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This seems to ignore that Carlsen himself has a life outside chess. Carlsen says his other interests involve chatting with friends on the internet, playing online poker, skiing, and playing football. But those enterprises are not the cognitively demanding interests that Nunn has—astronomy, physics, and extremely arcane and high-level math.

"If you're one hundred percent committed, it's very painful when things go wrong," Nunn says, "because you don't have anything else to fall back on."

Things will inevitably "go wrong" in most fields of endeavor, as performance and ability start to decline with age. Nunn coped with that by quitting. Numerous studies have shown that what's called fluid intelligence, which relies on working out abstract problems, and speed of mental processing, both decline in efficiency after about the age of thirty. On the other hand, another subset of intelligence, known as crystallized intelligence, which utilizes real-world information, maintains its peak level for many years before slowly declining. Nunn seems reluctant to accept that anything about his brain function has changed, and indeed says that his chess ranking has stayed about the same since his professional playing days.

"What changes is you have [a] family and have other priorities," he says. "You don't want to focus exclusively on playing chess. But just for age reasons you get tired more quickly. I still feel I can play as strongly as I did but, you know, you play a long tournament, it's exhausting."

I spoke to Neil Charness, professor of psychology and director of the Institute for Successful Longevity at Florida State University. Charness and his Florida colleague Roy Roring conducted a study of the change in chess ability across lifespan. Using a database of 5,011 chess players, they found that the average peak age—the age at which players on average attained their peak rating—was 43.8 years. They also found that age is "kinder to the more able," meaning that more highly skilled players tend to show milder declines in rating when past their peak age. "The problems for older players," Charness says, "are probably similar to those for any aging adult, namely that learning rate slows." Learning rate drops off by half between your twenties and sixties, and as a result there are lots of rising younger players who can outwork you and beat you. While we're on the maudlin topic of cognitive decline, Charness adds that there are probably some age-related changes in motivation. Also, brain efficiency declines in a number of ways, including memory, attention, and speed of processing. "So, although chess for humans is mainly a game drawing on pattern recognition and knowledge, and despite the fact that you can keep learning throughout life, you may have problems retrieving the relevant information in a timely fashion."

All this seems to tally with Nunn's experience. But I'm interested in how people at the peak of human potential have gotten there, and I want to find out what it was like when he was younger. Nunn says sure, he felt different from other kids. Was it obvious to him that he had this strength? "If you keep winning tournaments it's pretty obvious," he says. "I won the London under-twelve championship when I was nine." Did his success make him cocky? He says he was a balanced kid, if slightly solitary, with friends his own age.

What other signs were there, if any, that there was something different about him? "When I was very young, before I could read, my parents noticed I was looking through all the books in the bookcase, and they said, 'What are you doing? You can't read'—and I said I was looking at how many pages there are in each book. I'd worked out how the numbering worked at the bottom of the pages. So they asked me how many pages there were in certain books, and I knew. So I would say my mathematical talent was evident early on."

Nunn passed A-levels in pure math and applied math in his midteens. But why go to university so young? "I wanted to go. I was fourteen. If I didn't go, I'd be hanging about for years. Not a good idea, really, for a teenager. So I wanted to go, and my parents agreed. It all worked out quite well."

I wonder if there was a similar discussion in the Wolsey household when young Thomas (later to be Cardinal) Wolsey went up to Oxford to read theology at fourteen. There would be no younger undergraduate for more than five hundred years, until Nunn himself. (Incidentally, there has since been a younger undergraduate. In 1983 Ruth Lawrence went to Oxford at the age of twelve. Her field of study? Algebraic topology.)

What about looking after yourself at that age? Most students can't work the washing machine. "That was very tricky," he says, in a way that lets me know that it wasn't tricky at all, "but I figured it out."

More challenging was social life. At university, Nunn was too young to drink. "The difference between fifteen and eighteen is quite a lot. A lot of activities don't appeal very much. On the other hand, I had mathematician friends and friends at the chess club. By the time I was seventeen, it all felt normal."

Nunn's assessment of his ability and his success mirror the sort of thing Hambrick sees in his research: that expertise is built on innate skill. "I think my talent in chess and math was inherent," says Nunn. "But in any activity, if you want to go to the top, you have to have talent and put in the work."

I started by assuming that chess was a game of pure intellect. Does that mean people who are chess experts are also more intelligent than average? It appeals to common sense that this would be the case, but it's controversial. Chess experts tend to practice intensively for years, and it's hard to separate that from innate talent or intelligence.

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