Jake Gyllenhaal filmography character, a "sullen" and "schizophrenic" teenager, made him a cult hero. Although the film was critically acclaimed, it failed commercially. Gyllenhaal starred in the 2004 disaster film "The Day After Tomorrow", which, despite receiving mixed reviews from critics, was a commercial success at the box office. In 2005, he co-starred as Jack Twist opposite Heath Ledger in the romance drama "Brokeback Mountain". The actors portrayed two men that fall in love during a sheepherding expedition. The roles earned both Gyllenhaal and Ledger critical acclaim and Academy Award nominations. That same year, he starred in the drama films "Jarhead" and "Proof".
Proof (2005 film) Proof (2005 film) Proof is a 2005 American drama film directed by John Madden and starring Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal, and Hope Davis. It was written by Rebecca Miller, based on David Auburn's Pulitzer Prize-winning play "Proof". The plot alternates between events immediately following the death of Robert (Anthony Hopkins), a brilliant mathematician whose genius was undone by crippling mental illness, and flashbacks revealing the life he shared with his daughter Catherine (Gwyneth Paltrow). Catherine is also a mathematician, but she struggles with living in her father's shadow, with balancing her demanding studies with caring for her father