Mozart composed piano sonatas at the age of five. Picasso painted his first publicly acclaimed work at the age of eight.
But not all gifted children are encouraged from an early age, say researchers from Brunel University.
They say there is an absence of organised activities to develop and challenge very young gifted children. They cite five-year-old Matthew, who described himself as "a waiter", because he was always waiting for others to catch up.
The researchers observed 14 enrichment programmes for gifted children aged four to seven. Guided by adults, the pupils embarked on independent research and worked with peers of similar ability. The effect was dramatic.
One reception teacher spoke of a taciturn girl who was asked to do an independent project on butterflies. "A quiet dreamer became a passionate worker," she said.
"Ask the children about their interests and let them do a personal interest project and you will soon identify your gifted and talented children."
Parents also noticed transformations. One mother said: "The difference to Daniel is tremendous. He wants to carry on finding out more.
"Television time has now been replaced by talking about what he wants to find out before the next club time."
Last month, it was announced that the National Academy for Gifted and Talented Youth, at Warwick University, was to expand to include primary pupils.
From September, the national teacher training programme on gifted and talented education will extend to foundation stage and key stage 1 teachers.
The academics say such developments are crucial. "Personalised learning opportunities have been shown to contribute more to the well-being of individuals than the shackles of uniformity."