I must have been in about the 6th grade when I realized there was something special about mathematics.
I learned the formula for the area of a circle, pi-r-squared. And that was not so special. It seemed reasonable that a circle's area should depend on the "square" of the radius, and of course there would be some proportionality constant.
Then I learned that the area of a sphere was 4 -- exactly 4! -- times the area of a circle of the same radius, and that struck me a truly remarkable. From then on I was a geometry junkie.
As I went on with my education, that little constant pi started showing up everywhere. I remember my Dad, who was a quality control engineer, showing me how to calculate pi by dropping needles onto lined paper. Later 3.14159 threaded its way through my studies of engineering and physics, showing up in the darnedest places.
No one knows why mathematics -- presumably an invention of the human mind-- is so amazingly useful for understanding the world. Einstein said that "the creative principle resides in mathematics." Or is it the other way around?