If one were to look up in a library books about ancient Greek science and astronomy they would have a mountain of books to sift through. There seem to be so many individuals who have contributed towards the great scientific and astronomic revelations that the list of names seems to go on and on. Many of the theories that were structured in the ancient Greek culture are still put to use today.

The goal of this paper is to point out and describe just a few ancient Greek individuals and their works that whom without their work we might never have advanced as far and as fast as we have technologically or mentally.

Sometimes described as the first pure mathematician, Pythagoras of Samos, was a very important developer of modern mathematics. Unfortunately there is, in comparison, little known about his and his followers' achievements for they worked in a secret society where they kept strictly to themselves.

An odd note about the details of Pythagoras's life is that the information that is written about him in early biographies is done so by authors who make him out to be a god-like being that has divine powers bestowed upon him. The information that can be collected on Pythagoras is of great historical importance due to how early of a record it is. Some believe this information to be accurate while others think of it as mere legend.

Pythagoras was the founder of a philosophical and religious school in Croton, which is a city on the east of the heel of Italy, where he wasthe head of a society that had a circle of close, loyal followers called mathematikoi. The mathematikoi never left the society, had no personal possessions and they were all vegetarians. Pythagoras personally taught all the mathematikoi and shared with them five strict beliefs. The first belief was "that at its deepest level, reality is mathematical in nature." The second was "that philosophy can be used for spiritual purification." The third being "that the soul can rise to union with the divine." The fourth was "that certain symbols have a mystical significance." The fifth and last was "that all brother of the order should observe strict loyalty and secrecy."

There was also a not so strict group of followers known as the akousmatics who only attended the society during the day. They were allowed to live in their own homes, have personal possessions and were not required to be vegetarians.

Pythagoras and his followers were not the kind of mathematicians that you might think of in our modern society at, say, a university where they set out to solve great mathematical equations. Quite differently they only sought to understand the principles of mathematics, the concept of number, the concepts of different mathematical figures such as a triangle and the abstract idea of a proof.

Today with our use of pure mathematical abstraction it is said that it is quite difficult to appreciate the genius behind Pythagoras and his followers' contribution. Pythagoras believed that all relations could be reduced to number relations. Aristotle wrote, "The Pythagorean having been brought up in the study of mathematics, thought that all things are numbers and that the whole cosmos is a scale and a number."

Where Pythagoras's studies are linked to modern studies is when he would study the properties of even and odd number, triangular numbers, perfect numbers and others like them. The only difference was that Pythagoras believed "his" numbers had personalities such as masculine or feminine, perfect or incomplete, beautiful or ugly. Though modern mathematics has discarded...