Only one name in European history unites the realms of religion, mathematics, and philosophy, and that name is Pythagoras.  Yet it is this very achievement that so torments posterity when assessing his legacy.  Centuries of speculative accretions, hagiographic mythologizing, and the dubious testimonia of ancient authors have so obscured his original doctrines that the exasperated scholar must, at last, accept that fact and legend are in him inseparably woven.

The elusive character of Pythagoras is only one part of the problem.  There exists a vast corpus of anonymous Pythagorean and Neo-Pythagorean literature, which bears all the hallmarks of religious scripture.  More Pythagorean texts have come down to us than all the rest of the pre-Socratic philosophical writings combined.  The nature of the written corpus itself presents unique challenges:  the school was simultaneously a political movement (Pythagoreans governed many of the cities of southern Italy, or Magna Graecia), a religious sect, and an educational institution.  Pythagorean doctrines seeped into the foundations of so many classical philosophers that it is difficult to separate their ideas from his.  Platonism and Neoplatonism, in particular, owe him a profound debt.  We smile at these difficulties, and proceed with our account of this fascinating figure, trusting in the reader’s patience and forbearance. 

The principal sources for the life of Pythagoras are:  (1) two short biographies written by the Neoplatonist philosophers Porphyry and Iamblichus, both of moderate reliability; (2) the biographical sketch composed by Diogenes Laertius; and (3) the smattering of testimonia left by ancient writers and early Christian clerics.  Tradition dates Pythagoras’s birth to 580 B.C. on the Greek island of Samos; his father was said to be a gem-cutter named Mnesarchus.  He was no celibate; he had a wife named Theano, who gave him a daughter (Dano) and a son (Telauges).  He is supposed to have studied under the philosopher Pherecydes of Syros until his death; after this he embarked on a remarkable period of foreign travel that would permanently shape his thought.

The ancient sources are in agreement that he lived for a time in Egypt, studied with the priests at their holy sites, and absorbed their secret knowledge.  He also very likely spent time in Phoenicia, Syria, and Chaldea, where he imbibed what he could of the religions, mystic theories, mathematics, and astronomical sciences of those ancient nations.  We must not underestimate the influence that these travels had on him, for the cultures of the Near East and Egypt were arguably the world’s most advanced at that time.  After some years he returned to Samos.  The island was governed by the tyrant Polycrates; and Pythagoras, finding the island’s political climate uncongenial to his plans, resolved to migrate to southern Italy (Magna Graecia).  This he did, settling in the city of Crotona (modern Crotone).  Porphyry adds, “Aristoxenus says that the reason [Pythagoras] departed for Italy was that when he was forty years old, he saw that Polycrates’s tyranny was too harsh for it to be proper for a free man to endure that dominion and despotism.”[1] 

He began to lecture and instruct others after his arrival in Italy.  Like many religious leaders, he combined a stern charisma with the example of a modest life; and within a short time, he had attracted hundreds of followers.  From its inception his school took on a monastic flavor.  He accepted both men and women, and required his pupils to take vows of loyalty to themselves and to him; apparently there was to be a sharing in common of all physical property.  Pythagoras imposed dietary restrictions on his adherents:  the flesh of animals, eggs, and beans were prohibited, but it is not clear how strictly this rule was enforced.  The abstention from meat products was traceable to Pythagoras’s belief that animals, like men, had souls.  It is not entirely clear why he forbade eggs and beans; some sources say it was due to the fact that these foods caused intestinal turbulence, while others claim it was because eggs and beans resembled genitals.  Porphyry tells us:

He told [his followers] to abstain, among the sacrificial parts [animal products], from the loins, the testicles, the genitals, the marrow, the feet, and the head…So, too, he advised them to abstain from beans as though from human flesh…And he advised them to abstain from other things, too, like the womb, the small red mullet, and the sea anemone, and from almost all creatures of the sea.

These dietary requirements, like much of his thought, were likely legacies of his contacts with the mystery religions of Egypt and Syria.  Pythagoras did not accept every novice into this school; he was exacting in his admittance, and a prospect needed to be of good character.  With the scrutinizing eyes of a shrewd leader, he would evaluate candidates himself.  Iamblichus describes the rigorous evaluation process:

When young men wished to spend time with him [Pythagoras] came to him, prepared as he was in this way for the education of disciples, he did not admit them immediately, but waited until he had examined and judged them.  First he found out how their relations were with their parents and their other relatives; then he observed them for inopportune fits of laughter and inappropriate silence and chattering, and [observed] what their desires were, the friends they spent time with, their relation with these, how they mostly spent the day, and what caused them joy and grief.  He also observed their appearance, their gait, the whole motion of their body, and, by examining them physiognomically using the traits of their nature, he made what was visible into signs for the invisible character in their soul.

Aware that too much talking and debate interfered with the learning process, he maintained a rule of silence:  for their first five years, his disciples could not speak, but only listen.  This rule seems impractical, but the ancient sources attest to it.  Porphyry and Diogenes Laertius make it clear that Pythagoras had a very fine sense of communicative calibration:  he knew how to adjust his speech so that children, rulers, professionals, soldiers, athletes, women, and tradesmen could all understand his doctrines.  He was wise enough to understand the need for gradual initiation into degrees of knowledge; he separated his followers into “knowers” (mathematikoi) and “listeners” (akousmatikos).  The former were permitted to have advanced learning disclosed to them; the latter were allowed only basic instruction. 

Secrecy, in fact, was a principle closely linked the Pythagorean school.  This may have helped advance the master’s authority, but it could also trigger suspicion and resentment among the uninitiated.  A doubtful anecdote claims that the Pythagoreans rejoiced in the death of Hippasus of Metapontum for revealing to outsiders the existence of irrational numbers, and the secret of the construction of the dodecahedron inside a sphere.  Diogenes Laertius says that Pythagoras’s school persisted in southern Italy for around nine or ten generations; its longevity was probably much greater than this, but we have no way of knowing with certainty.  What is clear is that the Pythagorean community flourished in Magna Graecia, and formed the intellectual and political leadership element in the region for a significant period of time.

What were the master’s doctrines?  His curriculum was based on mathematics, astronomy, and music; this foundation was dyed with a tincture of his own mystical, or superstitious, doctrines.  In geometry and mathematics Pythagoras sensed the world’s ruling principle.  Through a rigorous study of proofs and theorems, he believed, a person could grasp the divine order of the universe.  Pythagoras is credited with a number of mathematical discoveries, including, of course, the famous theorem that bears his name.  Proclus says that Pythagoras was so overjoyed after discovering his theorem that he sacrificed an ox, but this tale is almost certainly a myth.  Number theory was probably even more important to him than geometry; it was he, or his followers, who originated the concepts of odd and even, prime and factorable, and rational and irrational, numbers.  As far as we know, he was the first thinker to use the term cosmos to describe the totality of existence. For Pythagoras appearances and matter were transitory things; what endured, and what therefore truly existed, were the mathematical relationships between the components of the universe.  In this doctrine we see the stirrings of the Platonic theory of ideas.    

Tradition also credits Pythagoras with the discovery of the link between mathematical ratios and the musical tones produced by stringed instruments.  He attempted to apply this discovery to observation of the celestial bodies, in the hope of finding a “music” of the heavens; he convinced himself of the truth of this proposition, but it is not a view held by astronomers today.  For Pythagoras, the immortality of the soul was a certainty.  Metempsychosis (the transmigration of the soul after death) was apparently also one of his beliefs, according to Herodotus (XIV.1) and Porphyry.  Some ancient writers claim he wrote nothing, but Diogenes Laertius credits him with three written treatises, none of which have come down to us:  On Education, On Statesmanship, and On Nature.  Pythagoras perhaps was less impressive when he tried to instruct on virtue.  One ancient source (the Magna Moralia of Pseudo-Aristotle) noted somewhat caustically:

Pythagoras was the first who tried to speak about virtue, but he did not do so correctly.  For in referring the virtues to numbers he did not establish an appropriate way to study the virtues.  For justice is not a number equal times equal [i.e., a square number].

The Pythagorean community in southern Italy was eventually dispersed.  Internecine conflict is the inevitable fate of all religious communities; for the competing claims of divine authority, grafted to the prideful nature of man, seldom admit of peaceful resolution.  Schisms proliferate as the authority of a sect’s founder wanes.  Iamblichus relates that a man named Cylon of Croton staged a violent assault against the Pythagorean community while the master was absent.  This Cylon had once sought to be a disciple of Pythagoras, but had been rejected by the master for having an intemperate and violent character.  “When this happened,” says Iamblichus, “he [Cylon] and his friends began a violent war against Pythagoras and his companions, and the rivalry of Cylon and his allies was so fierce and absolute that it extended to the very last Pythagoreans.” 

It seems likely that the aristocratic exclusivity, secrecy, and political domination of the Pythagoreans in Magna Graecia eventually stirred the explosive resentments of the local population.  One legend holds that he was killed in this civil conflict; another says that he escaped to the city of Metapontum and, tired of the burdens of life, starved himself to death at the age of eighty.  The reader may choose the legend which suits his proclivities. 

The influence of Pythagoras and his school was enduring and unprecedented.  No other single man has so imprinted the fields of science and philosophy with his seal.  We may rank him, in fact, as one of the most influential figures in world history.  He and his sect made countless mathematical and scientific advances in the centuries following his death.  Platonism absorbed his obsession with the mysticism of number, his theory of the soul’s nature, and his political ideas.  Cicero, whose opinion carries great weight on the subject, credits Pythagoras with inventing the very word philosophy (Tusculan Disputations V.3—4).  He also makes the claim that the Pythagoreans exerted an influence on the development of the Roman state:

Pythagorean ideas disseminated far and wide; and in my opinion, they percolated into our own state.  This speculation is likely grounded in fact, and is indicated by the vestiges of Pythagorean influence that remain.  Powerful and celebrated Greek cities, which collectively were called Magna Graecia, flourished in Italy in olden days.  The name of Pythagoras himself, and after him the fame of the Pythagorean school, carried a great deal of influence in those cities.  How could anyone imagine that the ears of our Roman people would be deaf to those learned Pythagorean voices?  [Tusc. Disp. IV.1]   

The passage of time does not obliterate the fluvial current of ideas.  Its flow, although banked, checked, or merged with disparate waters, retains the sediments and hues of all that preceded it.   

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[1] Laks & Most, Early Greek Philosophy:  Western Greek Thinkers (Part I), Cambridge:  Harvard Univ. Press (2016), p. 29. 

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Read more on philosophy and ethics in the new translation of Cicero’s On Moral Ends: