Absolute family values

Director John Madden’s emotionally rich, intellectually exciting Proof is a throwback to a time when Pulitzer Prize-winning plays routinely were made into movies. From 1934 to 1973, only six Pulitzer plays failed to make it to the screen, and even as late as the 1980s Hollywood still went regularly to the well. But after 1988’s prizewinner Driving Miss Daisy won the Best Picture Oscar in 1989, it’s been almost unheard of.

This has as much to do with Broadway economics as with anything else. More and more plays depend on small casts and a level of stage artifice that can look pinched and claustrophobic on film—unless, of course, it’s “opened up” to the point that the movie loses the play’s distinguishing qualities. Also, stage and movie audiences have been diverging for years, with theatergoers becoming more educated and elite as movies grew more adolescent and youth-oriented. With rare exceptions, Hollywood has preferred to leave Broadway plays (with or without Pulitzer Prizes) to PBS and cable TV.

So, Proof would be an unusual case and worth encouraging, even if it weren’t as good as it is. Based on David Auburn’s play (with a smooth screenplay by Auburn and Rebecca Miller), the movie stars Gwyneth Paltrow in the role she played in the London stage production under Madden’s direction. Catherine is leading a rather disordered life. Late at night in her messy kitchen, she has a rueful conversation with her father, Robert (Anthony Hopkins), who wishes her a happy 27th birthday. But the conversation isn’t real; Robert gently reminds Catherine that he is, in fact, dead.

At one time, Robert was a brilliant mathematician, one of the giants in his field. But as he—or his ghost—tells Catherine, his best work was behind him by the time he reached Catherine’s age. Then, after a distinguished professorial career at the University of Chicago, he gradually descended into madness and spent his final years in Catherine’s care. Suspending her own career to spare her father the indignity of confinement in an institution, she moved into his campus residence, holding out almost to the end a hope that Robert’s mind would clear and he would regain his former greatness.

It never happened. Now it’s too late for Robert, and Catherine worries that it may be too late for her, too. She inherited something of her father’s genius for mathematics. Did she inherit his madness as well?

Catherine also must contend with Hal (Jake Gyllenhaal), a former student of her father’s, who has persuaded her to let him go through Robert’s hundreds of notebooks. Hal hopes that somewhere in the compulsive, deranged notes left behind by the old man will be a final blaze of genius waiting to be discovered—and to make the reputation of its discoverer.

Into this situation sails Catherine’s sister, Claire (Hope Davis), who wants only to bury their father and persuade Catherine to sell the house and join her in New York. Claire is no mathematician like Catherine or Robert; in her case, the genius took a more mundane form, as a passion for order that has made Claire a well-meaning, passive-aggressive control freak.

The film confines itself mainly to the four characters in the play, with brief excursions into the outside world. Madden focuses sharply on Catherine, Claire and Hal, drawing fine performances from Gyllenhaal and Davis, and a superb one from Paltrow. Hal’s discovery of a notebook containing a potentially revolutionary mathematical proof (the kind of thing that has eluded the greatest minds for centuries) brings everything to a head: Catherine’s fears, Claire’s gentle bossiness and Hal’s drive to make a name for himself. Paltrow’s Catherine is haunted not only by her father but also by the woman she might have been, and she lashes out at both Claire and Hal.

In mathematics, “proof” means testing as well as validation, and Catherine, Claire and Hal all are tested by Robert’s death. Whether they’re validated by the test is harder to pin down, for them as for us. Human feelings don’t lend themselves easily to the elegance of mathematics, and people can’t always prove themselves to one another.

Meanwhile, Proof itself is a glorious aberration: If it hadn’t had echoes of A Beautiful Mind, or featured the director-star team from Shakespeare in Love, it probably wouldn’t have been made at all. Could it start a trend? Doubtful; it’s more likely just a breath of grown-up air between the last rehash of Rush Hour and the next variation on Scream. Let’s be grateful for it.