Pythagoras (582-500 BC) is best known for the Pythagorean theorem but he viewed mathematics as a religious-philosophical system. He believed in harmony of the universe, orderliness of thought, and transmigration of souls.

Nearly fifty years after Solon and Thales, Pythagoras was born on the island of Sámos, close to the coast of Turkey. The city, which is now called Pythagorion in his honor, was known for its man-made harbor in the shape of frying pan and a tunnel that brought in fresh mountain water. A strong, if not bitter, rival of Miletus, the island of Sámos was a major center for commerce, sculpture and philosophy.

Like Thales, much of what is known about Pythagoras is a combination of fact and fancy. There are apocryphal accounts of his travels to Egypt, the invention of musical scales, miraculous cures and secret writings. More reliable are the accounts that his mother was from Sámos, his father was a tradesman from Tyre, and that he was born sometime between 582-560 BC. In about 530 BC, Pythagoras moved to Crotona, Italy and founded his school of religious-philosophical thought. 

Although the Pythagorean Theorem is named in his honor, it is difficult to separate individual accomplishment from its larger context. The Pythagoreans studied prime numbers, the squaring of numbers, and mathematics as part of a religious, political and philosophical approach to life. They believed in the harmony of the universe, the ultimate principle of proportion, and the orderliness of thought. According to this view, the best way to understand the mysteries of life is through obedience, self-examination, and simplicity of food and dress. They believed that planets, including the earth, were not flat but were spheres rotating around a common fire. The Pythagoreans also believed in the transmigration of souls, so it was not unusual that Pythagoras said he could remember all of his previous lives, including having been a warrior in the Trojan War.

Believing that the ultimate explanation of everything could be found in numbers, the Pythagoreans observed the world around them and looked for patterns. At first, numbers were symbols used to describe reality. Eventually, numbers took on a life of their own and this numerology was used to explain everything. Life was a combination of opposites: odd-even, left-right, good-bad, dark-light, masculine-feminine.

Each number had its own properties and power. One was a point, 2 a line, 3 a surface, and 4 a solid. Five was the number of planets, and 6 was a perfect number for it is equal to the sum of its aliquot parts (could be divided by 1, 2 and 3). Seven was a prime number and regulated life (baby until 7, child until 14, married at 21, dead at 70). Eight was harmony for there are eight tones in an octave and 8 objects in the sky (5 planets, sun, moon and earth). Nine was the square of 3 and 10 was the sum of life (the sum of 1, 2, 3 and 4).

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