mathematician Alan Turing, who (among other things) was instrumental in breaking the German Enigma code in World War II, as well as coming up with the famous Turing Machine idea that is integral to computing and decidability. Turing was a homosexual, and the film focuses on his feeling like a perpetual outsider in society, both from his sexual preference in an era not at all ready to accept such things and his mathematical abilities and interests. While the film focuses on the social nonacceptance of being gay as the source of Turing's instability and eventual suicide, it nonetheless creates the association between mathematical ability and emotional instability and societal withdrawal.
  • Presumed Innocent (Scott Turow (novel), also 1990 movie): Bonnie Bedelia plays Harrison Ford's wife, who recently completed her math Ph.D. In the end, she turns out to be the one that brutally murdered her husband's mistress.

Compare these to the much more amiable depiction of physicists in movies like I.Q. (Einstein) and Infinity (Feynman), as well as plays such as Copenhagen and Tom Stoppard's works (Arcadia, etc).

What's interesting about this sort of depiction is that it hasn't always been this way. Science used to be scary; before Dr. Einstein, the prototypical scientist figure was Dr. Frankenstein. Early Hollywood is filled with black-and-white portrayals of the "mad scientist", surrounded by bubbling test tubes, high-voltage electrical wires and experimental subjects strapped to tables. Science represented change and the unknown, and people were scared of it. Movies like The Fly telegraphed the message that some secrets of the natural world were best left unexplored.

Then science started to make our lives so much better via the technology it was pumping out on a regular basis that our scientists turned into heroes. They harnessed the atom. They unraveled the secrets of DNA. They put us on the moon, and built the semiconductor. Mathematics played an integral part in most of this, of course, but this is apparently lost on the movie- and theatre-going public.

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References:
Internet movie database, www.imdb.com
"Math in the Movies", http://world.std.com/~reinhold/mathmovies.html

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