In 2005, Gyllenhaal starred in the critically praised films Proof, Jarhead, and Brokeback Mountain. The film was often referred to in the media with the shorthand phrase "the gay cowboy movie", though there was differing opinion on the sexual orientation of the characters.
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. The film won the Golden Lion prize at the Venice Film Festival.
Gyllenhaal was nominated for an Academy Award in the category of Best Supporting Actor for his performance but lost to George Clooney for Syriana.
Gyllenhaal also won the Best Supporting Actor BAFTA for the same role and received a Best Supporting Actor nomination and Best Film Ensemble nomination from the Screen Actors Guild.
Also for Brokeback Mountain, he and Ledger won an MTV Movie Award for "Best Kiss" in 2006.
♫ "My mother believes she thinks arranged marriages might be able to work," Gyllenhaal jokingly says.
He adds that if his mom were to ask him to meet someone, he would.