The movie "Proof" is quite faithful to the 2001 Pulitzer Prize-winning play it's based on. It sports a sympathetic lead turn by a major star. And it pumps passion into the rarefied pursuit of higher mathematics.

So why does this add up to such a respectable but mild, drab little film?

No one can accuse actress Gwyneth Paltrow and director John Madden (who paired so well on "Shakespeare in Love"), or co-screenwriters David Auburn (the play's author) and Rebecca Miller, of glamming-up "Proof."

It's still a bittersweet study of sardonic, grieving Catherine (Paltrow), a young woman who set aside her own promising math career to care for her mentally ill father.

Movie review

Showtimes and trailer

"Proof" with Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal. Directed by John Madden, from a screenplay by David Auburn and Rebecca Miller. 99 minutes. Rated PG-13 for some sexual content, language and drug references. Several theaters.

But a small-cast drama that crackles with life onstage can go strangely slack on film, if its intimacy isn't revitalized for the camera. And so it goes with "Proof," which also stars Anthony Hopkins as Catherine's erratic math-genius dad, Robert, Jake Gyllenhaal as Hal (a math prof mentored by Robert), and Hope Davis as Catherine's caring but bossy sister Claire.

In sweats and frayed ponytail, Paltrow's Catherine mopes around the run-down home she shared with her just-deceased father, while his chatty ghost appears to comfort and prod her. Gyllenhaal's flirty Hal also tries to nudge her out of her funk — while ransacking Robert's notebooks for a big math breakthrough. And Davis' prissy Claire bugs her sis to join her in New York for the yuppie good life — or maybe a stint in a mental hospital.

There's a gleaming kernel of mystery in "Proof," unwrapped via flashbacks. And the film gets more things right about mental illness (especially the toll it takes on loving caregivers) than the schizophrenic-math-whiz film "A Beautiful Mind" did.

Also, who could fault Paltrow's performance? Rumpled and depleted, she issues sarcastic retorts in a slurry Midwest accent, while her sad eyes bear the strain of survivor's guilt and fears for her own sanity.

But this is more of a one-woman show than it should be — relationships that made the play so rich barely click in. Whether wild-eyed and ranting, or calm and caring, Hopkins doesn't connect enough with Paltrow. Gyllenhaal does cute, likable "math geek" fine, but minus the callow careerism that gives Hal some complexity. Davis is Paltrow's best foil, but she's stuck with a smug-sibling role that was the weakest figure in the play's equation.

Good plays can, sometimes, make good movies. But "Proof" proves that they can't do it on automatic pilot.

Misha Berson: mberson@seattletimes.com