Devlin's Angle

December 2001

A Beautiful Mind

This coming January, the movie A Beautiful Mind hits the nation's screens. Inspired by the life of Princeton mathematician John Forbes Nash, winner of the 1994 Nobel Prize for Economics, this will be the latest in a small but growing list of films in which the central character is a mathematician, among them Straw Dogs (1971, starring Dustin Hoffman as the theoretical physicist), It's My Turn (1980, starring Jill Clayburgh as the algebraist), Good Will Hunting (1997, in which Matt Damon was the combinatorist), and Pi (1998, with Sean Gullette as the tortured discrete number theorist). [See pictures at bottom of page.]

As always, when someone attempts to portray mathematics and/or mathematicians for a general audience, I expect the reactions from mathematicians will fall into two camps: those who loudly applaud, and those who complain about all the inaccuracies, the "misrepresentations", the trivializations, and the "sensationalisationism". I get a fair amount of such criticisms when I try to explain mathematical ideas and results to nonmathematicians, either in print or on radio and television. How much worse, then, is it likely to be for director Ron Howard, writer Akiva Goldsman, and star Russell Crowe (whose portrayal of Nash draws significantly on his own interpretation both of a mathematician and of Nash himself)? For as all involved in the film have made very clear, it is not a film biography of Nash. Rather, inspired by author Sylvia Nasar's superb book of the same name - which was a biography, and an extremely well researched one at that - the movie folk set out to create a fictional account of an individual whose life had many of the individual elements of the real John Nash.

Here is how director Howard puts it. (You can find this and subsequent quotes on the movie's website.)

"[The movie] captures the spirit of the journey, and I think that it is authentic in what it conveys to a large extent. Certain aspects of it are dealt with symbolically. How do you understand what goes on inside a person's mind when under stress, when mentally ill, when operating at the highest levels of achievement. The script tries to offer some insight, but it's impossible to be entirely accurate. Most of what is presented in the script is a kind of synthesis of many aspects of Nash's life. I don't think it's outrageous.

We are using [Nash] as a figure, as a kind of symbol. We are using a lot of pivotal moments in his life and his life with Alicia as the sort of bedrock for this movie ... even though we are taking licence, we are trying to deal with it in a fairly authentic way so that an audience is transported and can begin to understand. But they can't begin to understand completely; they never could - no one could."

According to writer Goldsman:
"[W]hat we're doing here is not a literal representation of the life of John Nash, it's a story inspired by the life of John Nash, so what we hope to do is evoke a kind of emotional journey that is reminiscent of the emotional journey that John and Alicia went through. In that sense, it's true - we hope - but it's not factual. For me, it was taking the architecture of his life, the high points, the low points, and then using that as a kind of wire frame, draping invented scenes, invented interactions in order to tell a truthful but somewhat more metaphoric story.

I think that to vet this by exposing it to historical accuracy is absurd. This movie is not about the literal moment-to-moment life of John Nash. It's an invention ... What we did is we used from his life what served the story we are trying to tell, which is why we are saying this is not a biopic. It could never bear up to that kind of scrutiny, it never wanted to, it never pretended to be a biopic. It always wanted to be a human journey, based on someone, inspired by someone's life."

My response to all those mathematicians who will complain about the inaccuracies and "over- dramatizations" of the movie is the same as it is to those who criticize my own attempts to communicate to a general audience (or at least would be if I bothered to respond): You're not the intended audience! (One reader writing about me on recently said he was "insulted" by the way I tried to explain everything in simple terms.) In fact, I never ceased to be amazed that people who have sufficient knowledge and training in mathematics to see inaccuracies in popular portrayals and expositions approach them in the expectation of learning something about the field. Put bluntly, anyone who wants mathematical accuracy should read mathematical journals, research monographs, or textbooks. Popular expositions are an entirely different genre, written for a very different audience, with totally different goals, and they succeed to the extent that they meet the demands of that genre. Likewise movies are something else again.

One of the most derided scenes in Good Will Hunting is where the hero starts to write equations on a bathroom mirror. Conveniently forgetting that the great Irish mathematician Alexander Rowan Hamilton scratched the key identities for the quaternions on a stone bridge - the only writing surface available to him at the time inspiration struck him - the critics scoffed that no mathematician would ever do such a thing. Those critics will surely have another opportunity to trash Hollywood's romanticism with A Beautiful Mind, which has an almost identical scene, in which Crowe writes mathematics on a window pane. (You can see part of this scene on the movie trailer on the web.)

But think for a minute. Whether or not any real mathematician has ever done such a thing, how would you convey to an audience that knows diddly squat about mathematics or mathematicians, that some people live in a world of mathematics, are constantly engaged in mathematical thoughts, even when doing ordinary everyday things, and see the world through mathematical eyes - a mathematical filter on their environment if you will? Depicting a mathematician scribbling formulas on a sheet of paper might be more accurate (and you'll see Crowe doing that in A Beautiful Mind, just as we saw Damon doing it in Good Will Hunting) but it certainly doesn't convey the image of a person passionately involved in mathematics, as does seeing someone write those formulas in steam on a mirror or in wax on a window, nor is it as cinematographically dramatic. In fact, that kind of image is so powerful that we made liberal use of a similar idea in the PBS television documentary series Life by the Numbers, which was intended to be entirely factual. We superimposed numbers and symbols over head-and-upper-body shots of mathematicians to simultaneously convey the idea of an individual living in a symbolic world and the idea of symbolic reasoning being carried out inside that individual's head.

The point surely about a movie is that it is, after all, a movie. It's not a math lesson on celluloid. Nor, in the case of A Beautiful Mind, is it intended to be a history lesson. It's a story, a piece of fiction. Like many great stories, it's inspired by real events. According to the advance publicity (and I am writing this without having seen the film) it even remains true to many specific details of the life of John Nash. Moreover, the filmmakers went to great trouble to ensure that the mathematics in the film - and I'm told there's a lot - is mathematically realistic, by hiring a professional mathematician (Dave Bayer of Columbia University) as a consultant. But as the quotations from the director and the writer above make clear, their primary aim was to make a darned good human-drama film - a piece of quality entertainment.

The issue for those of us in the mathematics business is whether, on balance, we think it's a good thing for mathematics for films to be made in which the main character is a mathematician, seen to "do some mathematics," even if melodramatically, on the screen. Personally, I have no doubt whatsoever that only good can come of it for our profession, not least because one good movie can do more to inspire young children to view mathematics in a positive, indeed exciting, light than any number of federal or state educational initiatives. Or come to that, more than any number of popular expositions of mathematics written by MAA columnists. (Okay, so if I had the talents of Ron Howard or Russell Crowe, maybe I could do a better job.)

If you disagree (and I know some do, although my sense is that the vast majority of mathematicians these days think similarly to me), come along and say so at the special session on How the World Sees Mathematicians that the AMS is organizing at the Joint Mathematics Meetings in San Diego at 4:00PM on Sunday January 6. In addition to viewing some clips from A Beautiful Mind (and some other mathematician movies) you'll also be able to listen to Dave Bayer talk about his experiences working on the movie as math consultant, and to award winning science writer K.C. Cole (Los Angeles Times) letting you in on some of her secrets on how to make a mathematician seem appealing to a general audience. I'll be moderating, and I'll also present some disturbing research findings (not mine) that show just how far we have to go to improve our public image.

PBS will be airing a documentary on Nash on April 28. There is also a web site connected to this program.

Click here to see the trailer to A Beautiful Mind.

Devlin's Angle is updated at the beginning of each month.
Mathematician Keith Devlin ( is the Executive Director of the Center for the Study of Language and Information at Stanford University and "The Math Guy" on NPR's Weekend Edition. His latest book is The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip, published by Basic Books.

Mathematics in the movies