"If you are wondering if you are crazy, then you must not be crazy -- because you wouldn't be asking that question."
So muses Robert (Anthony Hopkins), a renowned mathematician, in an attempt to console his daughter Catherine (Gwyneth Paltrow), another budding number cruncher. The only problem is Robert died a few days ago, and his youngest is still having lucid discussions with him on the eve of his funeral.
Self-aware of her tendencies to hallucinate, fear grips the twenty-something's heart. For the past half-decade, she has cared for her dad, and has observed his fall from eccentric genius to mentally challenged geriatric. Now she wonders if she hasn't inherited a similar mental illness.
Other than her father, the only other person in her life is Hal (Jake Gyllenhaal), a former student of her father's who has been hired to work on the family's aging Chicago home. We get the feeling that prior to this evening, the two have never really talked. But now Hal is opening up and showing his fondness toward the fellow math lover by consoling her, while at the same time showing intense enthusiasm for a collection of Robert's notebooks he has stumbled upon. Unfortunately Catherine suspects his cross-purposes and the conversation ends with accusations that Hal wants to steal her father's property.
Torn between wanting to believe Hal's encouragement and her own insecurities, Catherine's sanity is stretched even further when her older sister arrives the next day. Claire (Hope Davis), a real estate broker from New York City, approaches the funeral and her trip to Chicago with a get-down-to-business attitude. On her pocket agenda she keeps tabs on a short list of to-dos: Bury dad, party with some friends, and convince Catherine to move back to NYC. The latter entry is motivated by the personal conviction her younger sibling is nearly incapable of living on her own.
Now, in the middle of paying last respects, Clair's desire to move her out of her home clashes with Hal's increasing affection, and a surprise that will eventually determine just how crazy--or gifted--Catherine actually is.
Heavy on dialogue, this movie's intelligent script pits mathematical theories against personality traits, and questions the definition of mad versus eccentric. This parallel between math and mental illness ingeniously illustrates how even a factual discipline can leave room for personal judgment, and still demand "proof."
Yet parents may not appreciate the extra-curricular content. A passionate bedroom scene between two unmarried adults with heavy breathing (no nudity), a variety of infrequent profanities (including two uses of a sexual expletive), and references about drug use enhancing creativity, may be enough to disqualify this otherwise thought provoking movie from viewing by teens. Weighing these content pluses and minuses will ultimately leave you with the difficult question of whether Proof sums up as either positive or negative.