Over the course of an hour, on a cloudless afternoon in Oslo, Magnus Carlsen sinks from an upright sitting position to an open-legged slouch, to an almost full stretch, as if on a psychiatrist's couch. And that, I'm sure, is where his opponents would like to see him, preferably after he has unravelled mentally, in the manner of one-time chess world champion Bobby Fischer.

Carlsen jokes that he's only 22, so there is "still plenty of time for the crazy". But for now the crazy seems a long way away. And before then the young Norwegian is likely to become chess world champion himself, when he has his first shot at the title in November. In one of the most anticipated clashes since Fischer-Spassky in the 1970s and Karpov-Kasparov in the 80s and 90s, Carlsen will be taking on the 43-year-old five-time world champion Viswanathan Anand in India. Vishy, as he is known, has been in intense training for the match for three months. Carlsen has a much more relaxed approach. It is part of his genius.

You might think that an overused and ill-defined word, but no other will suffice. This genius is the reason Carlsen is known as "the Mozart of chess". It's not so much to do with his mercurial gifts – such as his ability to memorise thousands of games, or to beat 10 strong players simultaneously, blindfolded – but his style of play. He makes his moves more by intuition than analysis, feeling for them rather than thinking them through. And there is harmony in his moves – music, you might say.

Not surprisingly then, chess fans, too, might like to see Carlsen on the couch, or rather hear what he has to say and get inside that beautiful mind of his. For he is still an enigma, despite his very public rise from child prodigy to youngest world number one at 19 and finally, last year, becoming the highest-rated player in history.

Check mate: aged 13 at the world championships in Tripoli. Photograph: Sabri Elmhedwi/EPA

I first met Carlsen when he was 13, at his grandparents' house overlooking an inlet of sea, on the outskirts of Oslo. He had just become the world's youngest grandmaster and had never done a newspaper interview before. He wasn't shy and introverted quite, more… bored. His father, Henrik, an oil executive who was a keen though average chess player, filled in the gaps in our conversation and revealed that from an early age Magnus had been able to perform impressive feats of memory, reciting countries, populations and so on, but that it wasn't until he was eight, when sibling rivalry drove him to beat his older sister at chess, that he really began to focus on the game. Back in 2004, young Magnus humoured me when I asked if I could play a game with him. It may not have been pretty, but at least it was over quickly, and he looked bored throughout. I have no intention of reminding him of that painful drubbing today.

The look of boredom is to do with his brooding features, a sulky mouth and a heavy, almost Neanderthal brow, which furrows when he concentrates. These looks, I should add, led to him being named one of "the sexiest men of 2013" by Cosmopolitan, and have earned him lucrative modelling contracts, appearing alongside the Hollywood actor Liv Tyler in advertising campaigns for the fashion brand G-Star. And they are combined with a slow-burn, lopsided smile that starts on one side of his mouth and creeps across his face like a shadow. He does that during matches, when he realises he has a checkmate in his sights. It must put the fear of God into his opponents.

I ask him if he ever feels sorry for them. "Not really," he says in a low, measured voice, traceried with Norwegian. "But I find it more difficult to play opponents who I feel, for whatever reason, aren't approaching the games with a sufficient level of seriousness. For instance, once at a big tournament I saw a player I was due to play the next day have a couple of drinks. Knowing that just ruined my concentration, because I thought how can I play seriously against someone who has drinks the day before?"

We describe him as a genius; does he think he is one? Carlsen sinks lower on the sofa. "No, I am not. I'm just really, really good at what I do. I'm fortunate to do something I love, but I'm not a genius." How would he describe himself then? "I guess I'm pretty laid back." As he says this he sinks lower still into the sofa, as if to illustrate what he means. Is it a pose? I don't think so. The posture suits his personality, his languor. "But I am also determined when it comes to chess. I don't like conflicts, apart from on the board. In general I am very different to how I am on the board."

From the age of 13 he was a household name in Norway. Did he get picked on at school for that? "Not really. Some people I didn't like, and they didn't like me and would occasionally call me names, but it didn't really bother me. I used to like provoking people and occasionally they would retaliate." I ask him if his three sisters kept his feet on the ground, teased him. "Yes, they didn't give me any special treatment." His father told me that he could be stubborn. "Yes definitely, especially with my sisters, because they are also stubborn."

An example of this stubbornness was his decision to forgo a university education. 'My parents wanted me to go, but at some point I lost interest in formal education and they were OK with it. I wasn't paying much attention so I wasn't great at school." That low boredom threshold again. Does he get bored easily? "Yes, in my later years at school I was bored, not necessarily because it was too easy, but because it didn't interest me."

Pawn star: getting ready back stage at the G-Star Spring 2011 fashion show in New York City. Photograph: Rob Loud/Getty Images

Today Carlsen is wearing a grey blazer adorned with his sponsors' logos, and the steel and glass building I meet him in is home to another of his sponsors, an investment bank. Unusually for a chess player he makes more than £1m a year in sponsorship, and he doesn't seem to mind performing stunts as part of his contractual obligations, such as the blindfold simultaneous games. In fact, he seems to enjoy doing them and says he wants to take on 20 players next time. "When you think about chess all the time you are playing blindfolded anyway, sort of. But I can understand why other people find it freaky. One of the beauties of chess is that you don't need a board either to play or analyse."

Boards are rarely set up around his home, he adds, because he doesn't need them to train. Nor does he rely on computers as much as other leading players. "I use them to analyse my openings, but in tournaments my assumption is that I am the best player there. That is why I seek positions where computer analysis can't play that much of a role, or where I can analyse it better than a computer." Not short of self-belief then.

Back in 1997 when Deep Blue, the IBM supercomputer, beat Kasparov, it caused a sensation and there was much debate about man v machines. There is no longer a debate. The best machines can beat the best humans. Carlsen tells me he doesn't play against them any more. "I never had any fun playing computers. It doesn't bring me satisfaction to beat them and losing to them is always painful."

Losing to Deep Blue disturbed Kasparov's equilibrium, I note. Big time. "Yeah, but I think every loss damages Kasparov. He's one of those people," says Carlsen. "He didn't think he was going to lose to Deep Blue, but towards the end of the match he was nervous and second guessing himself all the time, and I think basically he beat himself."

Computers don't suffer mental fatigue, of course. What about when Carlsen has been playing for seven hours at a stretch? Does he get headaches? "No, not really, but I do get tired. I can't sit there for seven hours straight. I need to freshen my mind by going for a walk."

Ah yes, the pacing, for which he is known. Is it gamesmanship? Chess, after all, lends itself to psychological warfare – Mikhail Tal's infamous hypnotic stare, for example, or the kicks that Petrosian administered under the table to his rival Korchnoi. "No, the pacing is to let my mind wander before getting back to the game with a fresh perspective."

There are more possible games in chess than there are atoms in the solar system — and even to try to think about that statistic makes you dizzy. Yet grandmasters welcome such intellectual vertigo and refer to being in "the tank", a place where they can enjoy losing themselves, their sense of time, as they swim around with ideas. Even so, when he considers a move for a long time, for an hour, say, running variations round and round in his head, does he ever feel like he's being driven mad?

"A little, maybe. But if I study a position for an hour then I am usually going in loops and I'm probably not going to come up with something useful. I usually know what I am going to do after 10 seconds; the rest is double checking." He calls this process verifying his intuition. "Often I cannot explain a certain move, only know that it feels right, and it seems that my intuition is right more often than not."

there are parallels between Carlsen and Bobby Fischer, the only other "western" chess world number one. Both made their name at a tender age with an audacious queen sacrifice, both had their childhoods distorted by fame and both are fanatical about physical fitness. Carlsen is a member of the gym in his new apartment complex; he is also a keen skier and football player. "I've recently started playing for a team here in Oslo. I play at left back where I can do least damage."

And yet I've heard that, when not exercising, he is quite lazy. Is that fair? "Yes, I am quite lazy, I like to sleep in until noon. Most of my friends have jobs." He does "a bit of yoga", although he adds: "So far I haven't thought of any brilliant chess moves while lying down."

Does he dream about chess in his sleep? A long sigh. "Occasionally, but these dreams are usually connected with something negative. I am losing to players I never normally lose to and I am arriving late and being defaulted; that happens so many times in my dreams – I don't know why."

Fischer was single for most of his troubled life. Carlsen doesn't have a girlfriend at the moment. "I haven't had too much time to develop any serious relationships, recently anyway. I'm hoping after the world championships I will be able to change that."

I imagine a girlfriend will have to be at least knowledgeable about chess. "Yeah. Probably. But it's also nice to…" He trails off. "I really don't like it when I go out and some girls start talking to me about how they played chess with their grandfather as a kid, I can't stand that. It's boring. I want to talk about whatever else."

I ask about his emotional landscape: does he cry? "I was really upset yesterday when I tried to install my new TV and there was no sound. But that was more frustration. Cry? I don't really. I get angry, but mostly about chess."

I suppose the issue I am circling around is the one he jokes about, "the crazy". Is he protective of his mental health, worried about losing his mind in the way Fischer did? "It was probably only the chess keeping him sane. He would have gone insane much quicker without it. His story is very different to mine. He had a difficult upbringing. Difficult relationship to his family. I have lived a much more sheltered, normal life. As normal as it could be, considering how much I travelled."

Shortly before he became a grandmaster at 13 (Fischer became one at 15, Kasparov at 17) Carlsen's parents sold their car, rented out their house and took him and his sisters out of school to explore the world for a year. Their travels took them to Reykjavik, Iceland, scene of the epic Cold War-by-proxy Fischer-Spassky match – and it was here that Magnus himself took a leap into legend when he found himself playing the great Kasparov. They drew, but not before the young Magnus had got bored and wandered off. Kasparov was rattled but has since become Carlsen's champion, even working as his coach for a while. He has said, indeed, that such will be Carlsen's dominance of the game for the next couple of decades, it will be known as "the Carlsen era".

In August, Carlsen was out in Chennai, India, doing a recce, and was greeted by 2,000 cheering fans, mostly female. One reason for the trip was to try the food in the hotel where the tournament will be held, to check it wouldn't make him sick. Still, he's planning to bring a Norwegian cook along anyway.

"I generally try to eat healthily, avoid quick carbs that make your blood sugar go up and down, which is bad for concentration." He eats one and a half hours before a game, and tries to sleep until as close to the start of the game as possible, "because my mind works best four or five hours after I wake up".

In the nearby harbour a foghorn sounds. Carlsen's manager enters and says our photographer is ready. As we head up to the roof terrace, he asks me if I play chess. Before I can answer, Carlsen says: "Yes, I played him when I was 13." He has remembered. Of course he has. He then vaults athletically over the railings. A grandmaster, yes. A typical one, no.