Forget the rest of the equation. When a film derives Gwyneth Paltrow in prime form, the returns are exponential, and any adjoining negative functions are canceled out. Um, sorry. "Proof" is the kind of drama from the math genre that delves into your head so far, it gets you talking exclusively in math terms. And in case you don't believe there is a "math genre," well, there is now. "Proof" joins "Good Will Hunting," "Pi" and "A Beautiful Mind" in the pantheon of films that make higher mathematics seem as invigorating and risky as parasailing. Paltrow plays Catherine, a disheveled 27-year-old Chicagoan whose brain isn't right. She has dedicated the past several years of her life to care for her insane father, Robert (Anthony Hopkins), who was a famed mathematician before his downturn. Catherine looks upon Robert with fear and admiration, relishing his words of advice. The problem with that is, Robert passed away a week ago. And Catherine still keeps seeing him. Because this isn't a ghost movie, this means Catherine is a little nuts. Her father's death has tossed her into a tailspin, as she relishes her newfound freedom while coping with the guilt of her loss. Catherine is in no condition to deal with other people, but that doesn't keep away moon-eyed Hal (Jake Gyllenhaal), Robert's former student. He's nosing around the house, looking for remnants of groundbreaking theories he imagines Robert may have put in one of the dozens of notebooks Robert left behind. Hal is also interested in a little cross multiplying with Catherine, who can't be sure whether he's trying to use her to possibly steal Robert's work for his own gain. Further complicating issues is Claire (Hope Davis), Catherine's controlling, condescending older sister, who swoops in with the intent to sell the house and put Claire in a mental institution. Having dropped out of school and given up a promising academic career, Catherine is too used to living passively, and at first wilts in submission as Hal and Claire work to exact their own ends. The conflict intensifies when Claire produces a possibly revolutionary mathematical proof and claims it's her own work, whereas evidence indicates that Robert was its author. What gives the narrative its strength is that it deals with three strong characters who carry deep flaws. All are in search of personal ends, and are held back by suppositions and insecurities. Another trait shared by Catherine, Hal and Claire is that they're desperately in search of evidence of what they want to believe about themselves and others, not quite able to make leaps of faith that defy logic but feel right. Davis is superbly conniving as her sister's forceful antagonist, and Gyllenhaal for once manages to try on a part that doesn't require him to dreamily stare off into space. You couldn't find a role more comfortable for Paltrow, who is at her best, ranging effortlessly from seething anger to trembling tenderness. Not only does she reunite with director John Madden, who coached her to a best-actress Oscar in "Shakespeare in Love," but the film is adapted from the Pulitzer Prize-winning David Auburn play, which starred Paltrow in its London run. Auburn combined with Rebecca Miller to write the screenplay. Anyone who thought Paltrow's Oscar win was a fluke can look to this film for proof of the opposite.