  Geometric number systems, obtained by extending the real number system to
include new anticommuting square roots of +1 and -1, provide a royal road to
higher mathematics by largely sidestepping the tedious languages of tensor
analysis and category theory. The well known consistency of real and complex
matrix algebras, together with Cartan-Bott periodicity, firmly establishes the
consistency of these geometric number systems, often referred to as Clifford
algebras. The geometrization of the real number system is the culmination of
the thousands of years of human effort at developing ever more sophisticated
and encompassing number systems underlying scientific progress and advanced
technology in the 21st Century. Complex geometric algebras are also considered.
