Jake dives in at the deep end

But for an actor who turned down a role in Bernardo Bertolucci's The Dreamers because the story was too explicit, the love scenes were difficult. "When you get naked in a movie, it needs to be in service of the story," he says, "and I really felt like this was."

It helped that Ledger was going through exactly the same dilemma: "He would take a step somewhere that I didn't want to step, and then I would follow him. Then I would take a step somewhere that he didn't want to step, and he would follow me."

Recently, Sir Ian McKellen has poured scorn on the notion that it is somehow "brave" or award-worthy for straight actors to play gay roles, with particular reference to comments Ledger has made in the press. Gyllenhaal, too, thinks the gay angle is overworked.

"For me, it's a story about how hard it is for two people to love each other," he says. "If you love each other, no matter what context that is - heterosexual or homosexual - it's just fucking hard. Movies continually teach us these ideas, drilling into our minds that love has no bounds.

"It's such a cliché now. It's bullshit. Our idea of love from movies is, 'guy gets girl, guy loses girl, guy loses girls again'. That's what it's about. But this film is flipping it on its head, saying, 'We can't tell this story anymore heterosexually.'"

Here, he could almost be talking about his own on-off relationship with America's current young female darling, Kirsten Dunst. Gyllenhaal was introduced to Dunst by his sister, Maggie, after the two women starred together in Mona Lisa Smile, and their relationship has been counted out in paparazzi flashbulbs. Marriage, pregnancy and separation have all been reported, although most recently a shared kiss at a pool-party in LA suggests they are an item again.

Gyllenhaal won't discuss their relationship "because of the insane interest in it". He does, however, address the rumours that he himself is bisexual and is looking for a way to come out. He has a huge gay fanbase, and recently told the US magazine Details: "I've never really been attracted to men sexually, but I don't think I would be afraid of it if it happened."

I don't really care about people questioning my sexuality," he says. "Of course they're going to. [But] I don't really know why it's such a big deal. I suppose that sexuality is a scary subject. It feeds into everyday life."

Thanks to his upbringing, he is at least aware that a star's private life and professional choices are always the subject of intense attention. "My dad always says to me that the job of any artist is to disturb the comfortable and to comfort the disturbed," he adds.

Still, for all his love of risk, he must be quaking at the thought of the reaction of the American press and public to Jarhead. Based on Anthony "Swoff" Swofford's bestselling Gulf War memoir, Sam Mendes' film cast Gyllenhaal as a disaffected marine desperate to satiate the bloodlust instilled in basic trainign.

His "Swoff" is not a sympathetic character, meanwhile, his sister Maggie's official website recently shutdown under a barrage of hate mail after she suggested that America was "responsible in some way" for the events of 11 September.

"I am proud to be an American but I am unhappy sometimes with the way my country behaves," Gyllenhaal says carefully, going on to defend Jarhead. "There is no agenda with this movie. Sam, he loves American culture - he's in awe of it as much as he criticises it."

He admits that he went into the film with pre-conceptions that "connected the military with the (Bush) administration", but came out of it with a new respect for soldiers.

He points out that he has a childhood friend in the Marines and a best friend in the navy: "I am close to it." And he was able to tap into the aggression of men who went off to war when they were, like him, in their early twenties.

"I could at least deal with a lot of feelings that I think are in me but that I hadn't really paid a lot of attention to [but which] Tony's book expressed pretty passionately," he says, "so I was just down to get angry and shoot at people."

Sam Mendes says he watched Gyllenhaal grow from a boy into a man on the set of Jarhead. And listening to this tall, muscular, self-possessed figure talk, it seems unlikely he will ever again be cast as the doe-eyed object-of-affection for older women, as he was for Catherine Keener in Lovely and Amazing and Jennifer Aniston in The Good Girl.

But, as a virtual swansong to himbo roles, he can be seen in Proof - his third film this winter, although it was shot two years ago - as a mathematics student who falls for the daughter (Gwyneth Paltrow) of his professor (Sir Anthony Hopkins).

A college dropout after he dumped his course in Eastern religions at Columbia University, Gyllenhaal wryly notes that "My maths teacher at school would probably be ashamed that I was cast in that role".

He sounds almost as unenthusiastic about Proof as he does about The Day After Tomorrow these days. They're old news, those movies, and after stirring up Hollywood's sexual preconceptions and its military and political pieties, he's already looking forward to the next challenge: working with the ever-controversial David Fincher on the serial-killer story, Zodiac, based on real people and real events.

"We're in a really funny time with movies right now," he says. " Audiences are aching for more ' peopledriven' movies. It's clear from how they responded to big films this summer, by not going. They want good stuff, so we should start to give them it and see how they respond."

Jake Gyllenhaal could be just the man to do it. He is charming and he is handsome but he is also a very serious and very determined young man.

Brokeback Mountain opens on 6 January, followed by Proof on 13 January and Jarhead on 10 February.