Blonde and smiling, Georgia Brown looks like any other cute, lovable toddler. But behind her blue eyes is one of the highest IQs in the country.

By the time she was 2¾ Georgia, one of five children, was in the record books as the youngest member of Mensa. At her first test she fell asleep; her IQ was still measured at 152. When she was quizzed a second time, her score shot up to 170, putting her in the top 0.01% of the population (100 is the average IQ).

Georgia’s mother, Lucy, chief executive of a charity, is unfazed by the challenge of filling her daughter’s racing brain, answering endless questions such as “Where does energy come from, Mum?”. But neither Brown’s maternal experience nor her common sense could stop her crying in front of Georgia last month.

The reason? A letter saying that her daughter, four this summer, had not been awarded a place to start at an excellent state primary school three miles from their home in Aldershot, Hampshire. Instead it was suggested that she try for places at more unpopular schools, which are, in Lucy’s view, totally unsuitable.

Georgia is one of an estimated 100,000 children who did not get a place at their first choice of school. But, her mother argues, supported by research showing that the higher the intelligence of a gifted child, the greater their vulnerability, she is more in need than most.

“Don’t cry in front of Georgia, Mum,” one of her older daughters counsels. “You’ll only upset her.”

Lucy sees her youngest daughter’s intelligence as a “serious psychological condition”, adding: “The school she goes to has to be the right one to deal with it. If we don’t get that right it could be detrimental to her wellbeing.”

The sad fact is, there is no track record in Britain of handling gifted children well. You would think that the future could only be glittering for such youngsters. But the past is littered with stories of prodigies whose gift turned out at times to be more akin to a curse.

The maths whiz-kid Sufiyah Yusof’s exposure as a hooker was the latest troubling tale. She went to Oxford aged 13 to study for a maths degree, after being taught by her father. At 15 she ran away from the university, refusing a reconciliation with her family before returning to Oxford. Last week it was revealed that she was charging £130 an hour as an “Asian escort”.

Ruth Lawrence’s story is less distasteful: home-schooled by her father, Harry, she became, aged 11, the youngest student at Oxford. Graduating with a first-class degree, she obtained a post at Harvard University at 19 and teaches maths in Israel, but has said she would have liked her childhood to be different.

Adam Dent went to Oxford aged 14 but left after being accused and then acquitted of sexual assault on an older student. After stacking supermarket shelves, he went back to Oxford, finally graduating with a first in chemistry six years ago.

Have schools and parents learnt any lessons from such stories? Do we understand the risks of hothousing clever kids? How crucial is it that they attend a school that can teach them so they are not bored but can also ensure that they make friends and learn to cope with every aspect of life?

Next week a television series will revisit seven of Britain’s most brilliant children, from Georgia Brown, 3, to Dante Minghella, 13, nephew of the late film director Anthony Minghella. Most of them were featured a year ago on the Channel 4 programme Child Genius. All have been tested by Joan Freeman, a psychologist, and found to have high IQs. The aim is to track them for the next 12 years to see if they fulfil their early promise.

Several of the families have struggled to find a suitable school for their child: some are now teaching them at home. Peter Williams, a chess genius, for instance, has not been to school since he was seven, after being refused permission to take time off to have chess coaching.

In the television programme Peter, now 11, has been chosen to represent England in an international chess tournament. Against other players of his age, instead of taking home the medal he had hoped for, he ends up 67th out of 91. He is visibly shaken by the outcome. Is it time to rethink the strategy? He starts going to Scouts – “I won’t die without friends, but they are nice,” he declares – and private tutors are hired. But neither Peter nor his dad, who has no formal qualifications, thinks he should go to school.

Even where gifted children are in good schools there can be problems. With an IQ of 170 Dante is moody at home and underperforming at his fee-paying school, which threatened him with expulsion when he brought in a replica gun. The saga ended with Dante having to have a psychiatric assessment. “I definitely fit the profile of brooding psychopath, don’t I?” he mocks.

His parents had taken him to see five therapists. Dante, however, who easily floors most adults in an argument, dismisses therapy as “the opiate of the middle classes”. With his father wondering “how much longer we have to survive in this dynamic” they have his brain scanned for abnormalities; there aren’t any.

Another family on the programme, the Napier-Smiths, deal with the challenge of how to educate their son Adam by sending him, aged eight, to a private boarding school 200 miles away that prepares children for Eton.

After moving house to try to find a suitable school five times in as many years, his mother, Emma, who was brought up on a council estate, thinks they have found the answer. Adam, now in his eighth month of boarding, is, Emma says, “really happy” and sufficiently stimulated at last.

One thing she notices is that Adam seems to be becoming just another little boy, enjoying toffee apples instead of endlessly reading. She admits she was dazzled by his gift. “We always looked for a school to cater for his academic needs. But then we became more relaxed about his abilities. I felt he should be somewhere he could enjoy himself,” she says.

“I have seen children who’ve never grown out of that geek, boffin stage. It is cute when someone is six doing very difficult maths and speaking in a small voice, but society doesn’t look kindly on teenagers or adults like that. It’s fine having a brain but if you can’t mix in society there’s no point.”

Back in Aldershot, Lucy Brown is considering whether to have a last shot at getting her daughter into the school she believes can handle her. “If Georgia does not have the right start in life I do think her gift could turn out to be a curse,” she says.

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