Pythagoreanism and Numerology

The fundamental principle of Pythagoreanism is that Numbers are Real self-subsistent causally efficacious entities with properties beyond mere quantity, e. g. One = Unity; Two = Multiplicity; Three = Balance, etc.  So, Pythagoreanism is a forerunner of Platonism, and, thus, of the entire tradition that follows.  Furthermore, relations obtain between Numbers, which are what Mathematical operations represent.  One such relation is Ratio, the basis, thus, of Pythagorean Rationalism.  Likewise, the spatial representation of the Numbers and some of their relations is what constitutes Geometry in Pythagoreanism.  Hence, while Mathematics, Geometry, and Rationalism area common characterizations Pythagoreanism, they each refer to one of its derivative features.  Instead, fundamentally, Pythagoreanism is Numerology, just a more rigorous version than some of its more popular varieties.