I remember I read an article saying that "The quaternions $\Bbb{H}$ are obsolete in pure mathematics since the theory of vectors has been developed enough, however it is useful in computer science".
Is this true?
I want to know the reason in detail.. How specifically does the theory on vectors affect quaternions?
Moreover, I don't get the point of that article. If quaternions are only for describing 3D motions, then what's the point of expanding it to octonion and other stuffs?
Back in the late 19th century, there was fierce competition between quaternions and vectors. See e.g. this talk by Michael J. Crowe. By 1910 or so, what we now call Vector Analysis had won the day, so e.g. nobody formulates Maxwell's equations using quaternions any more. But that's more "applied mathematics" than "pure". In terms of abstract algebra, the quaternions are still an important example, although perhaps not as important as some of the early quaternion enthusiasts believed.