Before all these concepts were unified by geometric algebra, the system of physical quantities as taught in most places was a huge mess of many different kinds of quantities, scalars, polar vectors, axial vectors, pseudoscalars, tensors, pseudotensors, complex numbers, quaternions, spinors and so on.

It was not at all obvious why there are so many kinds of quantities, which are the relationships between them, are there any other kinds of quantities besides those already studied, etc.

Geometric algebra has brought order in this chaos and it has enabled a much deeper and more complete understanding of physics, by reducing a long list of seemingly arbitrary rules to a much smaller set of axioms, and by deriving all the many kinds of physical quantities from the vectors in the strict sense, i.e. from the translations of the space, which are themselves derived from the points of the affine space (as equivalence classes of point pairs).

(Both logically and historically, in physics the vectors are more fundamental than the scalars. The scalars are obtained by dividing collinear vectors, i.e. they are equivalence classes of pairs of collinear vectors. This division operation is a.k.a. measurement and what are now named as "real numbers" were named as "measures" in the past, for more than two millennia. For any Archimedean group it is possible to define a division operation using the Axiom of Archimedes, generating a set of scalars over which the original group is a vector space).