Other forms: precocities
The noun precocity describes a smartness or skill that's achieved much earlier than usual. You'll be proud of your puppy's precocity if he is perfectly trained by the age of four months.
If you're precocious, you've got the quality of precocity. You could also call it precociousness, but either way it means you're way ahead of the curve in ability or intelligence. You might comment on the precocity of your niece who learned to read when she was three, or the neighbor who started college at the age of fifteen. The root word is Latin, praecox, or "maturing early," which comes from pre, "before," and coquere, "to ripen or cook."