Studio: Miramax Films
Rated: PG-13
Website: http://miramax.com/proof/
Release Date: 2005-09-30
Cast: Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal, Hope Davis, Colin Stinton
Director: John Madden, James D. Stern
Screenwriter: David Auburn, Rebecca Miller
Music Score: Stephen Warbeck
WorkNameSort: Proof

A filmed adaptation of a four-character play about math wizardry seems doomed to wallow in esoterica, but Proof is at its strongest the closer it veers toward the multiplication tables. The singular unknowability of mathematical genius – depicted here, with some familiarity, as the close companion of mental instability – inspires the most intriguing moments in filmmaker John Madden's (Shakespeare in Love) adaptation of David Auburn's Tony- and Pulitzer-winning drama. That's the movie at its best. At its worst, it's Gwyneth Paltrow being humped by Jake Gyllenhaal while a latter-day freedom-rock trio vamps in the background. I'll take the number-crunching, thanks.

On a basic level, the movie is a scholarly-minded mystery in which the daughter (Paltrow) of a master theoretician (Anthony Hopkins) struggles with the twin legacies he left behind: brilliance and schizophrenia. The latter affliction ruined her dad's once-respected ability to create groundbreaking mathematical proofs, but an innocuous-looking notebook found among his personal effects indicates that his latter years may have yielded a final breakthrough that was the mother of them all. Discerning what – if any – role Paltrow's Catherine played in that watershed is the dramatic through line of the story. Wrapped around it is a more mundane thread in which her own potential for mental instability complicates her already thorny relationship with her annoyingly efficient sister (Hope Davis) and her emerging attraction to a goofy-buff numbers nerd (Jake Gyllenhaal). Their crazy/cute courtship may have played well on the stage, but on the screen it feels like a sop and a distraction.

It would be easy to blame co-screenwriter Rebecca Miller (Personal Velocity, The Ballad of Jack and Rose) for such sluggish patches, so that's exactly what I've decided to do. One wishes to credit Auburn, who Miller helped adapt his play, with sprightlier constructs – like the movie's mischievous first act, which keeps pulling the rug out from under the audience with one story-altering revelation after another. Giddily disoriented by flashbacks, hallucinations and bits of verbal chicanery, we're made to feel like mathematicians ourselves, continually sent back to the drawing board to make another stab at discerning who's done what to whom.

One wonders how transcendent the film might have been in the hands of a more versatile actress than Paltrow, who has appeared in the stage play but approaches its cinematic cousin as if she couldn't decide which of her scenes was her big one and thus decided to play all of them that way. The note of shrill petulance she keeps striking meshes uncomfortably with her natural vocal tones, which can resemble a gooselike honk when she's good and worked up. Her often hysterical Catherine is easy to find interesting but difficult to fully sympathize with (unless, that is, one has a particular penchant for brainy but troubled ringnecks.)

As its award pedigree indicates, there's a fascinating story in here about the inscrutability of numbers and the ability of extraordinary ideas to change the world. And you can see it working, on those occasions when all the variables add up.