Pythagoras of Samos (c. 569-c. 496 BCE)

Pythagoras was a classical Greek philosopher, mathematician, scientist, and mystic from the Aegean island of Samos. Known as the “father of numbers,” he is best known for the Pythagorean theorem, which carries his name. Over the centuries, mathematicians, architects, artists, and musicians have built upon Pythagoras's theories, making those theories the very foundation of the modern understanding of music, astronomy, and mathematics.

Pythagoras was the son of Mnesarchus, a merchant from Tyre. As a child, he traveled widely with his father and gained a broad education from his experiences. He studied with three philosophers in particular—Pherecydes of Syros, Thales, and Anaximander. These men introduced Pythagoras to mathematics, cosmology, astronomy, and geometry. In 535 BCE, Pythagoras moved to Egypt and studied with Egyptian priests at a temple in Diospolis. The rites, rituals, and secrecy he learned in Egypt became part of the religious school he set up later in Italy. The Persians captured Pythagoras when they invaded Egypt in 525 BCE and took him to Babylon. He studied with the magi in Babylon where he learned about Babylonian mysticism, arithmetic, and music.

After his release, Pythagoras returned to Samos, where he set up and ran a school for a few years. Then he moved to southern Italy in 518 BCE, to a village named Croton where he established a secret religious society, emphasizing virtue and strict rules of conduct. The members of this society, known as Pythagoreans, were vegetarians, took vows of silence, and participated in purification rites. They believed in transmigration of the soul, meaning souls are continuously reincarnated as persons, animals, or plants. The Pythagoreans' way of life sought to release the soul from this cycle. Pythagoras lived in Croton until a village noble plotted against him and forced Pythagoras to flee. He went to Metapontum, where he died.

Pythagoras was deeply interested in mathematic principles, especially the abstract philosophy of numbers. He believed that everything, even the order of the universe, could be defined numerically, that is, in terms of harmonic ratios. He applied this theory to mathematics, music, and [Page 1070]astronomy. He discovered that music has proportional intervals based on the numbers one through four. Therefore, he held that the universe is based upon the sum of these numbers—10. Pythagoras, or one of his followers, discovered that when the side of a square is squared, the resulting figure equals the area of the square. from here came the concept of the square root.

Although its true origin is uncertain, Pythagoras generally gets credit for developing the so-called Pythagorean theorem, that is, the hypotenuse squared of a right-angled triangle is equal to the sum of the squares of the sides (a2 + b2 = c2). Unfortunately, none of his writings has survived to corroborate this association. Egyptian and Babylonian documents show that both of these societies knew about the theorem well before Pythagoras was born; however, some ancient sources believe Pythagoras was the first person to prove the theorem. Pythagoras believed that numbers connected music and math through ratios. Legend tells that Pythagoras discovered a relationship between tonal sound and simple ratios when he passed a blacksmith shop one day and heard the sound of the hammers beating on various size anvils. This principle of tonal harmony and size ratio is called Pythagorean tuning.

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