While I don't think one need be an autodidact to possess talent in a field, I do understand what Quantum is getting at. Of my two children, only DD10 has asked deep questions related to math and tried to concoct her own "tricks" and theories regarding math. She clearly THINKS about math. At 3 or 4, she came to us with the observation that some number have "middles" and some do not, and one could classify them that way, and this seemed important. (She had figured out even and odd.)
She is also good at calculation and a strong math student, though not actually highly outstanding. Math is NOT her favorite subject. Yet it's this interest in *thinking* about math which still makes me think that there may be some latent math spark that will emerge in later grades.
DS5, in contrast, has never come to us with any such mathematical musings. He is certainly ahead in math, but I don't see any interest in math concepts or ideas. He knows facts and operations about as well as DD did at this age, but I would be surprised if math ever was a topic of great interest. Yet he is the one with the unusual chess gift.
It's not that DD tends autodidactic and DS does not. They both tend autodidactic.
