7Mick7

While it's unlikely that many people can grasp and master calculus (or even algebra) at 12, it isn't impossible. I went through my dad's statistics and calculus books as a kid, and, though I wasn't completely self taught (dad answered some questions as they arose), all of the learning was outside of my school system, as my district was not equipped to teach calculus, even at the high school level. In fact, none of my teachers through my high school years had even taken a calculus course themselves. If this was the situation facing this student (and others in mathematics programs), I am surprised that this student didn't avoid math or act out during class for many years after such an experience. Sitting through classes on fractions and division after calculus isn't the least bit fun (not to mention how demeaning it is!). This being said, it is certainly possible to be an autodidact in higher level mathematics. I am self-taught from Calc III through enough mathematics to understand many papers in this field and related fields and to have had the pre-recs for an advanced degree waived after spending time talking with professors in my program. Time and motivation are essential, as well as a good grasp of research skills and cross-referencing what one reads. It is definitely easier to obtain material these days than it was when I was a child/teen in an area without Internet or a good public library, and I wouldn't be surprised to find a larger amount of students these days teaching themselves from such aforementioned resources to occupy their minds and expand their knowledge outside of school.