Gwyneth Paltrow, who won an Oscar for her performance in director John Madden's Shakespeare In Love, teams up again with Madden in Proof, a poignant drama based on David Auburn's Pulitzer Prize-winning play. Paltrow lights up the screen as Catherine, a young woman who has given up a seemingly bright future in order to take care of her ailing father, Robert (Anthony Hopkins), a formerly brilliant mathematician who went crazy. After he dies, Catherine's closed-off world is invaded by Hal (Jake Gyllenhaal), a young mathematician who worshipped Robert, and Claire (Hope Davis), her successful sister who fears that Catherine is too much like their father--a talented, supremely intelligent person with severe mental problems. During the last years of his life, Robert filled 103 notebooks with his writings, but one of them, written during a brief period of lucidity, could turn the math world on its head, while also threatening Catherine's already wavering sanity.