The problem with “Proof,” which dares to put math at its center, is that its sum isn’t quite equal to its parts. If “Proof” were an equation it wouldn’t add up. And with that analogy I’ve exhausted my meager store of math knowledge.

“Proof” is based on the play of the same name, which won both a Pulitzer and a Tony. It stars Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal, and Hope Davis. It’s directed by John Madden, one of those British stage directors (like Sam Mendes) who makes creating movies look easy. It has a top-notch pedigree and performers, so that’s not the cause of the faulty sum.

It’s the story of Catherine, a young woman (Paltrow), who’s been caring for her father, Robert (Hopkins), in the final years of his life. He’s “not all there,” as we used to say, but the exact nature of his mental impairment is never revealed. He was once a brilliant mathematician. Just how brilliant is attested to by the loyalty of one of his graduate students, Hal (Gyllenhaal), a eulogist at his memorial service. Caring for her father causes Catherine to miss out on most of her twenties, while her older sister Claire (Davis) makes a lot of money in New York. This is a situation that siblings with sick, aging parents can really relate to. So this plot element isn’t why things don’t add up.

There’s good reason to believe that Catherine may be as crazy as her father. This is a story line with great potential and resonance. The inheritability of crazy genes is something millions of adult children of Alzheimer’s patients have pondered. At the beginning of “Proof,” we find Catherine wondering whether she’s nuts. Her father assures her, “Crazy people don’t sit around wondering if they’re nuts. Crazy people don’t ask that question. If they do, they’re not crazy.” There’s a problem with this reassurance, which I won’t give away, but it leaves us as perplexed as Catherine looks as she tries to solve that assertion. Whether she inherited her father’s “instability” as well as his talent is an intriguing proposition. This can’t be where the calculating goes awry either.

Maybe it’s the math aspect of this movie that leaves one unsatisfied with the sum of the parts. It would have been nice if more effort had been made to let those of us, who are confused even when we have a calculator, understand the significance of Robert’s great accomplishment. He has apparently come up with the “proof” to beat all proofs. (In case you don’t know, in the world of math as practiced by geniuses, a proof is a validating hypothesis. It’s the formula that establishes a certainty. It’s what all those numbers and signs and stuff on a huge chalkboard are supposed to signify to dummies like me.)

When Robert’s proof is discovered locked away in a desk drawer, Hal can barely contain himself. He makes it sound like the Holy Grail of proofs. There will be press conferences. The New York Times might put it on the front page. Oh yeah? So what? What it proves may be beyond the grasp of most movie-goers, but they could have taken a shot at letting us know why it matters so much. A missed opportunity there or a wise strategic move to trust the audience to buy in on the basis of Hal’s excitement? Madden, I think, underestimates the capacity of the audience to grasp what the proof proves. Sure most of us are probably math illiterates, but the proof is central to the action that revolves around its discovery. By taking a pass on a creative explanation he squandered the chance to tie together the various elements of “Proof.”

There went the sum of the parts.

It took me a while to figure out why “Proof” was less than satisfying. The elements can be quite entertaining, but the cohesiveness that makes for an intellectually and emotionally rewarding movie-going experience was missing. I wanted it all to add up at the end because it touches on some fairly powerful dynamics in relationships that most anyone can relate to.

Take the tension between Catherine and Claire. Poor Catherine. She’s about to bury her dad when the prodigal sister blows into town full of small talk about carpeting and child care and big plans for selling the family home and taking her little sister back to New York. Catherine can’t stand Claire. She calls her out at one point with a stunningly simple question. Claire asks her if she’d like to use some of her shampoo. “It has jojoba,” she tells her. “What’s jojoba?” Catherine asks. Claire has no idea.

Then there’s the way we’re made to feel Catherine’s pain as she watches her father struggle with a madness that’s all the more maddening because he can seem at times to be lucid. He’s recaptured the genius that marked him as a great mathematician in his youth, it seems at one point. But his mind is playing a trick on him. All Catherine can do is hold him. And cry.

Paltrow does a wonderful job with the role of Catherine. That she may be her father’s equal when it comes to mind-numbingly difficult math seems not a stretch at all. You think you can be sure she’s not crazy. Until she does something that makes no sense.

Anthony Hopkins is at his best playing a character like this, one who has known greatness only to be humbled by a disease to which he won’t surrender. He’s got the cognitive awareness to sense when his “machinery,” as he calls his mind, is working once again. But is it? Can he really know? What kind of a cruel joke is insanity?

Perhaps what “Proof” is trying to tell us is that there’s no such thing as certainty. That at some point in these proceedings we call life we have to just trust that things are what they are. I know that’s not a very rational, scientific or mathematical idea to propose. But that the parts of a movie like “Proof” can come up short of a neat sum is perhaps the point of it all.

BILL GALLAGHER WRITES THE MONTHLY MOVIE REVIEW COLUMN FOR BRAINSTORMNW AND IS THE NEWS DIRECTOR OF AM 860 KPAM – THE TALK STATION.

BrainstormNW - Oct 2005