Proof

Gwyneth Paltrow received warm praise as Catherine during the London run of David Auden's play (on which the film is based), and will doubtless received further accolades for her on-screen rendition. Her subtle and deeply internal performance, given room and weight by John Madden's unobtrusive directing and equally nuanced supporting cast, defines the melancholic mood of the film.

The story is quieter and more complex than most Hollywood fare (thank you, Miramax). Catherine is the (possibly genius) daughter of a genius mathematician (Anthony Hopkins) who she has been caring for, forgoing her education, because of the onset of his senile dementia. When he dies, she must cope with the condescending concern and brusque misunderstandings of her elder sister Claire (Hope Davis), and the arrival of Hal (Jake Gyllenhaal), one of her father's old students, who hopes to find some new mathematical proof among the incoherent ramblings in a large collection of notebooks her father wrote during his illness.

The film does not unwind chronologically - told from Catherine's perspective, the narrative follows her thoughts and responses to Claire and Hal, allowing the audience to gradually understand Catherine's grief and intellectual capabilities as her rationality and abilities are challenged. The jumps in time are sometimes a little difficult to follow immediately, though this never really distracts from the story. Catherine has some lines in voice-over at the beginning and end of the film that aren't strictly necessary, though may serve to more firmly set the story in her perspective. The film uses this perspective to explore the internal workings of fear and sadness, resentment and responsibility, and the small moves made towards happiness and reconciliation.

Madden is a subtle director, and lets his excellent cast do most of the heavy lifting, lingering just long enough in silences to allow the actors full expression of what is left unsaid. Hopkins is forceful and tragic as Robert, a strong man and bona fide genius bereft of his mind and who must rely on his daughter for daily care. Davis' Claire annoys, but her controlling behavior and misunderstanding of Catherine clearly spring from fear kept on a short leash. Gyllenhaal's Hal is open and endearing; Jake leaves the angst and insecurity of his characters in earlier films, and plays a more mature, sympathetic man hesitantly edging nearer to Paltrow's defensive Catherine.

Proof is a tightly made film, a complicated internal story carried by excellent acting. None of the moments are overdone for 'dramatic effect' or accompanied by an overwrought score to evoke a stronger emotional response - it's entirely unnecessary; nor does it rely on a depressing ending to seem more realistic. Several of the moments will come back to you as they so perfectly capture in instants emotions that are impossible to describe in words, which is perhaps the highest praise one can give for a film like this - it shows something real and complicated and familiar, without trying too hard, without fanfare. Simply with skill.