Originally Posted by indigo
A child who has a gift for math... an interest in math and affinity for math... a love of math... would typically be asking for extra math at home, and would therefore typically have had substantial exposure to above-grade-level math.

... if their parents recognize their math talent for what it is, and have the knowledge and resources and time to provide this for them. And if the child has the kind of temperament suited for independent study, and has enough time and is in good enough health to pursue it.

You're making a lot of assumptions here.