“Anand is a much better player than me,” he said.

His modesty may not be exactly false. He is not the only chess prodigy to have emerged in recent years. Modern players — aided by powerful computers used for training, access to databases of games stretching back hundreds of years and unlimited opponents online — have gained the coveted grandmaster status at much younger ages than in the past.

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While Magnus earned the title at 13, two other players, Sergey Karjakin of Ukraine and Parimarjan Negi of India, did it at a younger age. Over the last 17 years another dozen players have broken the record set 40 years ago by Bobby Fischer, the American champion, who became a grandmaster at 15.

But Magnus stands out for more than just his age. His style of play and sang-froid are unusual. Since he began playing at the age of 8, he has favored tactically complicated positions, creating situations in which he is comfortable, and his opponents, even the best ones, often wilt. He is also mentally tough. He said that sometimes during games he loses his concentration, but then he silently scolds himself, saying: “You are not going to lose this game like an idiot. Try to pull yourself together.”

Some chess players are devastated by losses, letting them infect their mood and their subsequent play. Losing at chess does not bother him that much, Magnus said. “I get more upset at losing at other things than chess. I always get upset when I lose at Monopoly.” So much so that his sisters team up to beat him.

Their fervent sibling rivalry is the rare blot on a home life that seems almost idyllic. His father, Henrik, is an information technology consultant who has spent a good deal of time traveling with his son when not working; his mother, Sigrun Carlsen, is a chemical engineer. Both are active and down to earth. Magnus has three sisters: Ellen, 19; Ingrid, 14; and Signe, 11. Ingrid said her brother often teases her, almost to the point of bullying, something that he admitted with a devilish grin. “What kind of brother would I be if I didn’t tease her?” he asked.

Stories of chess prodigies often begin with a eureka moment when the child discovered the game or displayed some heretofore hidden talent for it. Magnus’s interest can be traced to competition with his sister Ellen. Their father, a good tournament-level player, tried to teach Magnus and Ellen to play when they were 5 and 6, but neither showed much interest. It was three years later, after Ellen had begun to play seriously, that Magnus started learning the game, mostly because he wanted to beat her.

One day, when he was 8, he challenged Ellen to a game and won. “The sad thing about that,” their father said, “was that she then quit for four years.”

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The boy, meanwhile, was hooked. He began playing regularly in tournaments, and his progress was, by chess measures, spectacular. A year after playing his first tournament against children his own age, he was competing against adults and beating them. For a while he studied with Simen Agdestein, a grandmaster and former Norwegian champion, but Magnus has now surpassed him and studies on his own to supplement the vast catalog of positions he has memorized. Last year he spent more than 200 days on the road playing and earned $250,000 after expenses, his father said. Given his results this year, his earnings will surpass that.

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Henrick Carlsen said his son’s progress in chess was typical for him. “Sometimes, he’s been thought to be slow,” he said. But when he gets interested in something, “then he accelerates.” He added, “I don’t think he is conscious of this approach. It is innate.” He said that his son, from a young age, exhibited an ability to focus single-mindedly. One day, the father recalled, when Magnus was 4, he spent six hours building a train out of Legos. A half-hour after he went to bed, Mr. Carlsen found him in the dark “wide awake and staring into space, and I thought, ‘O.K., this is too much.’ ”

Magnus’s parents have not had their son tested for developmental disorders because he is well-enough adjusted socially. “Magnus seems to be fortunate enough to have the right characteristics to be considered normal despite the fact that he has some traits that might lead others to call him abnormal,” his father said. “Most people like him.”

That includes his rivals, particularly Mr. Anand. Earlier this year, at a tournament in Mexico, Magnus and his father went to dinner with Mr. Anand and his wife, Aruna. At the table, according to chessbase.com, a chess news site, Magnus and Mr. Anand did a verbatim recitation of a Monty Python skit in which the pope, played by John Cleese, chastises Michelangelo for embellishing his painting of the Last Supper.

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Among the world’s top players, the thing that sets Magnus Carlsen apart, aside from his age, is that he still a student, though “he is not really interested in school,” his father said. For the last three years Magnus has attended the Norwegian College of Elite Sport, a school for gifted athletes. Since many of the academy’s students compete, they use the Internet to keep up with class work.

Students take academic classes as well as specialized ones in the discipline in which they excel. This year Magnus’s courses will include Norwegian, Norwegian dialects and modern history.

Whatever its benefits, his education is probably not the key to his future. Regardless of the outcome of the tournament at Bilbao, which ends Sept. 13, if he continues to be a top player well into his 30s, Magnus could earn millions, as Mr. Anand has and as did Kasparov, who retired from chess in 2005 at 42. By the time Magnus is 25, his father said, he expects that his son will have enough money for the rest of his life.

At the College for Elite Sport, Mr. Agdestein, the school’s chess instructor, said he has to be careful with Magnus. “He is not very disciplined,” he said. “But he is such a great talent. Now my main task is not to destroy anything.”

As the students milled around after a class earlier this year, Magnus was asked if he was learning much from it. No, he said, but “I’m certainly enjoying myself.”