Article abstract: Pythagoras set an inspiring example with his energetic search for knowledge of universal order. His specific discoveries and accomplishments in philosophy, mathematics, astronomy, and music theory make him an important figure in Western intellectual history.
Pythagoras, son of Mnesarchus, was born about 580 b.c.e. His birthplace was the island of Samos in the Mediterranean Sea. Aside from these details, information about his early life—most of it from the third and fourth centuries b.c.e., up to one hundred years after he died—is extremely sketchy. Sources roughly contemporary with him tend to contradict one another, possibly because those who had been his students developed in many different directions after his death.
Aristotle’s Metaphysica (second Athenian period, 335-323 b.c.e.; Metaphysics, 1801), one source of information about Pythagorean philosophy, never refers to Pythagoras himself but always to “the Pythagoreans.” Furthermore, it is known that many ideas attributed to Pythagoras have been filtered through Platonism. Nevertheless, certain doctrines and biographical events can be traced with reasonable certainty to Pythagoras himself. His teachers in Greece are said to have included Creophilus and Pherecydes of Syros; the latter (who is identified as history’s first prose writer) probably encouraged Pythagoras’s belief in the transmigration of souls, which became a major tenet of Pythagorean philosophy. A less certain but more detailed tradition has him also studying under Thales of Miletus, who built a philosophy on rational, positive integers. In fact, these integers were to prove a stumbling block to Pythagoras but would lead to his discovery of irrational numbers such as the square root of two.
Following his studies in Greece, Pythagoras traveled extensively in Egypt, Babylonia, and other Mediterranean lands, learning the rules of thumb that, collectively, passed for geometry at that time. He was to raise geometry to the level of a true science through his pioneering work on geometric proofs and the axioms, or postulates, from which these are derived.
A bust now housed at Rome’s Capitoline Museum (the sculptor is not known) portrays the philosopher as having close-cropped, wavy Greek hair and beard, his features expressing the relentlessly inquiring Ionian mind—a mind that insisted on knowing for metaphysical reasons the exact ratio of the side of a square to its diagonal. Pythagoras’s eyes suggest an inward focus even as they gaze intently at the viewer. The furrowed forehead conveys solemnity and powerful concentration, yet deeply etched lines around the mouth, and the hint of a crinkle about the eyes, reveal that this great man was fully capable of laughter.
When Pythagoras returned to Samos from his studies abroad, he found his native land in the grip of the tyrant Polycrates, who had come to power about 538 b.c.e. In the meantime, the Greek mainland had been partially overrun by the Persians. Probably because of these developments, in 529 b.c.e. Pythagoras migrated to Croton, a Dorian colony in southern Italy, and entered into what became the historically important period of his life.
At Croton he founded a school of philosophy that in some ways resembled a monastic order. Its members were pledged to a pure and devout life, close friendship, and political harmony. In the immediately preceding years, southern Italy had been nearly destroyed by the strife of political factions. Modern historians speculate that Pythagoras thought that political power would give his organization an opportunity to lead others to salvation through the disciplines of nonviolence, vegetarianism, personal alignment with the mathematical laws that govern the universe, and the practice of ethics in order to earn a superior reincarnation. Pythagoras believed in metempsychosis, the transmigration of souls from one body to another, possibly from humans to animals. Indeed, Pythagoras claimed that he could remember four previous human lifetimes in detail.
His adherents he divided into two hierarchical groups. The first was the akousmatikoi, or listeners, who were enjoined to remain silent, listen to and absorb Pythagoras’s spoken precepts, and practice the special way of life taught by him. The second group was the mathematikoi, students of theoretical subjects, or simply “those who know,” who pursued the subjects of arithmetic, the theory of music, astronomy, and cosmology. (Though mathematikoi later came to mean “scientists” or “mathematicians,” originally it meant those who had attained advanced knowledge in a broader sense.) The mathematikoi, after a long period of training, could ask questions and express opinions of their own.
Despite the later divergences among his students—fostered perhaps by his having divided them into two classes—Pythagoras himself drew a close connection between his metaphysical and scientific teachings. In his time, hardly anyone conceived of a split between science and religion or metaphysics. Nevertheless, some modern historians deny any real relation between the scientific doctrines of the Pythagorean society and its spiritualism and personal disciplines. In the twentieth century, Pythagoras’s findings in astronomy, mathematics, and music theory are much more widely appreciated than the metaphysical philosophy that, to him, was the logical outcome of those findings.
Pythagoras developed a philosophy of number to account for the essence of all things. This concept rested on three basic observations: the mathematical relationships of musical harmonies, the fact that any triangle whose sides are in a ratio of 3:4:5 is always a right triangle, and the fixed numerical relations among the movement of stars and planets. It was the consistency of ratios among musical harmonies and geometrical shapes in different sizes and materials that impressed Pythagoras.
His first perception (which some historians consider his greatest) was that musical intervals depend on arithmetical ratios among lengths of string on the lyre (the most widely played instrument of Pythagoras’s time), provided that these strings are at the same tension. For example, a ratio of 2:1 produces an octave; that is, a string twice as long as another string, at the same tension, produces the same note an octave below the shorter string. Similarly, 3:2 produces a fifth and...
(The entire section is 2680 words.)