At one point in the film Enigma (2002), Saffron Burrows asks the central character: 'Why are you a mathematician? Do you like sums?'
And she asks this in a silky whisper, against the background of a flickering log fire and a romantic soundtrack by John Barry.
Eventually, the answer comes: 'I like numbers, because, with numbers, truth and beauty are the same thing. You know you're getting somewhere when the equations start looking beautiful. Then you know the numbers are taking you closer to the secret of how things are.'
And soon after this, the kissing begins.
Sadly, this is not how mathematics is usually presented in the cinema. All too often, mathematicians are portrayed as withdrawn, paranoid or even mad. But at least our subject does now seem to be achieving a higher profile in the media, and the book under review captures something of this.
After a general essay on Mathematics in the Cinema, by Michele Emmer, there are short articles on individual films, including A Beautiful Mind, Good Will Hunting, Pi and Enigma, though the last of these is really more of an essay about code-breaking at Bletchley Park in the Second World War. The articles are mostly non-technical, though the one for Cube has a very detailed treatment of the mathematics that the characters need in order to get out of their 'imprisonment' in the film. The book introduced me to several films that I hadn't come across before, including Moebius (1996), in which an underground train full of people disappears because of a topological effect.
The book is not only about mathematics and the cinema; it includes also some other topics from the world of art and technology, ranging from well-illustrated articles on the sculptures of John Robinson and the optics of Euclid, to accounts of public-key cryptography and the problem of visualizing how a sphere can turn itself inside-out.
But it is the cinema part of the book that is the most coherent and distinctive. (I know of no other such book at present, though I would certainly recommend checking out one or two web sites, including http://world.std.com/~reinhold/mathmovies.html.) Both the design and layout of the book are good, though there are many typographical errors. The book may also have suffered somewhat in translation from the original (Italian) edition. In a short account of The Bank, for instance, we read that 'The film... is sprinkled with shots of Mandelbrot's sets... And there's also Julia, who's not only a fine actress but also has a lot of visual appeal.' Now, I have not actually seen The Bank, but I strongly suspect that there is nobody called Julia in it, and that the second sentence is, instead, an absurdly garbled translation of some remark or other about Julia sets.
The book was originally conceived as a contribution to World Mathematical Year 2000, and aims to reach out to non-mathematicians. I suspect, however, that it will be mathematicians who will find it of most interest, essentially as an account of how their subject is gradually finding its way into the media.
Just how effectively this is really happening is, of course, another matter. The book includes a published review of Good Will Hunting which observes that 'mathematics is referred to constantly, but in no scene is it presented coherently'. And the reviewer goes on to liken the film's mathematics to what Alfred Hitchcock used to call the 'MacGuffin', namely an object or idea (such as 'secret plans') which drives the plot and which matters greatly to everyone in the film, but doesn't, of itself, matter much to the audience.
Let us hope that mathematics isn't just a 'MacGuffin' in the cinema for too much longer.
David Acheson (http://www.jesus.ox.ac.uk/~dacheson) is Fellow in Mathematics at Jesus College, Oxford, and the author of 1089 and All That: A Journey into Mathematics.