To top it off, the defending world champion isn't a geek with the social skills of a handless sock puppet. He has an army of fans and his own app. He's even done spot of modelling.

Carlsen became a grandmaster at 13. A few days before his 22nd birthday in 2013, he bagged the title of world champion, and retained it the following year at a tournament in Sochi, defeating former champion Vishy Anand. Hailed by some as the best chess player the world has ever seen, he's appeared on TV, radio, billboards and the sides of buses. Ahead of our meeting, I half expect the 25-year-old to stride in with an entourage of doe-eyed groupies. Instead he wanders in clutching a sandwich, hands me a paper bag and says: "Sorry I'm late. I brought you a pastry."

Carlsen started playing chess with his father at five. "He started with one pawn, and I had all the pieces, and when I managed to beat him he got two pawns, and so on," he remembers. "So he made it progressively more difficult as I got better." Unlike other grandmasters, it took him until age eight to really engage with the game: "I needed to mature a bit at the start. I just wasn't ready." He needed to become a mature eight-year-old? "Well, some people can really focus on chess at a much earlier age, even four or five years old, but I couldn't. Age eight was the right time for me."

Now Carlsen believes he's already reached the peak of his brain power? "I still think people can learn at any age - I'm actually sure about that. It's just that the ceiling is lower for how far you want to go."

During an interview on the YouTube channel SoulPancake, Carlsen told actor and presenter Rainn Wilson that the first line of his autobiography would be: "I am not a genius." He's also claimed on numerous occasions to be somewhat lazy. So what catapulted this supposedly lazy, late-blooming non-genius to the top spot in the world? "It was no accident that it was me rather than my peers in Norway that made it. They may have had chess training once a week and then a tournament on the weekend, like a normal hobby. But it was something I wanted to do every day, so it was only natural that I surpassed them. How I managed to take the next steps rather than others, I cannot tell you."

Now, though constantly thinking about chess, Carlsen only sits down to practise for around an hour a day - not even necessarily at a chessboard, because he can recall the board perfectly in his head.

But Carlsen has also been applauded for making chess cool. While playing in Holland, he was spotted on TV by the head of the Dutch clothing brand G-Star - "apparently they thought chess and fashion was an interesting and unexpected mix" - and was offered a modelling contract. He did shoots and wore G-Star clothes during his 2010-11 and 2013-14 games, as well as appearing in G-Star Raw's spring/summer campaign with Lily Cole, in 2014. Now, however, he's "very happy just to play chess".

Except he's not just playing chess, he's also connecting with his fans via an app called Play Magnus: users play a computer version of Carlsen at different ages ("anyone can beat Magnus five ... the moves are absolutely random"). Does he play himself? "Yes," he grins, "a little bit." Supposedly that's a win-win situation for him? "It doesn't feel like that," says Carlsen, who admits he's both cried and punched walls over chess games, saying "it feels equally miserable to lose to myself".