Much of what I said about David Auburn's script when I reviewed the Saint John Theatre Company's production a couple of springs ago still applies. John Dryden said it, well over three centuries ago: "Great wits are sure to madness near allied, / And thin partitions do their bounds divide." Whether it's true or not, the idea has undergirded a substantial number of plays, novels and films. Most recently, it seems to have been mathematics rather than poetry that has teetered on that brink. Consider the success of the 2001 Ron Howard film, A Beautiful Mind, about the struggles of mathematician John Nash with schizophrenia, and the opening of David Auburn's Proof the year before at the Manhattan Theatre Club. Both works suggest that there's some connection between mental illness and the ability to manipulate the extreme, patterned complexity of higher-order mathematics.

Though the two stories are quite different, there's one fundamental similarity: both attempt to be about the people rather than the ideas, and in both -- unlike, for example, Tom Stoppard's Arcadia or Michael Frayn's Copenhagen -- the demands on the audience's ability to understand complex concepts are kept to a minimum. In fact, both have been sneered at for this (though both have been respectfully reviewed in mathematical journals).

Proof, indeed, is an immensely smart and well constructed script, full of neatly structured dialogue, real human emotion, clever storytelling and elegant stagecraft, as well as characters -- three of them, at least -- that you can come to care about. The premise is this (though things aren't presented in this order): Catherine is the potentially brilliant daughter of a certifiably brilliant mathematician, Robert, who spends the last couple of decades of his life, as he phrases it, "bughouse," with Catherine sacrificing her career and possibly her personal life to care for him, in the hope that she may be able to extend his rare periods of lucidity. During one of the longer periods of lucidity, he begins taking students again, at the University of Chicago, and Catherine thinks she may have a chance to study mathematics, at Northwestern. During this period he takes on a grad student, Hal, who worships him, and notices Catherine. As the play opens, it is four years after his last lucid period. Robert has recently died; Catherine is fantasizing (or dreaming) conversations with him; her sister Claire, who has been off pursuing her career in New York and handling finances, is home for the funeral and the usual tying up of loose ends (including Catherine and the ramshackle family home); and Hal, now an assistant professor, is in the attic going through the scores of notebooks left by the graphomanic Robert, looking for any glimpses of the genius which had once been there.

The entire play takes place on the back porch of the Chicago home, and is craftily structured to accommodate a couple of flashbacks and to help the audience see the parallels between, say, Catherine's caring for Robert and Claire's attempts to "care for" Catherine, between Robert's manic monologues and Catherine's, between the way the naive, geeky Hal worships Robert and the way he worships Catherine. In terms of plot, what happens is that Catherine, deeply suspicious of Hal at first, comes to trust him, shows him the one notebook with something of value in it (locked in a desk to which she awards him the key as a gesture of trust). The notebook contains what Hal is convinced is a monumental work of mathematical genius, a "proof" of something to do with prime numbers (it's never, of course, clear to us exactly what). After Catherine, as a wonderful first act closer, announces that it wasn't Robert who created it, but her, the question becomes who believes her and what would constitute "proof" that it was indeed her creation.

All this is folded around a romanticized (but plausible) presentation of the community of mathematicians (typified by the account of a rock band made up of mathematicians playing "i" -- three minutes of silence, an "imaginary number"), a dramatization of the mutual recriminations familiar to everyone who's shared with her siblings (inequitably, of course) the duty of caring for an aged or infirm parent, and the difficult, prickly building of a relationship between two not-very-socially-adept mathematicians.

It's an odd play to put in a space like the Black Box; a completely naturalistic porch and patio, for example, sit oddly against the black and "invisible" wall of the Box, and a script which is pretty much unremittingly naturalistic (even the opening scene, in which Catherine has a conversation with her dead father, depends on the audience's accepting the scene as exactly what's happening, up until the moment when he announces that, after all, he's dead). But Ilkay Silk's company convinced me again that the space is pretty much infinitely adaptable -- and that the script, while it has always seemed to me just a touch too neat, can yield a moving and powerful evening of theatre, in which we come to have deep sympathy for both sides of a number of conflicts. All four characters are elegantly designed to afford actors a chance to go after something complicated, and invite an audience to see them as at once sympathetic and understandable and at the same time contrary, opinionated, difficult. Even Hal, who on one reading, is the play's raissoneur -- the character who stands in for the author and, like a chorus, thinks what we think, is not entirely above suspicion: his academic ambitions, coupled with the fact that, at 28, he considers himself washed up as a mathematician, give us reason to suspect that Catherine's view -- that he's trying to profit from her father's legacy -- may have something to it. Step Taylor's Hal -- articulate to a fault, shuffling and unconfident, charming, boyish and open -- may not have allowed enough of that darkness to emerge: but even so, his skill at making dialogue feel like dialogue rather than lines provides a good deal of the lubrication need to keep us engaged in conversations. His Hal's interior life is suggested partly by a subtle speech tick, a pause between words in sentences which ought not to have pauses -- "it might / help"; "I don't have time / to do this" -- creates the impression that the machinery" (as
Robert terms the mind) is ticking along faster than his syntax. And in the end, despite our better judgment, we're brought to believe that the suspicious and perhaps paranoid Catherine might just have been persuaded by his charm to sit down on the porch steps with Hal and start explaining her proof.

The most challenging role in the play is that of Catherine's sister Claire -- uncomprehending of Catherine and of the world she lives in (as well as of Robert and Hal), she's everyone's nightmare of an older sister: competent, sympathetic, helpful, supremely confident, condescending, successful in her profession. As Auburn's script leads us deeper into the difficult world Catherine and her father have been living in, and the passion they and Hal share for mathematics, it also shuts Claire out.
She doesn't understand how someone could live as Catherine seems to, or why the notebook in which her proof is written out matters so much, or why someone wouldn't care about having a shampoo whose secret ingredient makes your hair shiny and healthy. To make her something other than a monster -- for instance, to make us feel badly when, at the end, Catherine says that she'd been silent for days because "I didn't want to talk to you" and she slumps for a moment, and then leaves, to go back to New York alone -- is a challenge that Leah Holder comes awfully close to meeting. She does so partly with the forced brightness with which she keeps telling Catherine how wonderful New York is, how much better than provincial Chicago, and her wounded, vulnerable responses when Catherine divines what she's doing, explaining to poor Claire that she knows what Claire's planning because "I'm smarter than you."

In a way, the role of Robert is easier: everyone knows that playing mad scenes is almost as easy as playing drunkards. But Darrell Mesheau's Robert is the most powerful performance I've seen him give in the Black Box, where often he's taken small roles as a kind of solid anchor, an island of mature competence to give student actors a sense of certainty. His Robert -- hands on hips or arms folded, voice sure and full -- exudes confidence and charisma, in the incarnation of him we first meet, which is, of course, Catherine's fantasy memory of him; but the real Robert we meet next, the Robert who's attained a delicate interval of sanity, a remission of his madness, during which he takes on Hal as a student, is another matter: more touchy, more irritable, more extreme in his emotions, and, in fact, a good deal more sympathetic. His monologue on how much he loves the fall in an academic context like Hyde Park, with the students coming back and crowding the bookstores and the vivid, exciting weather is a virtual elegy for what an academic life ought to be, and Mesheau gives it to us for all it's worth (so that we come to understand why Hal might have worshipped this sort of academic mentor). And finally, when Catherine comes home from Evanston to find him in full flight of madness, "working" on the porch in freezing weather, we watch him explode in energy and mania, and then crumple into a freezing, weak old age as he -- while she unwillingly reads it aloud -- realizes that the work he's been producing is meaningless gibberish (or, perhaps, poetry: certainly not mathematics). It's a scene calculated to give an actor a chance to make us care deeply, and Mesheau takes on the challenge with gusto, especially, perhaps, in the aging weakness in his body as he goes up the steps toward the house, and the break in his voice in his plaintive, "Don't leave me."

The pivotal, and most demanding role in the play, however, is the troubled and put-upon daughter, Catherine. Like the other three characters, she needs both to be sympathetic and repellent: we need to feel both that we understand why she would be so suspicious of Hal and of her sister that her near-hysterical responses make sense, and also realize that she really is pretty difficult to be around; we also have to see her when she's not labouring under a depression caused by her father's death and the years of sacrifice which seem to have produced nothing much -- a hundred notebooks of gibberish in an upstairs bedroom, a house in a state of collapse, a dead father and a dead end to a career. Megan Young's Catherine showed us those, and also showed us the lively, charming Catherine who argues with her recently sane father about pasta and dinner and going back to school at Northwestern to study math, who apologizes to Hal for her rudeness and offers him her trust. This is achieved as much through body language as through language; it almost seems as though a different person lives, for example, in the body that comes out on the porch to find her father sitting happily in the fall sunshine, and the one that comes out beaten, worn, and packed for her trip to New York. The achievement of this production and her role is best characterized by saying that we believe that, by the end, she has unwillingly been brought to trust Hal, in spite of the improbability of this conclusion (this is, I think, one of the weaknesses of Auburn's script).

All this is supported by extraordinarily strong production values. Props and costumes are well-nigh perfect. I particularly liked the plaid jacket which dwarfs Robert as his madness grows on him, and the elegant little black dress, just slightly ill-fitting, that Catherine wears to the party after the funeral. In general I couldn't see how the look of the production could be improved upon. Chris Saad's lighting and the sound design by Nick Vipond both needed to be excellent to bridge the sometimes longish pauses between scenes (occasioned by the frequent, radical, costume and hairstyle changes). And, in the event, both were excellent -- even though I'm doubtful about the musical tone that punctuates Robert's announcement that he's dead: it seemed condescending to me to explain to an audience that they might have just missed something (and if we were going to be reminded that the scene wasn't real, a better time might have been a few minutes later, when Hal enters and "awakens" Catherine, or jolts her back to reality). One particularly elegant touch was that no props are brought in or out between scenes: all come out with characters, and leave with them as well, adding to the sense the production gives -- absolutely appropriate to Auburn's polished and structurally elegant script -- that everything is under control, shaped and mathematically perfect, even while madness and the fear of madness threaten to sweep it all away.