Jake Gyllenhaal In "Proof", featuring Gwyneth Paltrow and Anthony Hopkins, Gyllenhaal played a graduate student in mathematics who tries to convince Paltrow's character to publish a revolutionary proof to a problem puzzling the mathematicians' community. In "Jarhead", Gyllenhaal played a violent U.S. Marine during the first Gulf War. He also auditioned to be Batman for the blockbuster "Batman Begins" and came close to getting the role, but Christian Bale was ultimately chosen for it. In "Brokeback Mountain", Gyllenhaal and Heath Ledger play young men who meet as sheep herders and embark upon a sexual relationship that begins in the summer of 1963
Moulin Rouge! In this way, Christian would appear to the other characters to be ahead-of-his-time as a musician and writer. Leonardo DiCaprio, who worked with Luhrmann on "Romeo + Juliet", auditioned for the role of Christian. Luhrmann also considered younger actors for the role, including Heath Ledger and Jake Gyllenhaal before Ewan McGregor won the part. Courtney Love auditioned for the role of Satine and assisted in clearing licensing rights for "Smells Like Teen Spirit" to be used in the film. Production began in November 1999 and was completed in May 2000, with a budget of $52.5 million. Filming generally went smoothly,