[lolinder]

"Prodigy" and "genius" both lack rigorous definitions, so your problem might simply be one of cherry picking. Going with my own gut on each definition, here are a few examples to add to those already provided by sibling comments:

* Magnus Carlsen (chess grandmaster by 14, world champion for 10 years as an adult)

* Frédéric Chopin (concert pianist at 7, one of the top composers for piano)

* Blaise Pascal (rediscovered Euclid on his own at 12 with no training, went on to become one of the most famous mathematicians of all time).

* John van Neumann (could divide two 8-digit numbers in his head at age 6, learned calculus by 8, went on to be a founding figure in computer science).

Shall I go on, or is this enough?