[Ivanov]

Being able to use something and knowing the whys are two different things. Many people know Calculus(practice), but not many know Real Analysis(theory behind Calculus, the academical bit).

"In mathematics, the quaternions are a number system that extends the complex numbers."

Naturals are a subset of integers. Integers are a subset of rationals. Rational are a subset of reals. Reals are a subset of complex numbers. The latter are a subset of quaternions. It's not difficult to construct each number system. If you look inside any undergrad math textbook, you'll find exact same writing style showcased in the Wikipedia article on quaternions.