Before I go further, I would like to remind the reader that the Ancient Greeks were a people who loved all manner of discussions. Their spirit of eternal questioning overshadowed all else in the quest for learning and advancing themselves. As well, the shadow of good and bad did not exist at birth as it does today. A child had only good in them from the moment he was born and with this attitude, the Greeks forged ahead to conquer philosophy and the sciences.
The Pythagorean Society didn't act as a research group and didn't concern themselves with attempting to formulate or solve mathematics problems. Rather this group was interested in the principles of mathematics and in the abstract idea of a proof. (In fact, Pythagoras' geometry theorem had been known to the Babylonians one thousand years earlier and he may have simply proved the theorem. A proof is the logical step by step demonstration of a truth, such as the statement that for a right-angled triangle, the square of the longest side is equal to the square of the other two sides.)
According to Pythagoras and the Ancient Greeks, although numbers were abstract, they were a thing. 2 telephones + 2 telephones = 4 is as real as 2 + 2 =4. Numbers had personalities - some were beautiful, some were ugly, yet others were male, still others female, perfect or incomplete. On the whole, this distinction has been done away today but is seen in fiction and poetry. For example, the number 7 is a lucky one while the number 13 is unlucky and ten is a perfect number to have to make a set complete.
Aristotle wrote: "The Pythagoreans...having been brought up in the study of mathematics, thought that things are numbers...and that the whole cosmos is a scale and a number." In other words, everything could be reduced to a relationship which involved only numbers.
