In psychology research literature, the term child prodigy is defined as a person under the age of ten who produces meaningful output in some domain to the level of an adult expert performer. Child prodigies are rare; and, in some domains, there are no child prodigies at all. Prodigiousness in childhood does not always predict adult eminence.
The term wunderkind (from German: Wunderkind, literally "wonder child") is sometimes used as a synonym for "prodigy", particularly in media accounts. Wunderkind also is used to recognize those who achieve success and acclaim early in their adult careers.
Examples of particularly extreme prodigies could include Wolfgang Amadeus Mozart, Felix Mendelssohn, Evgeny Kissin and Teresa Milanollo in music; Bobby Fischer, Samuel Reshevsky, Judit Polgár, Magnus Carlsen, Sergey Karjakin, Paul Morphy and José Capablanca in chess; Carl Friedrich Gauss, Shakuntala Devi, Srinivasa Ramanujan, John von Neumann and Terence Tao in mathematics; Pablo Picasso and Wang Ximeng in art; and Saul Kripke in philosophy. French composer Camille Saint-Saëns has been recognized by musical historians as one of the greatest musical child prodigies, but his mother was cautious, and didn't seek to exploit her son's skills, fearing it would cause him emotional trouble.
PET scans performed on several mathematics prodigies have suggested that they think in terms of long-term working memory (LTWM). This memory, specific to a field of expertise, is capable of holding relevant information for extended periods, usually hours. For example, experienced waiters have been found to hold the orders of up to twenty customers in their heads while they serve them, but perform only as well as an average person in number-sequence recognition. The PET scans also answer questions about which specific areas of the brain associate themselves with manipulating numbers.
One subject never excelled as a child in mathematics, but he taught himself algorithms and tricks for calculatory speed, becoming capable of extremely complex mental math. His brain, compared to six other controls, was studied using the PET scan, revealing separate areas of his brain that he manipulated to solve the complex problems. Some of the areas that he and presumably prodigies use are brain sectors dealing in visual and spatial memory, as well as visual mental imagery. Other areas of the brain showed use by the subject, including a sector of the brain generally related to childlike "finger counting," probably used in his mind to relate numbers to the visual cortex.