A Universe made of Numbers
PART 1 Pythagoras & His Philosophy
Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet there is relatively little known about his mathematical achievements. Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, there is nothing of Pythagoras's writings. The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure. This does not mean that we cannot gain some incite on who he was or what he taught or believed, because there are details of Pythagoras's life from early biographies which use important original sources. Yet these biographies are written by authors who attribute divine powers to him, and whose aim was to present him as a god-like figure. What will be presented in the rest of this paper is an attempt to collect together the most reliable sources to reconstruct an account of Pythagoras's meta-physic, epistemology, and ethics, but first, in order to understand Pythagoras more fully, a brief journey into his life will be dealt with first.
Pythagoras was born in 580 B.C. to a more than wealthy family. He received the finest formal education in gymnastics, music, mathematics, and natural sciences and was taught to think and see the world as a scientist. He traveled widely, from Egypt, to the Mediterranean, and most of Asia, where he learned culture customs, geometry, and astronomy. His traveling experiences, observation, and questions and ideas are probably the ferment of Pythagoras's philosophy.
At the age of fifty, Pythagoras moved to Italy and set up a school of antiquity. Over the gate of the Academy, a sign read: "Only mathematicians enter here" Members of this school took up strict rules in learning mathematics, science, music, the arts, and vocations in the care of the home and family. Pythagoras stressed solidarity, education of the mind, health and worship of Apollo, as well as the practice of divination. The main belief was that all can identify with the One and attune themselves to the cosmic rhythm.
Pythagoras was over all the community as chief philosopher and his followers were convinced that he performed miracles and magic. This school was eventually destroyed and the students, Pythagoras included, had to flee due to the fact that the city's people thought them to be a cultic group and a threat. The community lasted about a century and then vanished from history, with all its writings and doctrines.
The Basic meta-physic for Pythagoras was that everything has its own vibration and the entire universe is a matter-in-motion, a mathematic structure. Aristotle says that Pythagoreanism, as known in his day, is characterized by the view that the principles of mathematics are the principles of all things. Aristotle writes,
Contemporaneously with these philosophers and before them, the so-called Pythagoreans, who were the first to take up mathematics, not only advanced this study, but also having been brought up in it they thought its principles were the principles of all things. Since of these principles numbers are by nature the first, and in numbers they seemed to see many resemblances to the things that exist and come into beingmore than in fire and earth and water (such and such a modification of numbers being justice, another being soul and reason, another being opportunityand similarly almost all other things being numerically expressible); since, again, they saw that the modifications and the ratios of the musical scales were expressible in numbers;since, then, all other things seemed in their whole nature to be modeled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical...