If we define a Pythagorean as someone who follows Pythagoras' example in the pursuit of the Love of Wisdom, with the attainment of Wisdom being the goal, then anyone engaged in that pursuit could reasonably be called a Pythagorean. Some people, however, feel that a Pythagorean might be anyone engaged in the study of quantitative and qualitative reasoning.

Pythagoras went to every available culture to learn their mysteries in the pursuit of his "Love of Wisdom," or Philosophy. If the Pythagoras' Golden Verses and the biographical accounts of Pythagoras' life are at all a reflection of Pythagoras' interests then these things alone are enough to suggest that he was looking for something deeper than a good approach to quantitative reasoning.

Nicomachus of Gerasa was a fairly early Pythagorean who wrote a book called Introduction to Arithmetic. This document is an excellent point of reference for answering the question of what a Pythagorean is.

Nicomachus says that Love of Wisdom, or Philosophy, is the science and study of things that are. He goes on to carefully distinguish between temporal things and eternal and transcendent things. He says that eternal-transcendent things are those "things that truly are," and temporal things don't have real being but only have the appearance of having being because of their participation in that which is real. (His explanation is reflected later by the Platonic Philosopher, Plotinus, who explains that temporal things don't have real being because their mutable nature causes them to be perpetually in a state of becoming, and never achieve real being.) So, it follows that a Philosopher in the Pythagorean sense is a scientist and student of the things that truly are.