Pythagoras of Samos[a] (c. 570 – c. 495 BC)[b] was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement. His political and religious teachings were well-known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Knowledge of Pythagoras's life is largely clouded by legend and obfuscation, but he appears to have been the son of Mnesarchus, a seal engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, in around 530 BC, he travelled to Croton, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or he may have escaped to Metapontum, where he eventually died.
c. 570 BC|
c. 495 BC (aged around 75)|
either Croton or Metapontum
|Era||Ancient Greek philosophy|
The teaching most securely identified with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon death, enters into a new body. He may have also devised the doctrine of musica universalis, which holds that the planets move according to mathematical equations and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras himself developed the numerological and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly Philolaus of Croton. He probably prohibited his followers from eating beans, but he may or may not have advocated a strictly vegetarian diet.
In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus. It was said that he was the first man to call himself a philosopher ("lover of wisdom")[c] and that he was the first to divide the globe into five climatic zones. Classical historians debate whether Pythagoras made these discoveries, and many of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important, but it is debated to what extent, if at all, he actually contributed to mathematics or natural philosophy.
Pythagoras influenced Plato, whose dialogues, especially his Timaeus, exhibit Pythagorean teachings. Pythagorean ideas about mathematical perfection also impacted ancient Greek art. His teachings underwent a major revival in the first century BC among Middle Platonists, coinciding with the rise of Neopythagoreanism. Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was used throughout early modern European esotericism and his teachings as portrayed in Ovid's Metamorphoses influenced the growth of the vegetarian movement.
No authentic writings of Pythagoras have survived to the present day and almost nothing is known for certain about his life. The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical. The earliest source on Pythagoras's teachings is a satirical poem written by Xenophanes of Colophon, a contemporary of Pythagoras, which describes Pythagoras interceding on behalf of a dog that is being beaten, professing to recognize in its cries the voice of a departed friend.
Alcmaeon of Croton, a doctor who lived in Croton at around the same time Pythagoras lived there, incorporates many Pythagorean teachings into his writings and alludes to having possibly known Pythagoras personally. The poet Heraclitus of Ephesus, who was born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime, pegged Pythagoras as a clever charlatan, remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, and selecting from these writings he manufactured a wisdom for himself—much learning, artful knavery."
The Greek poets Ion of Chios (c. 480 – c. 421 BC) and Empedocles of Acragas (c. 493 – c. 432 BC) both express admiration for Pythagoras in their poems. The first concise early description of Pythagoras comes from the historian Herodotus of Halicarnassus (c. 484 – c. 420 BC), who describes Pythagoras as "not the most insignificant" of Greek sages and states that Pythagoras taught his followers how to attain immortality. The writings attributed to the Pythagorean philosopher Philolaus of Croton, who lived in the late fifth century BC, are the earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras. The Athenian rhetorician Isocrates (436–338 BC) was the first to describe Pythagoras as having visited Egypt. Aristotle wrote a treatise On the Pythagoreans, which is no longer extant. Some of it may be preserved in the Protrepticus. Aristotle's disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus also wrote on the same subject.
Most of the major sources on Pythagoras's life are from the Roman period, by which point "the history of Pythagoreanism was already... the laborious reconstruction of something lost and gone." Three lives of Pythagoras have survived from late antiquity, all of which are filled primarily with myths and legends. The earliest and most respectable of these is the one from Diogenes Laërtius's Lives and Opinions of Eminent Philosophers. The two later lives were written by the Neoplatonist philosophers Porphyry and Iamblichus and were partially intended as polemics against the rise of Christianity. The later sources are much lengthier than the earlier ones, and even more fantastic in their descriptions of Pythagoras's achievements. Porphyry and Iamblichus did use some material from the lost writings of Aristotle's disciples and material taken from these sources is generally considered to be the most reliable.
|“||There is not a single detail in the life of Pythagoras that stands uncontradicted. But it is possible, from a more or less critical selection of the data, to construct a plausible account.||”|
|— Walter Burkert, 1972|
Herodotus, Isocrates, and other early writers agree that Pythagoras was the son of Mnesarchus and that he was born on the Greek island of Samos, situated in the eastern Aegean. His father is said to have been a gem-engraver or a wealthy merchant, but his ancestry is disputed and unclear.[d] Pythagoras's name led him to be associated with Pythian Apollo; Aristippus of Cyrene explained his name by saying, "He spoke (ἀγορεύω, agoreúō) the truth no less than did the Pythian [sic] (Πῡθῐ́ᾱ, Pūthíā)", and Iamblichus tells the story that the Pythia prophesied that his pregnant mother would give birth to a man supremely beautiful, wise, and beneficial to humankind. A late source gives his mother's name as Pythais. As to the date of his birth, Aristoxenus stated that Pythagoras left Samos in the reign of Polycrates, at the age of 40, which would give a date of birth around 570 BC.
According to Antiphon, while he was still on Samos, Pythagoras founded a school known as the "semicircle", where prominent Samians could discuss matters of public concern. Pythagoras himself dwelled in a secret cave, where he studied in private.
Around 530 BC, he left Samos, possibly because he disagreed with the tyranny of Polycrates in Samos. His later admirers state that it was because Pythagoras was so overburdened with public duties in Samos, because of the high estimation in which he was held by his fellow-citizens. He arrived in the Greek colony of Croton (today's Crotone, in Calabria) in what was then Magna Graecia. At Croton, he founded the philosophical school of Pythagoreanism, whose practitioners adhered to a strict, disciplined way of life. Pythagoras acquired great political influence in Magna Graecia; later biographers tell fantastical stories of the effects of his eloquent speech in leading the people of Croton to abandon their luxurious and corrupt way of life and devote themselves to the purer system which he came to introduce.
Pythagoras's teachings of dedication and asceticism are credited with aiding in Croton's decisive victory over the neighboring colony of Sybaris in 510 BC. The forces of Croton were headed by the Pythagorean Milo, and it is likely that the members of the brotherhood took a prominent part. After the victory, a democratic constitution was proposed, but the Pythagoreans rejected it. The supporters of democracy, headed by Cylon and Ninon, the former of whom is said to have been irritated by his exclusion from Pythagoras's brotherhood, roused the populace against them. An attack was made upon them while assembled either in the house of Milo, or in some other meeting-place. The building was set on fire, and many of the assembled members perished; only the younger and more active members managed to escape. Sources disagree regarding whether Pythagoras was killed, or if he managed to flee to Metapontum, where he lived out the rest of his life. One legend reported by both Diogenes Laërtius and Iamblichus states that Pythagoras almost managed to escape his pursuers, but that he came to a bean field and refused to run through it because doing so would violate his own teachings, so instead he stopped and was killed as a result.
Diogenes Laërtius states that Pythagoras "did not indulge in the pleasures of love" and that he cautioned others to only have sex "whenever you are willing to be weaker than yourself". According to Porphyry, Pythagoras married Theano, a lady of Crete and the daughter of Pythenax and had several children with her. Porphyry writes that Pythagoras had two sons named Telauges and Arignote, and a daughter named Myia, who "took precedence among the maidens in Croton and, when a wife, among married women." Iamblichus mentions none of these children and instead only mentions a son named Mnesarchus after his grandfather. This son was raised by Pythagoras's appointed successor Aristaeus and eventually took over the school when Aristaeus was too old to continue running it.
The wrestler Milo of Croton was said to have been a close associate of Pythagoras and was credited with having saved the philosopher's life when a roof was about to collapse. This association may been the result of confusion with a different man named Pythagoras, who was an athletics trainer. Diogenes Laërtius records Milo's wife's name as Myia. Iamblichus mentions Theano as the wife of Brontinus of Croton. Diogenes Laërtius states that the same Theano was Pythagoras's pupil and that Pythagoras's wife Theano was her daughter. Diogenes Laërtius also records that works supposedly written by Theano were still extant during his own lifetime and quotes several opinions attributed to her. These writings are now known to be pseudepigraphical.
Scholars disagree regarding who Pythagoras's teacher was because reliable information on the subject is lacking. Some say his training was almost entirely Greek, others exclusively Egyptian and Oriental. Each of Pythagoras's alleged tutors seems to call attention to a different aspect of Pythagoras's own teachings. Various ancient sources list Hermodamas of Samos, or his father Creophylus of Samos (who both stand for the domestic rhapsodic tradition of Samos) among his possible tutors; whereas other traditions credit Bias of Priene, Thales, Anaximander (a pupil of Thales), and Pherecydes of Syros (all exponents of the Greek philosophical tradition). Of the various attributions regarding his Greek teachers, Pherecydes of Syros is mentioned most often.
Before 520 BC, on one of his visits to Egypt or Greece, Pythagoras might have met Thales of Miletus, who would have been around fifty-four years older than him. Thales was a philosopher, scientist, mathematician, and engineer, also known for a special case of the inscribed angle theorem. Pythagoras's birthplace, the island of Samos, is situated in the Northeast Aegean Sea not far from Miletus. Diogenes Laërtius cites a statement from Aristoxenus (fourth century BC) stating that Pythagoras learned most of his moral doctrines from the Delphic priestess Themistoclea. Porphyry affirms this assertion, but calls the priestess Aristoclea (Aristokleia). Ancient authorities furthermore note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphic or Cretan mysteries, or the Delphic oracle.
Following a similar logic, the Egyptians are said to have taught him geometry, the Phoenicians arithmetic, the Chaldeans astronomy, and the Magi the principles of religion and practical maxims for the conduct of life. According to Diogenes Laërtius, Pythagoras not only visited Egypt and learnt the Egyptian language (as reported by Antiphon in his On Men of Outstanding Merit), but also "journeyed among the Chaldaeans and Magi." Later in Crete, he went to the Cave of Ida with Epimenides, and entered Egyptian sanctuaries for the purpose to learn information concerning the secret lore of the different gods. The Middle Platonist biographer Plutarch (c. 46 – c. 120 AD) writes in his treatise On Isis and Osiris that, during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of Heliopolis (meanwhile Solon received lectures from a Sonchis of Sais). Other ancient writers also mention Pythagoras's visit to Egypt. According to the Christian theologian Clement of Alexandria (c. 150 – c. 215 AD), "Pythagoras was a disciple of Soches, an Egyptian archprophet, as well as Plato of Sechnuphis of Heliopolis."
Although the exact details of Pythagoras's teachings are uncertain, it is possible to reconstruct a general outline of his main ideas. Aristotle writes at length about the teachings of the Pythagoreans, but without mentioning Pythagoras directly. One of Pythagoras's main doctrines appears to have been metempsychosis, the belief that all souls are immortal and that, after death, a soul is transferred into a new body. This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus.
Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations. Diogenes Laërtius reports an account from Heraclides Ponticus that Pythagoras told people that he had lived four previous lives that he could remember in detail. The first of these lives was as Aethalides the son of Hermes, who granted him the ability to remember all his past incarnations. Next, he was incarnated as Euphorbus, a minor hero from the Trojan War briefly mentioned in the Iliad. He then became the philosopher Hermotimus, who recognized the shield of Euphorbus in the temple of Apollo. His final incarnation was as Pyrrhus, a fisherman from Delos. One of his past lives, as reported by Dicaearchus, was as a beautiful courtesan.
Another belief attributed to Pythagoras was that of the "harmony of the spheres", which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony. According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together. In his philosophical dialogue Protrepticus, Aristotle has his literary double say:
When Pythagoras was asked [why humans exist], he said, "to observe the heavens," and he used to claim that he himself was an observer of nature, and it was for the sake of this that he had passed over into life.
Pythagoras was said to have practised divination and prophecy. In the visits to various places in Greece—Delos, Sparta, Phlius, Crete, etc.—which are ascribed to him, he usually appears either in his religious or priestly guise, or else as a lawgiver.
|“||The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.||”|
|— Aristotle, Metaphysics 1–5, c. 350 BC|
According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons, devoid of practical application. They believed that all things were made of numbers. The number one (the monad) represented the origin of all things and the number two (the dyad) represented matter. The number three was an "ideal number" because it had a beginning, middle, and end and was the smallest number of points that could be used to define a plane triangle, which they revered as a symbol of the god Apollo. The number four signified the four seasons and the four elements. The number seven was also sacred because it was the number of planets and the number of strings on a lyre, and because Apollo's birthday was celebrated on the seventh day of each month. They believed that odd numbers were masculine, that even numbers were feminine, and that the number five represented marriage, because it was the sum of two and three.
Ten was regarded as the "perfect number" and the Pythagoreans honored it by never gathering in groups larger than ten. Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the perfect number, ten. The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance. Iamblichus, in his Life of Pythagoras, states that the tetractys was "so admirable, and so divinised by those who understood [it]," that Pythagoras's students would swear oaths by it.
Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton. In his landmark study Lore and Science in Ancient Pythagoreanism, Walter Burkert argues that Pythagoras was a charismatic political and religious teacher, but that the number philosophy attributed to him was really an innovation by Philolaus. According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics. Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, proofless arithmetic, but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics.
Both Plato and Isocrates affirm that, above all else, Pythagoras was famous for leaving behind him a way of life. Carl B. Boyer (1968) characterizes the Pythagorean school as "politically conservative and with a strict code of conduct." Leonid Zhmud (2012) identifies two camps within the early Pythagoreans: the scientific mathematikoi and the religious akousmatikoi, who engaged in politics. The study of mathematics and music may have been connected to the worship of Apollo.
The organization Pythagoras founded at Croton was called a "school", but, in many ways, resembled a monastery. The adherents were bound by a vow to Pythagoras and each other, for the purpose of pursuing the religious and ascetic observances, and of studying his religious and philosophical theories. The members of the sect shared all their possessions in common and were devoted to each other to the exclusion of outsiders. One Pythagorean maxim was "koinà tà phílōn" ("All things in common among friends"). Both Iamblichus and Porphyry provide detailed accounts of the organization of the school, although the primary interest of both writers is not historical accuracy, but rather to present Pythagoras as a divine figure, sent by the gods to benefit humankind. Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time.
Pythagorean teachings were known as "symbols" (symbolon) and members took a vow of silence that they would not reveal these symbols to non-members. Those who did not obey the laws of the community were expelled and the remaining members would erect tombstones for them as though they had died. A number of "oral sayings" (akoúsmata) attributed to Pythagoras have survived, dealing with how members of the Pythagorean community should perform sacrifices, how they should honor the gods, how they should "move from here", and how they should be buried. Many of these sayings emphasize the importance of ritual purity and avoiding defilement, but their exact meanings are frequently obscure. Iamblichus preserves Aristotle's descriptions of the original, ritualistic intentions behind a few of these sayings, but these apparently later fell out of fashion, because Porphyry provides markedly different ethical-philosophical interpretations of them:
|Pythagorean saying||Original ritual purpose according to Aristotle/Iamblichus||Porphyry's philosophical interpretation|
|"Do not take roads traveled by the public."||"Fear of being defiled by the impure"||"with this he forbade following the opinions of the masses, yet to follow the ones of the few and the educated."|
|"and [do] not wear images of the gods on rings"||"Fear of defiling them by wearing them."||"One should not have the teaching and knowledge of the gods quickly at hand and visible [for everyone], nor communicate them to the masses."|
|"and pour libations for the gods from a drinking cup's handle [the 'ear']"||"Efforts to keep the divine and the human strictly separate"||"thereby he enigmatically hints that the gods should be honored and praised with music; for it goes through the ears."|
New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five-year initiation period, during which they were required to remain silent. Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women and female members of Pythagoras's school appear to have played an active role in its operations. Iamblichus provides a list of 235 famous Pythagoreans, seventeen of whom are women. In later times, many prominent female philosophers contributed to the development of Neopythagoreanism.
Music and athletics
The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body. One anecdote of Pythagoras reports that when he encountered some drunken youths trying to break into the home of a virtuous woman, he sang a solemn tune with long spondees and the boys' "raging willfulness" was quelled. The Pythagoreans also placed particular emphasis on the importance of physical exercise; therapeutic dancing, daily morning walks along scenic routes, and athletics were major components of the Pythagorean lifestyle. Moments of contemplation at the beginning and end of each day were also advised.
Asceticism and possible vegetarianism
Pythagoreanism entailed a number of ascetic practices (many of which may have had symbolic meanings). It is more or less agreed that Pythagoras issued a prohibition against the consumption of beans and the meat of non-sacrificial animals, though both of these assumptions have been contradicted. It is also likely that he prohibited his followers from wearing woolen garments. Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet,[e] which may have been motivated due to the doctrine of metempsychosis. Eudoxus of Cnidus, a student of Archytas, writes, "Pythagoras was distinguished by such purity and so avoided killing and killers that he not only abstained from animal foods, but even kept his distance from cooks and hunters." Other authorities contradict this statement. According to Aristoxenus, Pythagoras allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and rams. According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices and established a diet for athletes dependent on meat. Temperance of all kinds seems to have been urged. It is also stated that they had common meals, resembling the Spartan system, at which they met in companies of ten.
Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends, which he may have personally encouraged. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure. In a fragment, Aristotle writes that Pythagoras had a golden thigh, which he publicly exhibited at the Olympic Games and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo".
Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications. He was once seen at both Metapontum and Croton at the same time. When Pythagoras crossed the river Casas, "several witnesses" reported that they heard it greet him by name. In Roman times, a legend claimed that Pythagoras was the son of Apollo. According to Muslim tradition, Pythagoras was said to have been initiated by Hermes (Egyptian Thoth).
Pythagoras was said to have dressed all in white with a golden wreath atop his head and to have worn trousers after the fashion of the Thracians. Diogenes Laërtius presents Pythagoras as having exercised remarkable self-control; he was always cheerful, but "abstained wholly from laughter, and from all such indulgences as jests and idle stories".
Pythagoras was said to have had extraordinary success in dealing with animals. A fragment from Aristotle records that, when a deadly snake bit Pythagoras, he bit it back and killed it. Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat beans and that he once convinced a notoriously destructive bear to swear that it would never harm a living thing again, and that the bear kept its word.
Anti-Pythagorean legends were also circulated. Diogenes Laërtes retells a story told by Hermippus of Samos, which states that Pythagoras had once gone into an underground room, telling everyone that he was descending to the underworld. He stayed in this room for months, while his mother secretly recorded everything that happened during his absence. After he returned from this room, Pythagoras recounted everything that had happened while he was gone, convincing everyone that he had really been in the underworld and leading them to trust him with their wives.
Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field. Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem, as well as discoveries in the fields of music, astronomy, and medicine.
Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides"—that is, . According to a popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole hecatomb, to the gods. Cicero rejected this story as spurious because of the much more widely held belief that Pythagoras forbade blood sacrifices. Porphyry attempted to explain the story by asserting that the ox was actually made of dough.
The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras, but it is possible that he may have been the first one to introduce it to the Greeks. Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof. Burkert rejects this suggestion as implausible, noting that Pythagoras was never credited with having proved any theorem in antiquity. Furthermore, the manner in which the Babylonians employed Pythagorean numbers implies that they knew that the principle was generally applicable, and knew some kind of proof, which has not yet been found in the (still largely unpublished) cuneiform sources.[f] Pythagoras's biographers state that he also was the first to identify the five regular solids and that he was the first to discover the Theory of Proportions.
According to legend, Pythagoras discovered that musical notes could be translated into mathematical equations when he passed blacksmiths at work one day and heard the sound of their hammers clanging against the anvils. Thinking that the sounds of the hammers were beautiful and harmonious, except for one, he rushed into the blacksmith shop and began testing the hammers. He then realized that the tune played when the hammer struck was directly proportional to the size of the hammer and therefore concluded that music was mathematical. However, this legend is demonstrably false, as these ratios are only relevant to string length (such as the string of a monochord), and not to hammer weight.
In ancient times, Pythagoras and his contemporary Parmenides of Elea were both credited with having been the first to teach that the Earth was spherical, the first to divide the globe into five climactic zones, and the first to identify the morning star and the evening star as the same celestial object. Of the two philosophers, Parmenides has a much stronger claim to having been the first and the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem. Empedocles, who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical. By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals.
On Greek philosophy
Sizeable Pythagorean communities existed in Magna Graecia, Phlius, and Thebes during the early fourth century BC. Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia. According to later tradition, Archytas was elected as strategos ("general") seven times, even though others were prohibited from serving for more than a year, and never lost a single battle. Archytas was also a renowned mathematician and musician. He was a close friend of Plato and he is quoted in Plato's Republic.
Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans. Cicero repeats this statement, remarking that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean"). According to Charles H. Kahn, Plato's middle dialogues, including Meno, Phaedo, and The Republic, have a strong "Pythagorean coloring", and his last few dialogues (particularly Philebus and Timaeus) are extremely Pythagorean in character.
According to R. M. Hare, Plato's Republic may be partially based on the "tightly organised community of like-minded thinkers" established by Pythagoras at Croton. Additionally, Plato may have taken from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy, as well as "for substantial theses in science and morals". Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world" and it is probable that both were influenced by Orphism. The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans. Bertrand Russell, in his A History of Western Philosophy, contends that the influence of Pythagoras on Plato and others was so great that he should be considered the most influential philosopher of all time. He concludes that "I do not know of any other man who has been as influential as he was in the school of thought."
A revival of Pythagorean teachings occurred in the first century BC when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed the rise of a "new" Pythagoreanism in Alexandria. At around the same time, Neopythagoreanism became prominent. The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings. The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy and probably understood the soul as a "kind of mathematical harmony." The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory. Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines.
On art and architecture
Greek sculpture sought to represent the permanent reality behind superficial appearances. Early Archaic sculpture represents life in simple forms, and may have been influenced by the earliest Greek natural philosophies.[g] The Greeks generally believed that nature expressed itself in ideal forms and was represented by a type (εἶδος), which was mathematically calculated. When dimensions changed, architects sought to relay permanence through mathematics. Maurice Bowra believes that these ideas influenced the theory of Pythagoras and his students, who believed that "all things are numbers".
During the sixth century BC, the number philosophy of the Pythagoreans triggered a revolution in Greek sculpture. Greek sculptors and architects attempted to find the mathematical relation (canon) behind aesthetic perfection. Possibly drawing on the ideas of Pythagoras, the sculptor Polykleitos writes in his Canon that beauty consists in the proportion, not of the elements (materials), but of the interrelation of parts with one another and with the whole. In the Greek architectural orders, every element was calculated and constructed by mathematical relations. Rhys Carpenter states that the ratio 2:1 was "the generative ratio of the Doric order, and in Hellenistic times an ordinary Doric colonnade, beats out a rhythm of notes."
The oldest known building designed according to Pythagorean teachings is the Porta Maggiore Basilica, a subterranean basilica which was built during the reign of the Roman emperor Nero as a secret place of worship for Pythagoreans. The basilica was built underground because of the Pythagorean emphasis on secrecy and also because of the legend that Pythagoras had sequestered himself in a cave on Samos. The basilica's apse is in the east and its atrium in the west out of respect for the rising sun. It has a narrow entrance leading to a small pool where the initiates could purify themselves. The building is also designed according to Pythagorean numerology, with each table in the sanctuary providing seats for seven people. Three aisles lead to a single altar, symbolizing the three parts of the soul approaching the unity of Apollo. The apse depicts a scene of the poetess Sappho leaping off the Leucadian cliffs, clutching her lyre to her breast, while Apollo stands beneath her, extending his right hand in a gesture of protection, symbolizing Pythagorean teachings about the immortality of the soul. The interior of the sanctuary is almost entirely white because the color white was regarded by Pythagoreans as sacred.
The emperor Hadrian's Pantheon in Rome was also built based on Pythagorean numerology. The temple's circular plan, central axis, hemispherical dome, and alignment with the four cardinal directions symbolize Pythagorean views on the order of the universe. The single oculus at the top of the dome symbolizes the monad and the sun-god Apollo. The twenty-eight ribs extending from the oculus symbolize the moon, because twenty-eight was the same number of months on the Pythagorean lunar calendar. The five coffered rings beneath the ribs represent the marriage of the sun and moon.
In the Middle Ages
During the Middle Ages, Pythagoras was revered as the founder of mathematics and music, two of the Seven Liberal Arts. He appears in numerous medieval depictions, in illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres. The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe, which led William of Conches (c. 1080-1160) to declare that Plato was Pythagorean. In the 1430s, the Camaldolese friar Ambrose Traversari translated Diogenes Laërtius's Lives and Opinions of Eminent Philosophers from Greek into Latin and, in the 1460s, the philosopher Marsilio Ficino translated Porphyry and Iamblichus's Lives of Pythagoras into Latin as well, thereby allowing them to be read and studied by western scholars. In 1494, the Greek Neopythagorean scholar Constantine Lascaris published The Golden Verses of Pythagoras, translated into Latin, with a printed edition of his Grammatica, thereby bringing them to a widespread audience. In 1499, he published the first Renaissance biography of Pythagoras in his work Vitae illustrium philosophorum siculorum et calabrorum, issued in Messina.
On modern science
In his preface to his book On the Revolution of the Heavenly Spheres (1543), Nicolaus Copernicus cites various Pythagoreans as the most important influences on the development of his heliocentric model of the universe, deliberately omitting mention of Aristarchus of Samos, a non-Pythagorean astronomer who had developed a fully heliocentric model in the fourth century BC, in effort to portray his model as fundamentally Pythagorean. Johannes Kepler considered himself to be a Pythagorean. He believed in the Pythagorean doctrine of musica universalis and it was his search for the mathematical equations behind this doctrine that led to his discovery of the laws of planetary motion. Kepler titled his book on the subject Harmonices Mundi (Harmonics of the World), after the Pythagorean teaching that had inspired him. Near the conclusion of the book, Kepler describes himself falling asleep to the sound of the heavenly music, "warmed by having drunk a generous draught... from the cup of Pythagoras."
Isaac Newton firmly believed in the Pythagorean teaching of the mathematical harmony and order of the universe. Though Newton was notorious for rarely giving others credit for their discoveries, he attributed the discovery of the Law of Universal Gravitation to Pythagoras. Albert Einstein believed that a scientist may also be "a Platonist or a Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research." The English philosopher Alfred North Whitehead argued that "In a sense, Plato and Pythagoras stand nearer to modern physical science than does Aristotle. The two former were mathematicians, whereas Aristotle was the son of a doctor". By this measure, Whitehead declared that Einstein and other modern scientists like him are "following the pure Pythagorean tradition."
A fictionalized portrayal of Pythagoras appears in Book XV of Ovid's Metamorphoses, in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet. It was through Arthur Golding's 1567 English translation of Ovid's Metamorphoses that Pythagoras was best known to English-speakers throughout the early modern period. John Donne's Progress of the Soul discusses the implications of the doctrines expounded in the speech and Michel de Montaigne quoted the speech no less than three times in his treatise Of Cruelty to voice his moral objections against eating meat. William Shakespeare references the speech in his play The Merchant of Venice. John Dryden included a translation of the scene with Pythagoras in his 1700 work Fables, Ancient and Modern and John Gay's 1726 fable "Pythagoras and the Countryman" reiterates its major themes, linking carnivorism with tyranny. Lord Chesterfield records that his conversion to vegetarianism had been motivated by reading Pythagoras's speech in Ovid's Metamorphoses. Until the word vegetarianism was coined in the 1840s, vegetarians were referred to in English as "Pythagoreans". Percy Bysshe Shelley wrote an ode entitled "To the Pythagorean Diet" and Leo Tolstoy adopted the Pythagorean diet himself.
On Western esotericism
Early modern European esotericism drew heavily on the teachings of Pythagoras. The German humanist scholar Johannes Reuchlin (1455–1522) synthesized Pythagoreanism with Christian theology and Jewish Kabbalah, arguing that Kabbalah and Pythagoreanism were both inspired by Mosaic tradition and that Pythagoras was therefore a kabbalist. In his dialogue De verbo mirifico (1494), Reuchlin compared the Pythagorean tetractys to the ineffable divine name YHWH, ascribing each of the four letters of the tetragrammaton a symbolic meaning according to Pythagorean mystical teachings.
Heinrich Cornelius Agrippa's popular and influential three-volume treatise De Occulta Philosophia cites Pythagoras as a "religious magi" and indicates that Pythagoras's mystical numerology operates on a supercelestial level. The freemasons deliberately modeled their society on the community founded by Pythagoras at Croton. Rosicrucianism used Pythagorean symbolism, as did Robert Fludd (1574–1637), who believed his own musical writings to have been inspired by Pythagoras. John Dee was heavily influenced by Pythagorean ideology, particularly the teaching that all things are made of numbers. Adam Weishaupt, the founder of the Illuminati, was a strong admirer of Pythagoras and, in his book Pythagoras (1787), he advocated that society should be reformed to be more like Pythagoras's commune at Croton. Wolfgang Amadeus Mozart incorporated Masonic and Pythagorean symbolism into his opera The Magic Flute. Sylvain Maréchal, in his six-volume 1799 biography The Voyages of Pythagoras, declared that all revolutionaries in all time periods are the "heirs of Pythagoras".
Dante Alighieri was fascinated by Pythagorean numerology and based his descriptions of Hell, Purgatory, and Heaven on Pythagorean numbers. Dante wrote that Pythagoras saw Unity as Good and Plurality as Evil and, in Paradiso XV, 56–57, he declares: "five and six, if understood, ray forth from unity." The number eleven and its multiples are found throughout the Divine Comedy, each book of which has thirty-three cantos, except for the Inferno, which has thirty-four, the first of which serves as a general introduction. Dante describes the ninth and tenth bolgias in the Eighth Circle of Hell as being twenty-two miles and eleven miles respectively, which correspond to the fraction 22/, which was the Pythagorean approximation of pi. Hell, Purgatory, and Heaven are all described as circular and Dante compares the wonder of God's majesty to the mathematical puzzle of squaring the circle. The number three also features prominently: the Divine Comedy has three parts and Beatrice is associated with the number nine, which is equal to three times three.
The Transcendentalists read the ancient Lives of Pythagoras as guides on how to live a model life. Henry David Thoreau was impacted by Thomas Taylor's translations of Iamblichus's Life of Pythagoras and Stobaeus's Pythagoric Sayings and his views on nature may have been influenced by the Pythagorean idea of images corresponding to archetypes. The Pythagorean teaching of musica universalis is a recurring theme throughout Thoreau's magnum opus, Walden.
- US: //, UK: /-/; Ancient Greek: Πυθαγόρας ὁ Σάμιος, translit. Pythagóras ho Sámios, lit. 'Pythagoras the Samian', or simply Πυθαγόρας; Πυθαγόρης in Ionian Greek
- "The dates of his life cannot be fixed exactly, but assuming the approximate correctness of the statement of Aristoxenus (ap. Porph. V.P. 9) that he left Samos to escape the tyranny of Polycrates at the age of forty, we may put his birth round about 570 BC, or a few years earlier. The length of his life was variously estimated in antiquity, but it is agreed that he lived to a fairly ripe old age, and most probably he died at about seventy-five or eighty." William Keith Chambers Guthrie, (1978), A history of Greek philosophy, Volume 1: The earlier Presocratics and the Pythagoreans, p. 173. Cambridge University Press
- Cicero, Tusculan Disputations, 5.3.8–9 (citing Heraclides Ponticus fr. 88 Wehrli), Diogenes Laërtius 1.12, 8.8, Iamblichus VP 58. Burkert attempted to discredit this ancient tradition, but it has been defended by C.J. De Vogel, Pythagoras and Early Pythagoreanism (1966), pp. 97–102, and C. Riedweg, Pythagoras: His Life, Teaching, And Influence (2005), p. 92.
- Some writers call him a Tyrrhenian or Phliasian, and give Marmacus, or Demaratus, as the name of his father: Diogenes Laërtius, viii. 1; Porphyry, Vit. Pyth. 1, 2; Justin, xx. 4; Pausanias, ii. 13.
- as Empedocles did afterwards, Aristotle, Rhet. i. 14. § 2; Sextus Empiricus, ix. 127. This was also one of the Orphic precepts, Aristoph. Ran. 1032
- There are about 100,000 unpublished cuneiform sources in the British Museum alone. Babylonian knowledge of proof of the Pythagorean Theorem is discussed by J. Høyrup, 'The Pythagorean "Rule" and "Theorem" – Mirror of the Relation between Babylonian and Greek Mathematics,' in: J. Renger (red.): Babylon. Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne (1999).
- "For Thales, the origin was water, and for Anaximander the infinite (apeiron), which must be considered a material form"
- Joost-Gaugier 2006, p. 143.
- "American: Pythagoras". Collins Dictionary. n.d. Retrieved 25 September 2014.
- "British: Pythagoras". Collins Dictionary. n.d. Retrieved 25 September 2014.
- Dillon 2005, p. 163.
- Joost-Gaugier 2006, p. 11.
- Grafton, Most & Settis 2010, p. 796.
- Ferguson 2008, p. 4.
- Ferguson 2008, pp. 3–5.
- Copleston 2003, p. 29.
- Kahn 2001, p. 2.
- Burkert 1985, p. 299.
- Joost-Gaugier 2006, p. 12.
- Riedweg 2005, p. 62.
- Diogenes Laërtius, viii. 36
- Copleston 2003, p. 31.
- Joost-Gaugier 2006, pp. 12–13.
- Joost-Gaugier 2006, p. 13.
- Joost-Gaugier 2006, pp. 14–15.
- Joost-Gaugier 2006, p. 16.
- 4. 95.
- Joost-Gaugier 2006, p. 88.
- He alludes to it himself, Met. i. 5. p. 986. 12, ed. Bekker.
- Burkert 1972, p. 109.
- Kahn 2001, p. 5.
- Zhmud 2012, p. 9.
- Burkert 1972, p. 106.
- Kahn 2001, p. 6.
- Ferguson 2008, p. 12.
- Clemens von Alexandria: Stromata I 62, 2–3, cit. Eugene V. Afonasin; John M. Dillon; John Finamore, eds. (2012). Iamblichus and the Foundations of Late Platonism. Leiden and Boston: Brill. p. 15. ISBN 9789004230118.
- Joost-Gaugier 2006, p. 21.
- Ferguson 2008, pp. 11–12.
- Riedweg 2005, pp. 5–6, 59, 73.
- Apollonius of Tyana ap. Porphyry, Vit. Pyth. 2.
- Porphyry, Vit. Pyth. 9
- Cornelli & McKirahan 2013, p. 64.
- Ferguson 2008, p. 5.
- Boyer, Carl B. (1968). A History of Mathematics.
- Iamblichus, Vit. Pyth. 28; Porphyry, Vit. Pyth. 9
- Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism. Assen 1966, pp. 21ff. Cfr. Cicero, De re publica 2, 28–30.
- Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism, Assen 1966, S. 148–150.
- Porphyry, Vit. Pyth. 18; Iamblichus, Vit. Pyth. 37, etc.
- Kahn 2001, pp. 6–7.
- Kahn 2001, p. 7.
- Iamblichus, Vit. Pyth. 255–259; Porphyry, Vit. Pyth. 54–57; Diogenes Laërtius, viii. 39; comp. Plutarch, de Gen. Socr. p. 583
- Grant 1989, p. 278.
- Simoons 1998, p. 227.
- Simoons 1998, pp. 225–228.
- Kahn 2001, p. 8.
- Pomeroy 2013, p. 1.
- Pomeroy 2013, p. xvi.
- Ferguson 2008, p. 58.
- Ferguson 2008, p. 59.
- Riedweg 2005, p. 10.
- Diogenes Laërtius, Lives of Eminent Philosophers, viii. 1, 8.
- Mary Ellen Waithe, Ancient women philosophers, 600 B.C.–500 A.D., p. 11
- Malone, John C. (30 June 2009). Psychology: Pythagoras to present. MIT Press. p. 22. ISBN 978-0-262-01296-6. Retrieved 25 October 2010.
- Riedweg 2005, p. 8.
- Porphyry, Vit. Pyth. 2, Diogenes Laërtius, viii. 2.
- Iamblichus, Vit. Pyth. 9.
- Porphyry, Vit. Pyth. 2.
- Aristoxenus and others in Diogenes Laërtius, i. 118, 119; Cicero, de Div. i. 49
- Riedweg 2005, p. 9.
- C. B. Boyer (1968)
- Zhmud 2012, pp. 2, 16.
- Porphyry, Life of Pythagoras, 41.
- Gilles Ménage: The history of women philosophers. Translated from the Latin with an introduction by Beatrice H. Zedler. University Press of America, Lanham 1984, p. 48. "The person who is referred to as Themistoclea in Laertius and Theoclea in Suidas, Porphyry calls Aristoclea."
- Iamblichus, Vit. Pyth. 25; Porphyry, Vit. Pyth. 17; Diogenes Laërtius, viii. 3.
- Ariston. ap. Diogenes Laërtius, viii. 8, 21; Porphyry, Vit. Pyth. 41.
- Porphyry, Vit. Pyth. 6.
- Diogenes Laërtius, viii. 1, 3.
- Plutarch, On Isis And Osiris, ch. 10.
- Antiphon. ap. Porphyry, Vit. Pyth. 7; Isocrates, Busiris, 28–9; Cicero, de Finibus, v. 27; Strabo, xiv.
- Press 2003, p. 83.
- Bruhn 2005, p. 66.
- Burkert 1972, pp. 106–109.
- Kahn 2001, pp. 5–6.
- Kahn 2001, pp. 9–11.
- Burkert 1972, pp. 29–30.
- Kahn 2001, p. 11.
- Zhmud 2012, p. 232.
- Burkert 1985, pp. 300–301.
- Copleston 2003, pp. 30–31.
- Diogenes Laërtius, viii. 36, comp. Aristotle, de Anima, i. 3; Herodotus, ii. 123.
- Kahn 2001, p. 12.
- Diogenes Laërtius, viii. 3–4
- Cornelli & McKirahan 2013, pp. 164–167.
- Porphyry, Vit. Pyth. 26; Pausanias, ii. 17; Diogenes Laërtius, viii. 5; Horace, Od. i. 28,1. 10
- Cornelli & McKirahan 2013, pp. 164–165.
- Cornelli & McKirahan 2013, pp. 165–166.
- Cornelli & McKirahan 2013, p. 167.
- Aulus Gellius, iv. 11
- Riedweg 2005, pp. 29–30.
- Riedweg 2005, p. 30.
- D. S. Hutchinson; Monte Ransome Johnson (25 January 2015). "New Reconstruction, includes Greek text". p. 48.
- Cicero, de Divin. i. 3, 46; Porphyry, Vit. Pyth. 29.
- Iamblichus, Vit. Pyth. 25; Porphyry, Vit. Pyth. 17; Diogenes Laërtius, viii. 3, 13; Cicero, Tusc. Qu. v. 3.
- Bruhn 2005, pp. 65–66.
- Riedweg 2005, p. 29.
- Kahn 2001, pp. 1–2.
- Burkert 1972, pp. 467–468.
- Burkert 1972, p. 265.
- Kahn 2001, p. 27.
- Riedweg 2005, p. 23.
- Joost-Gaugier 2006, pp. 170–172.
- Joost-Gaugier 2006, p. 172.
- Burkert 1972, p. 433.
- Burkert 1972, p. 467.
- Joost-Gaugier 2006, p. 170.
- Joost-Gaugier 2006, p. 161.
- Iamblichus, Vit. Pyth., 29
- Joost-Gaugier 2006, pp. 87–88.
- Kahn 2001, pp. 2–3.
- Kahn 2001, p. 3.
- Burkert 1972, pp. 428–433.
- Burkert 1972, p. 465.
- Plato, Republic, 600a, Isocrates, Busiris, 28
- Cornelli & McKirahan 2013, p. 168.
- Grant 1989, p. 277.
- Aelian, Varia Historia, ii. 26; Diogenes Laërtius, viii. 13; Iamblichus, Vit. Pyth. 8, 91, 141
- Porphyry, Vit. Pyth. 19
- Thirlwall, Hist. of Greece, vol. ii. p. 148
- Riedweg 2005, p. 31.
- comp. Cicero, de Leg. i. 12, de Off. i. 7; Diogenes Laërtius, viii. 10
- Cornelli & McKirahan 2013, p. 65.
- Aristonexus ap. Iamblichus, Vit. Pyth. 94, 101, etc., 229, etc.; comp. the story of Damon and Phintias; Porphyry, Vit. Pyth. 60; Iamblichus, Vit. Pyth. 233, etc.
- Cornelli & McKirahan 2013, pp. 68–69.
- John Dillon and Jackson Hershbell, (1991), Iamblichus, On the Pythagorean Way of Life, page 14. Scholars Press.; D. J. O'Meara, (1989), Pythagoras Revived. Mathematics and Philosophy in Late Antiquity, pages 35–40. Clarendon Press.
- Scholion ad Aristophanes, Nub. 611; Iamblichus, Vit. Pyth. 237, 238
- Cornelli & McKirahan 2013, p. 69.
- Riedweg 2005, pp. 64-67.
- Riedweg 2005, p. 64.
- Riedweg 2005, p. 65.
- Riedweg 2005, pp. 65-67.
- Riedweg 2005, pp. 65-66.
- Riedweg 2005, pp. 66-67.
- Riedweg 2005, p. 66.
- Pomeroy 2013, pp. xvi–xvii.
- Riedweg 2005, pp. 33–34.
- comp. Porphyry, Vit. Pyth. 32; Iamblichus, Vit. Pyth. 96, etc.
- Zhmud 2012, pp. 137, 200.
- Zhmud 2012, p. 200.
- Copleston 2003, p. 30.
- Diogenes Laërtius, viii. 19, 34; Aulus Gellius, iv. 11; Porphyry, Vit. Pyth. 34, de Abst. i. 26; Iamblichus, Vit. Pyth. 98
- Kahn 2001, p. 9.
- Plutarch, de Esu Carn. pp. 993, 996, 997
- Eudoxus, frg. 325
- Zhmud 2012, p. 235.
- Aristo ap. Diogenes Laërtius, viii. 20; comp. Porphyry, Vit. Pyth. 7; Iamblichus, Vit. Pyth. 85, 108
- Aristoxenus ap. Diogenes Laërtius, viii. 20
- comp. Porphyry, Vit. Pyth. 7; Iamblichus, Vit. Pyth. 85, 108
- Iamblichus, Vit. Pyth. 98; Strabo, vi.
- Riedweg 2005, p. 1.
- Riedweg 2005, p. 2.
- Ferguson 2008, p. 60.
- Porphyry, Vit. Pyth. 20; Iamblichus, Vit. Pyth. 31, 140; Aelian, Varia Historia, ii. 26; Diogenes Laërtius, viii. 36.
- McKeown 2013, p. 155.
- Comp. Herodian, iv. 94, etc.
- Ferguson 2008, p. 10.
- See Antoine Faivre, in The Eternal Hermes (1995)
- Joost-Gaugier 2006, p. 47.
- Ferguson 2008, pp. 58–59.
- Cornelli & McKirahan 2013, p. 160.
- Ferguson 2008, pp. 60–61.
- Ferguson 2008, p. 61.
- Diogenes Laërtius, viii. 12; Plutarch, Non posse suav. vivi sec. Ep. p. 1094
- Porphyry, in Ptol. Harm. p. 213; Diogenes Laërtius, viii. 12.
- Diogenes Laërtius, viii. 14 ; Pliny, Hist. Nat. ii. 8.
- Diogenes Laërtius, viii. 12, 14, 32.
- Kahn 2001, pp. 32–33.
- Riedweg 2005, pp. 26–27.
- Riedweg 2005, p. 27.
- Burkert 1972, p. 428.
- Burkert 1972, pp. 429, 462.
- Kahn 2001, p. 32.
- Ferguson 2008, pp. 6–7.
- Burkert 1972, p. 429.
- Kahn 2001, p. 33.
- Riedweg 2005, pp. 27–28.
- Riedweg 2005, p. 28.
- Christensen 2002, p. 143.
- Burkert 1972, p. 306.
- Burkert 1972, pp. 307–308.
- Burkert 1972, pp. 306–308.
- Kahn 2001, p. 53.
- Dicks 1970, p. 68.
- Kahn 2001, pp. 55–62.
- Kahn 2001, pp. 48–49.
- Kahn 2001, p. 39.
- Kahn 2001, pp. 39–43.
- Kahn 2001, pp. 39–40.
- Kahn 2001, pp. 40, 44–45.
- Plato, Republic VII, 530d
- Metaphysics, 1.6.1 (987a)
- Kahn 2001, p. 1.
- Tusc. Disput. 1.17.39.
- Kahn 2001, p. 55.
- Hare 1999, pp. 117–119.
- Copleston 2003, p. 37.
- Russell 2008, pp. 33–37.
- Russell 2008, p. 37.
- Riedweg 2005, pp. 123–124.
- Riedweg 2005, p. 124.
- Riedweg 2005, pp. 125–126.
- Riedweg 2005, p. 125.
- Riedweg 2005, pp. 126–127.
- Joost-Gaugier 2006, pp. 166–181.
- Homann-Wedeking 1968, p. 63.
- Homann-Wedeking 1968, p. 62.
- Carpenter 1921, pp. 107, 122, 128.
- Homann-Wedeking 1968, pp. 62–63.
- Bowra 1994, p. 166.
- Homann-Wedeking 1968, pp. 62–65.
- "Each part (finger, palm, arm, etc) transmitted its individual existence to the next, and then to the whole": Canon of Polykleitos, also Plotinus, Ennead I.vi.i: Nigel Spivey, pp. 290–294.
- Joost-Gaugier 2006, p. 154.
- Joost-Gaugier 2006, pp. 154–156.
- Joost-Gaugier 2006, pp. 157–158.
- Joost-Gaugier 2006, p. 158.
- Joost-Gaugier 2006, pp. 158–159.
- Joost-Gaugier 2006, p. 159.
- Joost-Gaugier 2006, pp. 159–161.
- Joost-Gaugier 2006, p. 162.
- Joost-Gaugier 2006, pp. 162–164.
- Joost-Gaugier 2006, pp. 167–168.
- Joost-Gaugier 2006, p. 168.
- Joost-Gaugier 2006, pp. 169–170.
- Grafton, Most & Settis 2010, p. 798.
- Russo 2004, pp. 5–87, especially 51–53.
- Kahn 2001, p. 160.
- Kahn 2001, pp. 161–171.
- Ferguson 2008, p. 265.
- Ferguson 2008, pp. 264–274.
- Kahn 2001, p. 162.
- Ferguson 2008, p. 274.
- Ferguson 2008, p. 279.
- Ferguson 2008, pp. 279–280.
- Kahn 2001, p. 172.
- Whitehead 1953, pp. 36–37.
- Whitehead 1953, p. 36.
- Borlik 2011, p. 192.
- Borlik 2011, p. 189.
- Borlik 2011, pp. 189–190.
- Borlik 2011, p. 190.
- Ferguson 2008, p. 282.
- Ferguson 2008, p. 294.
- Riedweg 2005, pp. 127–128.
- Riedweg 2005, p. 128.
- French 2002, p. 30.
- Riedweg 2005, p. 133.
- Sherman 1995, p. 15.
- Ferguson 2008, pp. 284–288.
- Ferguson 2008, pp. 287–288.
- Ferguson 2008, pp. 286–287.
- Ferguson 2008, p. 288.
- Haag 2013, p. 89.
- Haag 2013, p. 90.
- Haag 2013, pp. 90–91.
- Haag 2013, p. 91.
- Haag 2013, pp. 91–92.
- Haag 2013, p. 92.
- Bregman 2002, p. 186.
Classical secondary sources
Only a few relevant source texts deal with Pythagoras and the Pythagoreans, most are available in different translations. Other texts usually build solely on information in these works.
- Diogenes Laërtius, Vitae philosophorum VIII (Lives of Eminent Philosophers), c. 200 AD, which in turn references the lost work Successions of Philosophers by Alexander Polyhistor — Laërtius, Diogenes (1925). "Pythagoreans: Pythagoras". Lives of the Eminent Philosophers. 2:8. Translated by Hicks, Robert Drew (Two volume ed.). Loeb Classical Library.
- Porphyry, Vita Pythagorae (Life of Pythagoras), c. 270 AD — Porphyry, Life of Pythagoras, translated by Kenneth Sylvan Guthrie (1920)
- Iamblichus, De Vita Pythagorica (On the Pythagorean Life), c. 300 AD — Iamblichus, Life of Pythagoras, translated by Kenneth Sylvan Guthrie (1920)
- Apuleius, following Aristoxenus, writes about Pythagoras in Apologia, c. 150 AD, including a story of his being taught by Zoroaster—a story also found in Clement of Alexandria.[a]
- Hierocles of Alexandria, Golden Verses of Pythagoras, c. 430 AD
Modern secondary sources
- Bowra, C. M. (1994) , The Greek Experience, London, England: Weidenfeld & Nicolson History, ISBN 978-1-85799-122-2
- Bregman, Jay (2002), "Neoplatonism and American Aesthetics", in Alexandrakis, Aphrodite; Moulafakis, Nicholas J., Neoplatonism and Western Aesthetics, Studies in Neoplatonism: Ancient and Modern, 12, Albany, New York: State University of New York Press, ISBN 0-7914-5280-8
- Bruhn, Siglind (2005), The Musical Order of the Universe: Kepler, Hesse, and Hindemith, Interfaces Series, Hillsdale, New York: Pendragon Press, ISBN 978-1-57647-117-3
- Borlik, Todd A. (2011), Ecocriticism and Early Modern English Literature: Green Pastures, New York City, New York and London, England: Routledge, ISBN 978-0-203-81924-1
- Burkert, Walter (1 June 1972), Lore and Science in Ancient Pythagoreanism, Cambridge, Massachusetts: Harvard University Press, ISBN 0-674-53918-4
- Burkert, Walter (1985), Greek Religion, Cambridge, Massachusetts: Harvard University Press, ISBN 0-674-36281-0
- Carpenter, Rhys (1921), The Esthetic Basis Of Greek Art: Of The Fifth And Fourth Centuries B.C., Bryn Mawr, Pennsylvania: Bryn Mawr College, ISBN 978-1-165-68068-9
- Christensen, Thomas (2002), The Cambridge History of Western Music Theory, Cambridge, England: Cambridge University Press, ISBN 978-0-521-62371-1
- Cornelli, Gabriele; McKirahan, Richard (2013), In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category, Berlin, Germany: Walter de Gruyter, ISBN 978-3-11-030650-7
- Copleston, Frederick (2003) , "The Pythagorean Society", A History of Philosophy, 1 Greece and Rome, London, England and New York City, New York: Continuum, ISBN 0-8264-6947-7
- Dicks, D.R. (1970), Early Greek Astronomy to Aristotle, Ithaca, New York: Cornell University Press, ISBN 978-0-8014-0561-7
- Dillon, Sheila (24 December 2005), Ancient Greek Portrait Sculpture: Context, Subjects, and Styles, Cambridge, England: Cambridge University Press, ISBN 978-1-107-61078-1
- Ferguson, Kitty (2008), The Music of Pythagoras: How an Ancient Brotherhood Cracked the Code of the Universe and Lit the Path from Antiquity to Outer Space, New York City, New York: Walker & Company, ISBN 978-0-8027-1631-6
- French, Peter J. (2002) , John Dee: The World of the Elizabethan Magus, New York City, New York and London, England: Routledge, ISBN 0-7448-0079-X
- Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (2010), The Classical Tradition, Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press, ISBN 978-0-674-03572-0
- Grant, Michael (1989), The Classical Greeks, History of Civilization, New York City, New York: Charles Schribner's Sons, ISBN 0-684-19126-1
- Guthrie, W. K. (1979), A History of Greek Philosophy: Earlier Presocratics and the Pythagoreans, Cambridge, England: Cambridge University Press, ISBN 0-521-29420-7
- Haag, Michael (2013), Inferno Decoded: The Essential Companion to the Myths, Mysteries and Locations of Dan Brown's Inferno, London, England: Profile Books, Ltd., ISBN 978-1-78125-180-5
- Hare, R.M. (1999) , "Plato", in Taylor, C.C.W.; Hare, R.M.; Barnes, Jonathan, Greek Philosophers: Socrates, Plato, and Aristotle, Past Masters, Oxford, England: Oxford University Press, pp. 103–189, ISBN 978-0-19-285422-3
- Hermann, Arnold (2005), To Think Like God: Pythagoras and Parmenides—the Origins of Philosophy, Las Vegas, Nevada: Parmenides Publishing, ISBN 978-1-930972-00-1
- Homann-Wedeking, Ernst (1968), The Art of Archaic Greece, Art of the World, New York City, New York: Crown Publishers
- Horky, Philip Sydney (2013), Plato and Pythagoreanism, Oxford, England: Oxford University Press, ISBN 978-0-19-989822-0
- Joost-Gaugier, Christiane L. (2006), Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages, Ithaca, New York: Cornell University Press, ISBN 978-0-8014-7409-5
- Kahn, Charles H. (2001), Pythagoras and the Pythagoreans: A Brief History, Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company, ISBN 978-0-87220-575-8
- Kingsley, Peter (1995), Ancient Philosophy, Mystery, and Magic: Empedocles and the Pythagorean Tradition, Oxford, England: Oxford University Press
- McKeown, J. C. (2013), A Cabinet of Greek Curiosities: Strange Tales and Surprising Facts from the Cradle of Western Civilization, Oxford, England: Oxford University Press, ISBN 978-0-19-998210-3
- O'Meara, Dominic J. (1989), Pythagoras Revived, Oxford, England: Oxford University Press, ISBN 0-19-823913-0
- Press, Gerald A. (2003) , Development of the Idea of History in Antiquity, Montreal, Canada and Kingston, New York: McGill-Queen's University Press, ISBN 0-7735-1002-8
- Pomeroy, Sarah B. (2013), Pythagorean Women: The History and Writings, Baltimore, Maryland: The Johns Hopkins University Press, ISBN 978-1-4214-0956-6
- Riedweg, Christoph (2005) , Pythagoras: His Life, Teachings, and Influence, Ithaca, New York: Cornell University Press, ISBN 978-0-8014-7452-1
- Russell, Bertrand (2008) , A History of Western Philosophy, A Touchstone Book, New York City, New York: Simon & Schuster, ISBN 978-0-671-31400-2
- Russo, Attilio (2004), "Costantino Lascaris tra fama e oblio nel Cinquecento messinese", Archivio Storico Messinese, Messina, LXXXIV-LXXXV: 5–87, especially 51–53, ISSN 0392-0240
- Schofield, Malcolm (2013), Aristotle, Plato and Pythagoreanism in the First Century BC: New Directions for Philosophy, Cambridge, England: Cambridge University Press, ISBN 978-1-107-02011-5
- Sherman, William Howard (1995), John Dee: The Politics of Reading and Writing in the English Renaissance, Amherst, Massachusetts: The University of Massachusetts Press, ISBN 1-55849-070-1
- Simoons, Frederick J. (1998), Plants of Life, Plants of Death, Madison, Wisconsin: University of Wisconsin Press, ISBN 0-299-15904-3
- Whitehead, Afred North (1953) , Science and the Modern World, Cambridge, England: Cambridge University Press, ISBN 978-0-521-23778-9
- Zhmud, Leonid (2012), Pythagoras and the Early Pythagoreans, translated by Windle, Kevin; Ireland, Rosh, Oxford, England: Oxford University Press, ISBN 978-0-19-928931-8
|Wikisource has the text of the 1911 Encyclopædia Britannica article Pythagoras.|
- Pythagoras on In Our Time at the BBC
- Huffman, Carl. "Pythagoras". In Zalta, Edward N. Stanford Encyclopedia of Philosophy.
- Pythagoras of Samos, The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland
- Pythagoras and the Pythagoreans, Fragments and Commentary, Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History
- Pythagoras and the Pythagoreans, Department of Mathematics, Texas A&M University
- Pythagoras and Pythagoreanism, The Catholic Encyclopedia
- Works by or about Pythagoras at Internet Archive
- Works by Pythagoras at LibriVox (public domain audiobooks)