Is there really such a thing? Are there really people who can "just do" math when they are very young? Or is it a learned talent passed down to them by a great teacher? I'm sure you've heard of 8 year old kids who can work out partial differential equations. But is it because they are born with an innate ability that lets them digest math? Or were they trained rigorously by a very motivating teacher? I mean how do these kids even hear about these advanced math topics. It would have to come from a parent or some expert in the field, which would no doubt press the child from an early age to go beyond the school's cirriculum. And a young mind can easily absorb a lot of information at once, so why not a language called math. These pupils wouldn't be able to shine just by knowing addition in gradeschool, so I imagine someone is pushing them ahead. Use yourself as an example. If you had a father who was a mathemetician, and he gave you a lot of algebra as a toddler you'd no doubt seem as a genius to your peers. Would you have been able to grasp it? Or are prodigies the only ones?