When six-year-old boys start going to university, surely something must be going on?

Justin Chapman has started studying ancient culture at the University of Rochester in New York state, even though the doors to the lecture theatre are too heavy for him to open.

He's just the latest in a line of super-intelligent children which, although stretching back to Mozart and earlier, some experts think is becoming more common.

Yet while most parents will hope their children are bright, having a super intelligent child poses all sorts of problems of its own.

As well as having the stress of answering all the questions thrown up by an unquenchable curiosity, there are complicated issues of schooling. Will their school stretch them enough, for instance; will other children bully them, and will they forever remain bookish types who can't relate normally to other people?

Many people hold the parents of gifted children with some suspicion, imagining that they must be pushing them at every step of the way, training them in Latin verbs while they also train them to use the potty.

But it's not quite like that, according to child psychologist Edward Chitham who advises parents through the National Association for Gifted Children. He says many parents are reluctant to admit that their children are bright.

"They will say that they don't think their child is gifted. They are very frightened of the idea that their child is gifted, they don't want publicity or a high profile," he says.

It is easy to tell which parents are those who genuinely want what is best for their children, whatever it might be, and those who are trying to live their lives through their children, perhaps to make up for their own failings.

But their fears of publicity may be valid - for as the news of Justin Chapman has gone around the world, it seems the interest in child prodigies is as high as ever. Most British readers will have strong memories of Ruth Lawrence, the brilliant mathematician who rose to national fame when she went to Oxford University aged 12.

And last year, 12-year-old Hero Joy Nightingale, who cannot speak or use her body, won an international award for her internet magazine, From the Window, which she edits.

Or the remarkable Yusof children. Sufiah Yusof earned a place at Oxford at 12 while her bother and sister, Iskander and Aisha, started at Warwick University at ages 12 and 16 respectively.

The degree of notoriety many child prodigies achieve - along with society's tendency to think of child geniuses as circus performers - cannot be good for a child, the thinking goes.

And, Mr Chitham says, finding a way of making the most of the intellect and socialising children properly is a very difficult balancing act for parents and schools to perform.

But he says the amount of stimuli available to young children has led some people to conclude that the number of gifted youngsters is on the increase.

For instance, many children are showing a very high ability on computers by the time they are only three or four. But unless their school can find the right approach, it will run the risk of "standardising" bright kids by the time they are seven or eight, he says.

And there were other problems too. One mother had told Mr Chitham that her 10-year-old son's school had been good about recognising his gift. But it had gone the other way and was actually putting too much pressure on him.

"They are saying: 'You got it wrong. You mustn't get it wrong, you're bright.' This little lad doesn't need pressure, he needs opportunities - perhaps the chance to do extra work or interesting work."

None of which detracts from Justin Chapman's success. "It's a very high achievement for a little boy like this," he says.