has another flashback. It is revealed that, while living together, her father challenged her to work on math, which she does, ultimately completing a proof, which she describes in one of the many notebooks in the house. Catherine goes to tell her father about the breakthrough, but he insists she read aloud the proof that he is working on. To Catherine's disappointment, Robert's notebook contains not a proof, but a rambling and desperate observation of the passage of the seasons, that the year is divided into months of cold, months of warmth and months of indeterminate temperature, that the future of heat is the future of cold, that the future of cold is infinite, and that he will never be as cold as he will be in the future. Reading her father's work, Catherine realizes that Robert has not overcome his mental illness. A dispirited Catherine leaves her notebook in Robert's desk, where Hal will later find it. Catherine has begun to come to terms with herself, aided by Hal's confidence in her. She decides that she does not need to go with her sister to New York and runs out of the airport. She returns to the University of Chicago, and the film ends with her and Hal meeting up on campus and discussing the proof. Cast Gwyneth Paltrow as Catherine Llewellyn, the protagonist Anthony Hopkins as Robert Llewellyn, Catherine and Claire's father Jake Gyllenhaal as Hal, a former graduate student of Robert's Hope Davis as Claire Llewellyn, Catherine's sister, a financial analyst Production The film is based on the four-character stage play Proof. The film adds many bit parts for the sake of realism, and "opens up" the setting considerably. The role of Catherine was first played by Mary-Louise Parker in the play's 2000 Manhattan Theatre Club original production. Gwyneth Paltrow played Catherine in a London stage production before being cast in the film. Hopkins' character is a mathematics professor at the University of Chicago. Although many scenes were filmed on the university's campus, the mathematics building itself (Eckhart Hall) was not used. Instead, many scenes that were set in the math building were actually shot at the Divinity School. The film opens with a pan of Gwyneth Paltrow's character bicycling across the Midway Plaisance and shows many scenes in the quadrangle before Harper Library. Reception Box office Proof opened at #35 in its opening weekend with $193,840