Hamilton introduced the terms "vector", "scalar" and many others. The Wikipedia article [Classical Hamiltonion quaternions](https://en.wikipedia.org/wiki/Classical_Hamiltonian_quaternions) states > A quaternion can be represented as the sum of a scalar and a vector. By the middle of the nineteenth century the concept of vector spaces was not yet developed fully although linear algebra with its systems of equations goes back to antiquity. Thus, Hamilton and his followers, used quaternions as a substitute for three dimensional vector analytic geometry. That is, the three quaternions **i, j, k** units represented the three unit vector basis of ordinary space. After the development of vector spaces, the three unit vectors lost their association with quaternions and stood on their own. Same with the real scalars. The multiplication of two vector quaternions is given by $\,u v = -u\cdot v+u\times v.\,$ Later, the dot product and the cross product became independent and also lost their association with quaternions. Almost all of the machinery, notation and terminology that Hamilton developed for quaternions as mentioned in the Wikipedia article, is now obsolete, or else repurposed. More about the history of this development is in the Wikipedia article [History of Quaternions](https://en.wikipedia.org/wiki/History_of_quaternions) For example, this excerpt > Since quaternions demand their readers to imagine four dimensions, there is a metaphysical aspect to their invocation. Quaternions are a philosophical object. Setting quaternions before freshmen students of engineering asks too much. Yet the utility of dot products and cross products in three-dimensional space, for illustration of processes, calls for the uses of these operations which are cut out of the quaternion product. Thus Willard Gibbs and Oliver Heaviside made this accommodation, for pragmatism, to avoid the distracting superstructure. In answer to the question > Whatever happened to quaternions? the Wikipedia article also states > Quaternions continued to be a well-studied mathematical structure in the twentieth century, as the third term in the Cayley–Dickson construction of hypercomplex number systems over the reals, followed by the octonions and the sedenions; they are also a useful tool in number theory, particularly in the study of the representation of numbers as sums of squares. The group of eight basic unit quaternions, positive and negative, the quaternion group, is also the simplest non-commutative Sylow group.