The university is one of eight running courses as part of the National Academy for Gifted and Talented Youth, which is providing two-week residential places this summer for more than 1,000 pupils.

Kevin, aged 15, from Wadham business and enterprise school in Crewkerne, Somerset, said he could not recall ever being teased by his classmates because of his success in subjects such as maths.

“I get on with every social group in my school,” he said. “It’s more about personality. It’s the older generation who think that there’s a lot of bullying going on.”

Other teenagers said they felt lucky because they attended schools where intelligence was a source of pride - although they appreciated that they might have been picked on elsewhere.

The courses at Imperial included a maths summer school, which Kevin attended, and a robotics and engineering course in which students constructed a geodesic dome out of pipes and bin bags.

Alison Rowan, spokeswoman for the academy, said: “A lot of the young people feel they get unfairly portrayed by the media - if they are outside they are louts, if they are inside they are obese, and if they are at their desks they are nerds.”