Proof

Reprising the role with which she made her London stage debut under director John Madden, Gwyneth Paltrow stars as Catherine, the 27-year-old daughter of Robert (Anthony Hopkins), a John Nash-like mathematician whose genius has been supplanted by madness. Putting her own education on hold, Catherine has avoided institutionalizing her father by caring for him full-time. When Robert dies suddenly, former student Hal (Jake Gyllenhaal) arrives to go through his paperwork, hoping to glimpse evidence that his mentor managed to produce something of value in his final years. Meanwhile, Robert's elder daughter Claire (Hope Davis) jets into Chicago from New York to get her father's affairs -- and her sister's life -- in order.

Predictably, given the pedigree of the cast, the performances here are stellar across the board. Paltrow plays her role as a plain Jane, fully inhabiting a young woman crippled by grief, exhaustion and doubt. Gyllenhaal brings a confident self-deprecation that renders math-geek Hal both likable and forgivable. Meanwhile, with a full beard, Hopkins appears younger and more vigorous than in some other recent roles, even as a dead man, and Davis lends nuance to a difficult character who in other hands would have been too easily portrayed as a shrew.

With lines culled directly from David Auburn's 2001 Pulitzer Prize- and Tony-winning stageplay, the dialogue here at times sounds too theatrical for cinema, but the freedom film affords has allowed Auburn and co-writer Rebecca Miller ("The Ballad of Jack and Rose") to open up the material and, remarkably, deepen it, adding a layer of pathos to Catherine's angst. She at first hides, then denies, that she possesses her father's gift because she fears that might mean she has also inherited his illness. But further -- and this is where the cinematic version takes a darker and more interesting turn -- she's also afraid that by inheriting his genius she's somehow stolen it from him, both inadvertently and through her actions. Starring Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal and Hope Davis. Directed by John Madden. Written by David Auburn and Rebecca Miller. Produced by Jeffrey Sharp, John N. Hart Jr., Robert Kessel and Alison Owen. A Miramax release. Drama. Rated PG-13 for some sexual content, language and drug references. Running time: 100 min