The Pythagoreans: Founded by Pythagoras in southern Italy. Based on a mixture of science and religion. Pythagoras himself was regarded as semi-divine. Very influential to subsequent ideas and religion, including Christianity.
Believed that human souls transmigrated into animals, and that all animals were therefore kindred. Women are equal. Everything cycles. “Hippy” culture – property is common to all, including discoveries. Pythagoras theorem could therefore have been discovered by disciples. Used geometry based on Euclid in preference to other methods as found a problem with the fact that if h2=a2+b2, h could not be expressed as x/y.
Created a set of rules to be followed, eg Do not eat beans. Do not walk on highways. When you remove a pot from the fire always stir the ashes with a stick to remove the mark left.
Created a set of values. The highest form of life is the search for disinterested truth – ie “disinterested science”. There are 3 classes of man in life, illustrated by the people attending the Olympic games:
The lowest class – come to buy and sell
The next class – come to compete
The highest class – come simply to observe
Developed the method of deductive reasoning. Start with a self-evident axiom, apply logical argument and derive a theorem which is not self-evident.