And why do descriptions of quaternions include a rigorous proof? I trust quaternions work, so skip the proof and show me how to use them in a practical, efficient way.
The fact that the quaternions “work” (are a finite-dimensional real vector space with an associative real-bilinear multiplication, and a division operation) is quite special. In fact there are only three objects satisfying this criteria: the real numbers themselves, the complex numbers, and the quaternions.
> there are only three objects satisfying this criteria: the real numbers themselves, the complex numbers, and the quaternions.
Does a proof exist that these are the only three of such objects?
In mathematics often proofs lead to understanding why something works (on the other hand, many proofs aren’t written in a way that make the main ideas clear or easy to tease out from details)