Why maths dramas don't add up

Maths and mathematicians are surprisingly popular subjects for films (the Oscar-winning 'A Beautiful Mind', for example) and plays (the forthcoming 'Proof'). But why, wonders Paul Taylor, do so few of them bother to engage seriously with the subject?

There's a revealingly risible moment towards the beginning of A Beautiful Mind, the Oscar-winning biopic about the mathematician, schizophrenic and Nobel laureate, John Nash. Having sketched in this real-life hero's early academic career ("Princeton, September 1947"), Ron Howard's film shifts the story to "The Pentagon 1953, five years later". It's not just that the first caption manages to get the date of his entry to university wrong (it was, in fact, the autumn of 1948). It's also that the second caption, "1953, five years later" would appear to patronise the audience as a bunch of no-brainers. The movie can't be aspiring to take us all that far into the mathematical mind, you reckon, if it feels obliged to nanny us (however confusingly) through a pretty basic piece of arithmetic.

That hunch proves accurate. As he sinks into paranoid torment, Russell Crowe's Nash gets to draw a lot of complex-looking equations on leaded Ivy League windows – a photogenic eccentricity. But as in Good Will Hunting (where we have to take it on trust that Matt Damon is a trouble-making maths prodigy), these algebraic strings are there primarily as high-tone decor. Next week, Gwyneth Paltrow takes to the Donmar stage in David Auburn's Proof, a Pulitzer prize-winning Broadway play centring on the daughter of a mathematician whose brilliant, unstable career (periods of schizophrenia, followed by remission, followed – in his case – by relapse) bears some resemblance to that of John Nash. The occasion prompts us to consider what distinguishes those plays and films that try to grab bogus cachet by having a brilliant mathematician as protagonist from those that make a genuine effort to turn mathematical and scientific endeavour into far-reaching metaphor.

In A Beautiful Mind, the attempts to dramatise its hero's ideas are few and far between, and undermined by laughable special effects. The young Nash hits on his celebrated "Game Theory" of human behaviour in a bar while working out the odds on getting laid, for him and his mates, when they are confronted by a bevy of brunettes and one busty blonde. Fine, if somewhat foreshortened: but, as he experiences a flash of insight into the key role of co-operation for mutual gain in certain competitive situations, the friends vanish in puffs of smoke. Nash then strides purposefully past the nonplussed blonde and back to his study, where he feverishly scribbles his way into immortality.

The movie is overwhelmingly less interested in Nash as an intellect than as the epitome of self-help Redemption (cue a tearful Nobel prize acceptance speech that would not be out of place at the Oscars ceremony). Crucially, in turning his paranoid delusions into a parody of a Cold War conspiracy thriller, A Beautiful Mind fails to stress the mathematical irony of it. The mad hunt for cryptic messages in newspapers and magazines was essentially like a cartoon travesty – in its belief that all things are secretly connected – of his scientific pursuit of underlying patterns in the universe. Mathematics had flipped over into its insane alter ego: numerology.

In that regard, the movie is not a patch on Darren Aronofsky's extraordinary 1997 film, Pi. Low-budget, shot in black and white on a twitchy hand-held camera, this film pulls you into a monomania that is categorically steeped in maths, as it follows the harrowing horror-comic decline of an obsessive young New York computer whiz, Max Cohen. An increasingly disordered mind in quest of the ultimate numerically patterned order, our pill-popping protagonist is nightmarishly harassed (or so he thinks) by a firm of avaricious Wall Street brokers and a cabal of millenarian Hasidic Jews who share his belief in the all explanatory importance of a 216-digit number. But here the jumbled imagery of paranoia tellingly incorporates diverse diagrams demonstrating the compulsive clarity of maths (everything from the Japanese Go board to the Golden Spiral). Watching this movie, you feel that you know what it would be like to be literally mad about maths.

"Even your depression is mathematical" is a line that would sit well in Pi. It is actually a remark from the play Proof, spoken by the ghost of her father to Catherine, the 25-year-old daughter who gave up her university career to look after him in his sickness and who is now troubled by the cocktail of mental instability and mathematical brilliance she appears to have inherited. The play has many solid virtues, but an ability to turn maths into serious metaphor is not one of them. Just as you can't have an upper storey without a ground floor, this piece suggests that you can't have maths-as-metaphor without first having the maths.

The "proof" of the title refers both to the ground-breaking proof of a theorem in number theory, found in the father's desk after his death, and to the more contentious proof of its authorship. But on the precise nature of mathematical proof, and how this differs, in kind, from proving things about human beings, the play is disappointingly facile and hurried. There's a betraying moment when Hal, a pushy ex-pupil of the father, is about to try to explain the proof to Catherine's sceptical sister Claire, a currency analyst. Proof simply bottles out of that problem, bringing the scene to an abrupt halt with a fade. A professor of maths once told me that the old-timer mathematicians on prize-awarding committees often have to rely on instinct and soundings – the maths itself of the contenders being considered is beyond their comprehension. So, obviously, one is not expecting Auburn to lay out chapter and verse for the theatre audience. But the play needs a deeper examination of the principles involved in distinguishing one type of proof from another.

There is no such cop-out in Tom Stoppard's play Arcadia, which, along with Michael Frayn's superb Copenhagen, offers the most stirring instance of a drama that brilliantly brings home the human implications of mathematical theory, and makes that theory felt on every level, from story to structure. Premiered in 1993, Arcadia has been deeply influential. Its oscillations between 1809 and the present have inspired similar shuttlings between the past and now in such plays about science as Shelagh Stephenson's An Experiment With An Air Pump, and Oxygen by father-of-the-Pill Carl Djerassi and Roald Hoffmann. But the temporal toing-and-froing of Arcadia has the truly profound justification.

Stoppard's play imagines that at the start of the 19th century, a precocious young teenager named Thomasina anticipates the insights of chaos theory as she tries to find a geometry of regular forms. The idea is not so fanciful. Stoppard recognises that work on iterated algorithms – the simple equations that, feeding back y as the next value for x, generate behaviour at once disturbingly unpredictable and deterministic – needs only a pencil, paper and patience. A beautiful mix of intellectual comedy and poignancy, Arcadia gives you the wistful sense that the play's back-and-forth motion is art's attempt to put up a pocket of resistance to the bleak conclusions of Thomasina's discoveries: that all equations are not reversible, as in the Newtonian universe, and that time and energy move entropically in one direction only. The drama acknowledges that, even with this format, only some kinds of things can be recovered.

Arcadia earns its right to metaphor by being prepared to do the groundwork of the maths. The same is true of Frayn's Copenhagen, which hauntingly applies his own Uncertainty Principle to the life of German physicist, Werner Heisenberg. Why, in 1941, did he travel to occupied Denmark to visit his mentor and former colleague, Niels Bohr? In an afterlife limbo, the various possibilities are played out. Was he on an official mission to find out whether the Allies had started building an atom bomb, or on an unofficial mission to let the Allies know that he was surreptitiously slowing down the German atom-bomb programme? Or was he aiming for an anti-nuclear agreement? The Uncertainty Principle states that the more precisely you try to measure the position of a particle, the less you will be able to measure its momentum. This is because the means of observation (ie, the observer and his equipment) will inevitably distort the experiment. By analogy, Frayn's play intimates that precise knowledge of your own motivations is a doomed project, because you inevitably get in the way of yourself. Fundamentally, we are all mysteries. Never have a mathematical theory and a human theme been more deeply enmeshed in drama.

There's a moment towards the end of A Beautiful Mind when the elderly Nash remarks to a student that: "Mathematics... is an art form, no matter what people tell you round here." But that movie and most of its ilk on stage and screen demonstrate the great difficulty of turning mathematical endeavour into dramatic art.

'Proof' opens on 15 May at the Donmar Warehouse, London WC2 (020-7369 1732)