ABSTRACT

Ernst Mach (1883/1956) once defined mathematics as “the economy of counting” (p. 1790). The dependence of mathematics and the quantitative sciences on this ability is obvious; perhaps less immediately apparent but no less real is the importance of counting to the very existence of any technology or organized society beyond the most primitive. How and when counting was invented, or discovered, no one knows; we can only speculate. Our debt to the fact that it was is immeasurable.