The workaholic actor is one of the finest of his generation – and his new sci-fi horror Life the latest example of his skilful character-building. But perhaps it’s best not to ask him about Taylor Swift ...

Jake Gyllenhaal arrives at today’s interview carrying his own chair. Specifically, the chair he dragged across the fancy hotel suite so that he could sit in a normal, upright position, rather than recline on the designated chaise longue that had been set up for him next to me. The chair is a good call – having Gyllenhaal lie back while I ask about his life story might have made this encounter seem a little bit too much like a therapy session.

“Oh, was that the kind of interview you were expecting?” he says, with a cheeky widening of those intense eyes. “We can do that. If you don’t mind me lying down, you’ll definitely get some interesting stuff.”

We laugh, although in an hour’s time, when things aren’t quite so amicable, a therapist’s couch might have come in handy. Which is a shame, because there’s no reason why this chat with Jake Gyllenhaal should have been anything other than cordial. He’s easy enough to talk to, with a pleasing dose of oddball intensity lurking beneath his sleepy exterior. And it’s not as if he needs to be defensive about his career – he’s one of his generation’s finest actors, rising to fame while still in his teens, and taking on roles loaded with inner turmoil: a troubled, rabbit-hallucinating teenager in cult-hit Donnie Darko; Brokeback Mountain’s yearning, repressed gay sheep-herder Jack Twist; Tony Hastings, a man tormented over his failure to prevent the rape and murder of his wife and daughter in Nocturnal Animals.

Today he’s promoting Life, a sci-fi/horror film in which a six-person crew on the International Space Station discover the first evidence of life outside Earth, only for their curiosity with it to get the better of them: cue things spiralling rapidly out of control. Life follows many tropes of the genre, but with enough neat twists and lessons on human nature to keep it interesting. The screenplay, says Gyllenhaal, left him “legitimately terrified”, although he admits his main reason for taking the part was that “after playing role after role where I’ve given a ton of time in preparation, I made a resolution to just enjoy myself making a big, fun movie”.

And so he did just that. The director, Daniel Espinosa, gave him the freedom to build his own character, Dr David Jordan, and Gyllenhaal opted for a largely speechless introvert with minimal desire to ever return to Earth. “Could I relate to that? Yes!” he laughs. “But also no. I think I am fully committed to being here.”

Despite his attempts to just have fun, Gyllenhaal, a renowned workaholic, still couldn’t help pushing himself. He spoke to astronauts, took guidance from a trauma doctor and worked with a zero-gravity-movement coach, so that his personality would be better reflected in the way he floated through space.

Many of his roles don’t actively require such punishing levels of preparation but Gyllenhaal does it anyway – he bulked up for boxing movie Southpaw, with 2,000 sit-ups and six-hour training sessions each day, before starving himself back down to play wiry Lou Bloom in Nightcrawler, a morally bankrupt ambulance-chaser emblematic of all the scummiest aspects of tabloid news.

“My sister [the actor Maggie] and I have this argument often,” he says. “I’ve lost weight or learned a new skill and she’s said: ‘You don’t have to change your body to play a character,’ and there are times where I agree and other times I don’t.”

Does he ever get frustrated on set, when he’s been doing thousands of sit-ups every day, and other people aren’t matching his intensity?

He seems horrified by this question. “Oh, so you think doing sit-ups are equated with craft? Is that what you’re saying? Well maybe you don’t know what the craft of acting is. I mean, putting the time into preparation, being agile … no, I don’t think transforming your body physically has anything to do with the craft of acting.”

Facebook Twitter Pinterest Gyllenhaal in Southpaw. Photograph: Allstar/The Weinstein Company

To make his point he cites upcoming film Stronger, in which he plays Jeff Bauman who lost both his legs in the Boston marathon bombing, as the movie in which he’s pushed himself the hardest, on a purely psychological level. “Although no matter how far you push yourself, to understand even the idea of that is almost close to impossible,” he says.

If all this seems to make Gyllenhaal stand out from his peers, then he believes it’s a sign of the times. “Because it seems to me that anybody feels they can be an actor nowadays,” he says.

Really? “Yeah. People say: ‘How hard can it be?’ But the truth is, the creation of a character, the understanding of human behaviour, is a craft and to be learned and worked and experimented with and discovered. My favourite actors are like artists, and when you see their career, you see someone who is able to actually physically draw a perfect figure and then deconstruct it, or not, based on a foundation of skill or practice. Whereas I noticed that some people just throw some paint up on the wall and call it art.”

It is, of course, nice to hear an actor so evidently engaged with their work. Yet after reading past interviews, I do wonder if his desire to deep dive into his techniques isn’t partly a way to avoid talking about, well, anything else. Gyllenhaal is a man who remains fiercely guarded about his private life, to an extent that borders on the bizarre – in one newspaper interview he declined to share with the journalist the filling of a sandwich he had recently consumed: “There are some things I keep to myself, that are my business,” he explained. Does he consider himself intensely private?

“Well, aren’t you?” he says, throwing the question back, as if the answer is completely obvious, which is a deflective trick he often uses. But in this case the answer is: “Well, no, not really. In fact, ask me anything, Jake, and I will almost certainly tell you.”

He smiles, and says: “Well, I have a firm belief that I enter space with an open heart and a mind that’s strong enough to protect it. I’m not necessarily guarded, but I consider intimacy to be very important and I don’t think everybody needs to know about my family or my personal details. I’m old school in that way.”

Facebook Twitter Pinterest With Heath Ledger in Brokeback Mountain. Photograph: Focus/Sportsphoto/Allstar

Which is, of course, fair enough. Gyllenhaal has never been one for disclosing details of his past relationships – he has dated Kirsten Dunst and Reese Witherspoon, and more recently the model Alyssa Miller – and has occasionally got a bit narky in interviews when the subject of his childhood privilege has been brought up (he is descended from Swedish nobility and a family armed with Hollywood connections). I’m not particularly interested in the tabloid side of his life either, to be honest, but I did find it interesting that one of his former girlfriends, Taylor Swift, is renowned for using past relationships as source material in her songs. For someone so intensely private, wasn’t it playing with fire a little to start dating her?

Asking this proves to be a mistake. “I think when you’re in a relationship, you are constantly scrutinised, your friends are scrutinised, but ...”

He trails off and stares at me, ramping up the intensity of his eyes like he’s done in so many roles.

But what? Gyllenhaal just continues to stare. Then he performs an exaggerated shrug.

So, er, did he listen to any of the many songs rumoured to be about him? More silence. The atmosphere has become uncomfortably tense. Would he like to move on? “I would love to not talk about my personal life.”

I don’t think this is, massively. “Oh, really? You don’t?” he asks.

Well, I say, it’s not prying for intimate details, is it? It’s asking how you responded to things that have been put out there in the public domain. But he disagrees and we end up engaging in a bizarre stand-off where anything I say is met same response, repeated through a cold smile: “I would love to talk about the movie.”

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Wanting to avert disaster, I ask about the music of Stephen Sondheim; Gyllenhaal is currently wowing critics in a Broadway production of Sondheim’s Sunday in the Park With George.

“I’ve sung since I was a kid,” he says, “and again, as I said in the previous part of our conversation, everything requires work. Everything is craft. Some things come somewhat naturally to some people, but after that, if you want to do it in a professional sphere, it requires a lot of work. I’ve put a lot of work into understanding my own voice and how to communicate with it. I’m by no means a professional singer. I’m an actor, and why I love Sondheim is because he’s a playwright – with lyrics and music – but everything has intention, and so is absolutely actable on almost every measure.”

We’re now back on relatively safe ground. I’m not sure you can really get to know a person solely by talking about their profession, but don’t imagine delving into Gyllenhaal’s family history is an option at this point either, so we end up spending our final 10 minutes on politics.

Gyllenhaal has been rereading David McCullough’s biography of the second US president, John Adams, and is unsettling himself by noticing the “surprising and terrifying correlations in America to the civil war and pre-civil war times”. He thinks today’s actors have a duty to speak out, “especially given that, even today, learning that the national endowment for the arts could potentially be cut more than in half”.

He speaks movingly and insightfully about the power of the arts – explaining how Sunday in the Park With George was funded by an endowment, and that to “see people’s responses to that expression that Sondheim and James Lapine created, and to think that minds like theirs won’t be funded to create things like that, is beyond heartbreaking. There should be a revolution to make sure we maintain that, because when you take away from expression it becomes very dangerous.”

Does he fear America is slipping towards fascism? “I think that democracy should not be underestimated,” he says, before a rousing final speech about the artist’s role in society.

“I had the privilege to meet President Obama,” he begins, “and he told me: ‘You have a job as an artist to help people through difficult times, to illuminate things through art.’ He said: ‘That’s your job.’ And my parents have always said that, too. And I’m sure you know it, because you seem like a very smart person who has done their research, particularly into tabloid research, which is obviously the most important of all research.”

Oh come on, I say, I only asked one question!

“It was two questions!” A hybrid speech follows about a) defeating fascism through art and b) really not liking being asked about Taylor Swift 15 minutes ago. His press officer joins us to signal that it is time to wrap things up. I start to realise that I might not be the sole intended audience for this exaggerated monologue after all. In fact, I seem to have been cast for this performance in the Lou Bloom role of scummy tabloid newshound.

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“Art, movies ... they’re political whether you’re saying something overtly or not,” he says. “No wonder it’s dangerous! No wonder, probably, people are trying to defund it! So, it’s an irony to me when people say: ‘An entertainer or actor should not be political,’ because it’s very easy to sideline people and, for instance, ask about past relationships or things that I believe are meant to be private.

“So, I will just tell you now that I respect your form of questioning,” he continues, “but also it is within my belief that in what I do, I will express the most. So I hope, in the future, you will see more of my work. If you’ve ever even seen my work.”

I burst out laughing at the sheer ridiculousness of this. I’ve asked him about Life and End of Watch and Brokeback Mountain and Nightcrawler and Stronger and Southpaw. We’ve talked about preparation for roles and the responsibility that comes with them. We’ve delved into the deeper meanings of his sci-fi movie and the importance of physicality in a role and even musical theatre. In fact, we’ve spent approximately 95% of this interview talking about “craft” compared with about 0.5% asking if he has ever listened to some Taylor Swift’s songs that may or may not have been about him. So, yes, of course I’ve seen his work!

“Well, in that case,” he concludes, “maybe you’ll get an answer there.”

And with that he’s off, out the door and down the corridor, muttering: “It’s always the last [interview of the day],” to his press officer.

I hang around for a few moments, half-expecting someone to pop in and explain what just happened. But nobody comes, leaving just me and an empty chaise longue that I could do with a nice lie-down on.

• Life is released in the UK on 24 March

• This article was amended on 21 March 2017 to correct the surname of Jake Gyllenhaal’s character in Life.