The Boston Globe has an excellent article about the psychology of gifted children and how many of them have fared in adult life. It describes the difficulties some have in adjusting, and the importance of maintaining traditonal childhood activities.
Consider the contrasting fates of two prodigies from the early 20th century. Norbert Wiener entered Tufts University in 1906 at age 11 and went on to graduate studies at Harvard in 1909. That same year, a brilliant 11-year-old named William James Sidis also enrolled at Harvard. Wiener became the father of cybernetics. Sidis became a recluse who collected streetcar transfers. He died alone and disillusioned at the age of 46.
On a related note, neuropsychologist Brian Butterworth has studied brain activity in a ‘mathematical prodigy’, and found that compared to others, he used different brain areas to perform calculations.