You can be a child genius but not have any knowledge - which means you still have to learn - prodigies learn at an accelerated rate - and once identified by educators, are put into special advanced classes. Some will move through complex subjects like the Calculus at age 13 - and that gets the attention of special educational entities that have the student "challenge" each class through testing.
I asked a similar question in February. There were 14 answers, some of them very interesting. You might find the answer to your question there.
Caluvox opted for a "genetic mutation". lossless suggested environment and superior intelligence. TruthIsObvious thought that perhaps they were the normal ones but the rest of us were lacking. Sasquatch took a humorous approach. Noveltman blamed the parents (and there's evidence for that in some areas but not all). Yosey blamed it on an evolutionary anomaly. Kwojcik's answer was one of the most interesting but hard to express in a simple sentence.
But something that was NOT mentioned by anybody was the theory that prodigies are reincarnations of people who were gifted in a particular field in a previous life and somehow brought their abilities with them.