In One Form

1. The human mind is so constructed that it must see every perception in a time-relation -- in an order -- and every perception of an object in a space-relation -- as outside or beside our perceiving selves.

2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra.

3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry.

Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind.  To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.

-- Nicholas Murray Butler (1862 - 1947), American philosopher, diplomat, and educator, Editor's Introduction, The Teaching of Elementary Mathematics (1906) by David Eugene Smith