Paltrow gives a careful, convincing performance in 'Proof'

"Proof" proves a couple of things.

First, even the best adaptation of a successful play can't always capture the electrifying theatricality of its source.

Second, it's possible to give an excellent performance, even when an actor is badly miscast.

Miramax Films 'Proof' B- The verdict: Can't match the play's blazing theatricality, but intelligent, absorbing and very well-acted. Director: John Madden Starring: Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal, Hope Davis, Gary Houston Run time: 99 minutes Release date: Sept. 16, 2005 Rating: PG-13 for some sexual content, language and drug references. See showtimes On the web Official movie site View the trailer    Trailers require Quicktime Rate "Proof"   Go see it   Make it a matinee   Wait to rent   Don't bother Voter Limit: Once per Hour View Poll Results

The actor is Gwyneth Paltrow, who stars as Catherine, the woebegone daughter of Robert (Anthony Hopkins), a world-famous mathematician, who turned the numbers world on its ear by the time he was 22.

And then promptly went mad.

When he refused to be hospitalized, Catherine was more or less forced to give up her life — college, friends, romance — to look after him.

The one who really needs looking after is Catherine herself, who hopes she's inherited some of her father's genius but fears she may have inherited his mental instability instead. A mathematical proof turns up — long hidden in her father's desk drawer — and her sanity is openly questioned by her superefficient older sister, Claire (Hope Davis), who's just bustled in from New York to rearrange Catherine's life. And by Hal (Jake Gyllenhaal), one of Robert's most ardent acolytes, who's been going through his idol's voluminous notebooks in hopes of finding one last flash of brilliance among the incoherent scribblings. It doesn't help that Catherine and Hal have been dancing around a possible romance.

Paltrow starred in the London production of David Auburn's Pulitzer Prize-winning play, under the guidance of her "Shakespeare in Love" director, John Madden. They've reteamed for the movie, and it's clear they treasure the script. There've been a few attempts to open it up (Hal running breathlessly after a taxicab is the most egregious), but mostly Madden sticks to the basics: character and dialogue.

Hopkins is at his stentorian best, alternating between hissing viciously at the hunched-over Catherine ("By your age, I'd already done my best work!") and giving her grand, fatherly embraces. Their exchanges, be they confrontational or loving, are intelligently played, making it all the easier to think "Proof" must have been positively thrilling onstage.

It's not not thrilling here, but a certain charge is missing, despite the generally fine cast (the exception being a curiously blank Gyllenhaal). Davis dazzles as the bossy Claire, who thinks her sister's problems can be solved by a good breakfast, fresh air and jojoba shampoo.

Of course, by the looks of Paltrow's golden locks, whatever she's using works just fine. Which brings up the problem of her casting. She obviously understands the role. She delivers her lines flawlessly, with nuance and insight. But we never buy her as possibly insane. Bedraggled, yes. Mopey. Insecure. But there's no hint of the abyss that could be awaiting her. She's more depressed than anything else.

Maybe Claire is right. Maybe a banana would help.

Still, you never feel that Paltrow is at fault. Instead, her careful, vulnerable portrayal brings to mind the underappreciated "Sylvia," in which she played poet Sylvia Plath and was quite convincingly unhinged when need be.

Miscast yet marvelous, Paltrow and the rest of the cast hold you to the movie, even when you intuitively sense something is lacking. And don't worry if you couldn't get through eighth-grade algebra and wouldn't know a multiplication table from a kumquat. "Proof" is about people, not numbers, approval (even self-approval), not theorems. It's worth a look — even if it doesn't quite add up.