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Pythagoras

January 16, 2023

"Pythagoras of Samos" redirects here. For the Samian statuary, see Pythagoras (sculptor).
For other uses, see Pythagoras (disambiguation).

Pythagoras of Samos[a] (Ancient Greek: Πυθαγόρας ὁ Σάμιος, romanized: Pythagóras ho Sámios, lit. 'Pythagoras the Samian', or simply Πυθαγόρας; Πυθαγόρης in Ionian Greek; c. 570 – c. 495 BC)[b] was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he ever advocated complete vegetarianism.

Pythagoras
Bust of Pythagoras of Samos in the
Capitoline Museums, Rome[1]
Bornc. 570 BC
Samos
Diedc. 495 BC (aged around 75)
either Croton or Metapontum
EraPre-Socratic philosophy
RegionWestern philosophy
SchoolPythagoreanism
Main interests
Notable ideas

Attributed ideas:
Influences
Influenced

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 developed the numerological and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly Philolaus of Croton. 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 and died there.

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 on 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 modern vegetarian movement.

Biographical sources

 
Fictionalized portrait of Pythagoras from a 17th-century engraving

No authentic writings of Pythagoras have survived,[5][6][7] and almost nothing is known for certain about his life.[8][9][10] The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical.[7][11][12] The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by Xenophanes of Colophon, who had been one of his contemporaries.[13][14] In the poem, Xenophanes describes Pythagoras interceding on behalf of a dog that is being beaten, professing to recognize in its cries the voice of a departed friend.[12][13][15][16] Alcmaeon of Croton, a doctor who lived in Croton at around the same time Pythagoras lived there,[13] incorporates many Pythagorean teachings into his writings[17] and alludes to having possibly known Pythagoras personally.[17] 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,[18] mocked Pythagoras as a clever charlatan,[11][18] 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."[11][18]

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.[19] The first concise description of Pythagoras comes from the historian Herodotus of Halicarnassus (c. 484 – c. 420 BC),[20] who describes him as "not the most insignificant" of Greek sages[21] and states that Pythagoras taught his followers how to attain immortality.[20] The accuracy of the works of Herodotus is controversial.[22][23][24][25][26] 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.[27] The Athenian rhetorician Isocrates (436–338 BC) was the first to describe Pythagoras as having visited Egypt.[20] Aristotle wrote a treatise On the Pythagoreans, which is no longer extant.[28] Some of it may be preserved in the Protrepticus. Aristotle's disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus also wrote on the same subject.[29]

Most of the major sources on Pythagoras's life are from the Roman period,[30] by which point, according to the German classicist Walter Burkert, "the history of Pythagoreanism was already... the laborious reconstruction of something lost and gone."[29] Three ancient biographies of Pythagoras have survived from late antiquity,[10][30] all of which are filled primarily with myths and legends.[10][30][31] The earliest and most respectable of these is the one from Diogenes Laërtius's Lives and Opinions of Eminent Philosophers.[30][31] The two later biographies were written by the Neoplatonist philosophers Porphyry and Iamblichus[30][31] and were partially intended as polemics against the rise of Christianity.[31] The later sources are much lengthier than the earlier ones,[30] and even more fantastic in their descriptions of Pythagoras's achievements.[30][31] Porphyry and Iamblichus used material from the lost writings of Aristotle's disciples[29] and material taken from these sources is generally considered to be the most reliable.[29]

Life

Early life

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[32]

Herodotus,[33] Isocrates, and other early writers agree that Pythagoras was the son of Mnesarchus,[20][34] and that he was born on the Greek island of Samos in the eastern Aegean.[5][34][35][36] According to these biographers, Pythagoras' father wasn't born on the island, although he got naturalized there,[35] but according to Iamblichus he was a native of the island.[37] He is said to have been a gem-engraver or a wealthy merchant,[38][39][40] but his ancestry is disputed and unclear.[41][d] His mother was a native of Samos, descending from a geomoroi family.[42] Apollonius of Tyana, gives her name as Pythaïs.[43][44] Iamblichus tells the story that the Pythia prophesied to her while she was pregnant with him that she would give birth to a man supremely beautiful, wise, and beneficial to humankind.[45] 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.[46] Pythagoras's name led him to be associated with Pythian Apollo (Pūthíā); Aristippus of Cyrene in the 4th century BC explained his name by saying, "He spoke [ἀγορεύω, agoreúō] the truth no less than did the Pythian [πυθικός puthikós]".[45]

During Pythagoras's formative years, Samos was a thriving cultural hub known for its feats of advanced architectural engineering, including the building of the Tunnel of Eupalinos, and for its riotous festival culture.[47] It was a major center of trade in the Aegean where traders brought goods from the Near East.[5] According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions.[5] Pythagoras's early life also coincided with the flowering of early Ionian natural philosophy.[34][48] He was a contemporary of the philosophers Anaximander, Anaximenes, and the historian Hecataeus, all of whom lived in Miletus, across the sea from Samos.[48]

Reputed travels

Pythagoras is traditionally thought to have received most of his education in the Near East.[49] Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures.[49] Like many other important Greek thinkers, Pythagoras was said to have studied in Egypt.[20][50][51] By the time of Isocrates in the fourth century BC, Pythagoras's reputed studies in Egypt were already taken as fact.[20][45] The writer Antiphon, who may have lived during the Hellenistic Era, claimed in his lost work On Men of Outstanding Merit, used as a source by Porphyry, that Pythagoras learned to speak Egyptian from the Pharaoh Amasis II himself, that he studied with the Egyptian priests at Diospolis (Thebes), and that he was the only foreigner ever to be granted the privilege of taking part in their worship.[49][52] 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).[53] 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."[54] Some ancient writers claimed that Pythagoras learned geometry and the doctrine of metempsychosis from the Egyptians.[50][55]

Other ancient writers, however, claimed that Pythagoras had learned these teachings from the Magi in Persia or even from Zoroaster himself.[56][57] Diogenes Laërtius asserts that Pythagoras later visited Crete, where he went to the Cave of Ida with Epimenides.[56] The Phoenicians are reputed to have taught Pythagoras arithmetic and the Chaldeans to have taught him astronomy.[57] By the third century BC, Pythagoras was already reported to have studied under the Jews as well.[57] Contradicting all these reports, the novelist Antonius Diogenes, writing in the second century BC, reports that Pythagoras discovered all his doctrines himself by interpreting dreams.[57] The third-century AD Sophist Philostratus claims that, in addition to the Egyptians, Pythagoras also studied under sages or gymnosophists in India.[57] Iamblichus expands this list even further by claiming that Pythagoras also studied with the Celts and Iberians.[57]

Alleged Greek teachers

 
Bust of Pythagoras in the Vatican Museums, Vatican City, showing him as a "tired-looking older man"[1]
 
Bronze bust of a philosopher wearing a tainia from Villa of the Papyri, Herculaneum, possibly a fictional bust of Pythagoras[58][1]

Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers.[57] Some identify Hermodamas of Samos as a possible tutor.[57][59] Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer.[57] Others credit Bias of Priene, Thales,[60] or Anaximander (a pupil of Thales).[57][60][61] Other traditions claim the mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphic Mysteries.[57] The Neoplatonists wrote of a "sacred discourse" Pythagoras had written on the gods in the Doric Greek dialect, which they believed had been dictated to Pythagoras by the Orphic priest Aglaophamus upon his initiation to the orphic Mysteries at Leibethra.[57] Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship.[62] Iamblichus describes Pythagoreanism as a synthesis of everything Pythagoras had learned from Orpheus, from the Egyptian priests, from the Eleusinian Mysteries, and from other religious and philosophical traditions.[62] Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent.[63]

Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros is mentioned most often.[63][64] Similar miracle stories were told about both Pythagoras and Pherecydes, including one in which the hero predicts a shipwreck, one in which he predicts the conquest of Messina, and one in which he drinks from a well and predicts an earthquake.[63] Apollonius Paradoxographus, a paradoxographer who may have lived in the second century BC, identified Pythagoras's thaumaturgic ideas as a result of Pherecydes's influence.[63] Another story, which may be traced to the Neopythagorean philosopher Nicomachus, tells that, when Pherecydes was old and dying on the island of Delos, Pythagoras returned to care for him and pay his respects.[63] Duris, the historian and tyrant of Samos, is reported to have patriotically boasted of an epitaph supposedly penned by Pherecydes which declared that Pythagoras's wisdom exceeded his own.[63] On the grounds of all these references connecting Pythagoras with Pherecydes, Riedweg concludes that there may well be some historical foundation to the tradition that Pherecydes was Pythagoras's teacher.[63] Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis.[63]

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,[65] 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.[66] Diogenes Laërtius cites a statement from Aristoxenus (fourth century BC) stating that Pythagoras learned most of his moral doctrines from the Delphic priestess Themistoclea.[67][68][69] Porphyry agrees with this assertion,[70] but calls the priestess Aristoclea (Aristokleia).[71] Ancient authorities furthermore note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphic or Cretan mysteries,[72] or the Delphic oracle.[73]

In Croton

class=notpageimage|
Map of Italy showing locations associated with Pythagoras

Porphyry repeats an account from Antiphon, who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle".[74][75] Here, Samians debated matters of public concern.[74][75] Supposedly, the school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach.[74] Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends.[74][75] Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos,[74] but cautions that Antiphon's account, which makes reference to a specific building that was still in use during his own time, appears to be motivated by Samian patriotic interest.[74]

Around 530 BC, when Pythagoras was about forty years old, he left Samos.[5][34][76][77][78] His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos,[65][76] Riedweg notes that this explanation closely aligns with Nicomachus's emphasis on Pythagoras's purported love of freedom, but that Pythagoras's enemies portrayed him as having a proclivity towards tyranny.[76] Other accounts claim that Pythagoras left Samos because he was so overburdened with public duties in Samos, because of the high estimation in which he was held by his fellow-citizens.[79] He arrived in the Greek colony of Croton (today's Crotone, in Calabria) in what was then Magna Graecia.[34][78][80][81] All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment.[34][82][83] He served as an advisor to the elites in Croton and gave them frequent advice.[84] Later biographers tell fantastical stories of the effects of his eloquent speeches 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.[85][86]

Family and friends

 
Illustration from 1913 showing Pythagoras teaching a class of women. Many prominent members of his school were women[87][88] and some modern scholars think that he may have believed that women should be taught philosophy as well as men.[89]

Diogenes Laërtius states that Pythagoras "did not indulge in the pleasures of love"[90] and that he cautioned others to only have sex "whenever you are willing to be weaker than yourself".[91] According to Porphyry, Pythagoras married Theano, a lady of Crete and the daughter of Pythenax[91] and had several children with her.[91] Porphyry writes that Pythagoras had two sons named Telauges and Arignote,[91] and a daughter named Myia,[91] who "took precedence among the maidens in Croton and, when a wife, among married women."[91] Iamblichus mentions none of these children[91] and instead only mentions a son named Mnesarchus after his grandfather.[91] 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.[91] Suda writes that Pythagoras had 4 children (Telauges, Mnesarchus, Myia and Arignote).[92]

The wrestler Milo of Croton was said to have been a close associate of Pythagoras[93] and was credited with having saved the philosopher's life when a roof was about to collapse.[93] This association may been the result of confusion with a different man named Pythagoras, who was an athletics trainer.[74] Diogenes Laërtius records Milo's wife's name as Myia.[91] Iamblichus mentions Theano as the wife of Brontinus of Croton.[91] Diogenes Laërtius states that the same Theano was Pythagoras's pupil[91] and that Pythagoras's wife Theano was her daughter.[91] Diogenes Laërtius also records that works supposedly written by Theano were still extant during his own lifetime[91] and quotes several opinions attributed to her.[91] These writings are now known to be pseudepigraphical.[91]

Death

Pythagoras's emphasis on dedication and asceticism are credited with aiding in Croton's decisive victory over the neighboring colony of Sybaris in 510 BC.[94] After the victory, some prominent citizens of Croton proposed a democratic constitution, which the Pythagoreans rejected.[94] 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.[95] Followers of Cylon and Ninon attacked the Pythagoreans during one of their meetings, either in the house of Milo or in some other meeting-place.[96][97] Accounts of the attack are often contradictory and many probably confused it with later anti-Pythagorean rebellions.[95] The building was apparently set on fire,[96] and many of the assembled members perished;[96] only the younger and more active members managed to escape.[98]

Sources disagree regarding whether Pythagoras was present when the attack occurred and, if he was, whether or not he managed to escape.[32][97] In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes.[97] According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape,[99] leading a small group of followers to the nearby city of Locris, where they pleaded for sanctuary, but were denied.[99] They reached the city of Metapontum, where they took shelter in the temple of the Muses and died there of starvation after forty days without food.[32][96][99][100] Another tale recorded by Porphyry claims that, as Pythagoras's enemies were burning the house, his devoted students laid down on the ground to make a path for him to escape by walking over their bodies across the flames like a bridge.[99] Pythagoras managed to escape, but was so despondent at the deaths of his beloved students that he committed suicide.[99] A different legend reported by both Diogenes Laërtius and Iamblichus states that Pythagoras almost managed to escape, but that he came to a fava bean field and refused to run through it, since doing so would violate his teachings, so he stopped instead and was killed.[99][101] This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself.[99]

Teachings

Metempsychosis

 
In Raphael's fresco The School of Athens, Pythagoras is shown writing in a book as a young man presents him with a tablet showing a diagrammatic representation of a lyre above a drawing of the sacred tetractys.[102]

Although the exact details of Pythagoras's teachings are uncertain,[103][104] it is possible to reconstruct a general outline of his main ideas.[103][105] Aristotle writes at length about the teachings of the Pythagoreans,[16][106] but without mentioning Pythagoras directly.[16][106] One of Pythagoras's main doctrines appears to have been metempsychosis,[77][107][108][109][110][111] the belief that all souls are immortal and that, after death, a soul is transferred into a new body.[107][110] This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus.[107][112] Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur.[113]

Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations.[114] 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.[115][116][117] The first of these lives was as Aethalides the son of Hermes, who granted him the ability to remember all his past incarnations.[118] Next, he was incarnated as Euphorbus, a minor hero from the Trojan War briefly mentioned in the Iliad.[119] He then became the philosopher Hermotimus,[120] who recognized the shield of Euphorbus in the temple of Apollo.[120] His final incarnation was as Pyrrhus, a fisherman from Delos.[120] One of his past lives, as reported by Dicaearchus, was as a beautiful courtesan.[108][121]

Mysticism

Another belief attributed to Pythagoras was that of the "harmony of the spheres",[122][123] which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony.[122][123] According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together.[124] 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.[125]

Pythagoras was said to have practiced divination and prophecy.[126] 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.[127]

Numerology

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
 
Pythagoras is credited with having devised the tetractys,[128][129] an important sacred symbol in later Pythagoreanism.[130][131]

According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons, devoid of practical application.[132] They believed that all things were made of numbers.[133][134] The number one (the monad) represented the origin of all things[135] and the number two (the dyad) represented matter.[135] The number three was an "ideal number" because it had a beginning, middle, and end[136] 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.[136] The number four signified the four seasons and the four elements.[137] The number seven was also sacred because it was the number of planets and the number of strings on a lyre,[137] and because Apollo's birthday was celebrated on the seventh day of each month.[137] They believed that odd numbers were masculine,[138] that even numbers were feminine,[138] and that the number five represented marriage, because it was the sum of two and three.[139][140]

Ten was regarded as the "perfect number"[132] and the Pythagoreans honored it by never gathering in groups larger than ten.[141] Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the perfect number, ten.[128][129] The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance.[128][129][130] 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.[102][129][130][142] Andrew Gregory concludes that the tradition linking Pythagoras to the tetractys is probably genuine.[143]

Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton.[144] In his landmark study Lore and Science in Ancient Pythagoreanism, Walter Burkert argues that Pythagoras was a charismatic political and religious teacher,[145] but that the number philosophy attributed to him was really an innovation by Philolaus.[146] According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics.[145] Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, proofless arithmetic,[147] but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics.[148]

Pythagoreanism

Communal lifestyle

 
Pythagoreans Celebrate the Sunrise (1869) by Fyodor Bronnikov
Main article: Pythagoreanism

Both Plato and Isocrates state that, above all else, Pythagoras was known as the founder of a new way of life.[149][150][151] The organization Pythagoras founded at Croton was called a "school",[152][153][65] but, in many ways, resembled a monastery.[154] 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.[155] The members of the sect shared all their possessions in common[156] and were devoted to each other to the exclusion of outsiders.[157][158] Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans.[159][160] One Pythagorean maxim was "koinà tà phílōn" ("All things in common among friends").[156] 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.[161] Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time.[154]

Two groups existed within early Pythagoreanism: the mathematikoi ("learners") and the akousmatikoi ("listeners").[66][162] The akousmatikoi are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings;[162] whereas the mathematikoi are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific.[162] Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed the two approaches were compatible.[162] The study of mathematics and music may have been connected to the worship of Apollo.[163] The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body.[124] 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.[124] The Pythagoreans also placed particular emphasis on the importance of physical exercise;[154] therapeutic dancing, daily morning walks along scenic routes, and athletics were major components of the Pythagorean lifestyle.[154] Moments of contemplation at the beginning and end of each day were also advised.[164]

Prohibitions and regulations

 
French manuscript from 1512/1514, showing Pythagoras turning his face away from fava beans in revulsion

Pythagorean teachings were known as "symbols" (symbola)[87] and members took a vow of silence that they would not reveal these symbols to non-members.[87][150][165] Those who did not obey the laws of the community were expelled[166] and the remaining members would erect tombstones for them as though they had died.[166] A number of "oral sayings" (akoúsmata) attributed to Pythagoras have survived,[16][167] 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.[168] Many of these sayings emphasize the importance of ritual purity and avoiding defilement.[169][111] For instance, a saying which Leonid Zhmud concludes can probably be genuinely traced back to Pythagoras himself forbids his followers from wearing woolen garments.[170] Other extant oral sayings forbid Pythagoreans from breaking bread, poking fires with swords, or picking up crumbs[160] and teach that a person should always put the right sandal on before the left.[160] The exact meanings of these sayings, however, are frequently obscure.[171] Iamblichus preserves Aristotle's descriptions of the original, ritualistic intentions behind a few of these sayings,[172] but these apparently later fell out of fashion, because Porphyry provides markedly different ethical-philosophical interpretations of them:[173]

Pythagorean saying Original ritual purpose according to Aristotle/Iamblichus Porphyry's philosophical interpretation
"Do not take roads traveled by the public."[174][16] "Fear of being defiled by the impure"[174] "with this he forbade following the opinions of the masses, yet to follow the ones of the few and the educated."[174]
"and [do] not wear images of the gods on rings"[174] "Fear of defiling them by wearing them."[174] "One should not have the teaching and knowledge of the gods quickly at hand and visible [for everyone], nor communicate them to the masses."[174]
"and pour libations for the gods from a drinking cup's handle [the 'ear']"[174] "Efforts to keep the divine and the human strictly separate"[174] "thereby he enigmatically hints that the gods should be honored and praised with music; for it goes through the ears."[174]

New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five-year initiation period,[75] during which they were required to remain silent.[75] Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women[89] and female members of Pythagoras's school appear to have played an active role in its operations.[87][89] Iamblichus provides a list of 235 famous Pythagoreans,[88] seventeen of whom are women.[88] In later times, many prominent female philosophers contributed to the development of Neopythagoreanism.[175]

Pythagoreanism also entailed a number of dietary prohibitions.[111][160][176] It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beans[177][160] and the meat of non-sacrificial animals such as fish and poultry.[170][160] Both of these assumptions, however, have been contradicted.[178][179] Pythagorean dietary restrictions may have been motivated by belief in the doctrine of metempsychosis.[150][180][181][182] Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet.[e][150][181] 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."[183][184] Other authorities contradict this statement.[185] According to Aristoxenus,[186] Pythagoras allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and rams.[184][187] According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices[184] and established a diet for athletes dependent on meat.[184]

Legends

 
Pythagoras Emerging from the Underworld (1662) by Salvator Rosa

Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends.[30][188] Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure.[189][190] In a fragment, Aristotle writes that Pythagoras had a golden thigh,[189][191][192] which he publicly exhibited at the Olympic Games[189][193] and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo".[189][194] Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications.[195] He was supposedly once seen at both Metapontum and Croton at the same time.[196][30][193][191][192] When Pythagoras crossed the river Kosas (the modern-day Basento), "several witnesses" reported that they heard it greet him by name.[197][193][191] In Roman times, a legend claimed that Pythagoras was the son of Apollo.[198][192] According to Muslim tradition, Pythagoras was said to have been initiated by Hermes (Egyptian Thoth).[199]

Pythagoras was said to have dressed all in white.[189][200] He is also said to have borne a golden wreath atop his head[189] and to have worn trousers after the fashion of the Thracians.[189] Diogenes Laërtius presents Pythagoras as having exercised remarkable self-control;[201] he was always cheerful,[201] but "abstained wholly from laughter, and from all such indulgences as jests and idle stories".[91] Pythagoras was said to have had extraordinary success in dealing with animals.[30][202][193] A fragment from Aristotle records that, when a deadly snake bit Pythagoras, he bit it back and killed it.[195][193][191] Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans[30][202] 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.[30][202]

Riedweg suggests that Pythagoras may have personally encouraged these legends,[188] but Gregory states that there is no direct evidence of this.[162] Anti-Pythagorean legends were also circulated.[203] 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.[204] He stayed in this room for months, while his mother secretly recorded everything that happened during his absence.[204] After he returned from this room, Pythagoras recounted everything that had happened while he was gone,[204] convincing everyone that he had really been in the underworld[204] and leading them to trust him with their wives.[204]

Attributed discoveries

In mathematics

 
The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

Although Pythagoras is most famous today for his alleged mathematical discoveries,[131][205] classical historians dispute whether he himself ever actually made any significant contributions to the field.[147][145] Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem,[206] as well as discoveries in the fields of music,[207] astronomy,[208] and medicine.[209] Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem,[210][211] 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"[212]—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.[212][213] Cicero rejected this story as spurious[212] because of the much more widely held belief that Pythagoras forbade blood sacrifices.[212] Porphyry attempted to explain the story by asserting that the ox was actually made of dough.[212]

The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras,[214][212][215][216] but he may have been the first to introduce it to the Greeks.[217][215] Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof.[218] Burkert rejects this suggestion as implausible,[217] noting that Pythagoras was never credited with having proved any theorem in antiquity.[217] 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[131] and that he was the first to discover the Theory of Proportions.[131]

In music

 
Late medieval woodcut from Franchino Gafurio's Theoria musice (1492), showing Pythagoras with bells and other instruments in Pythagorean tuning[143]
See also: Pythagorean tuning and Pythagorean hammers

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.[219][220] Thinking that the sounds of the hammers were beautiful and harmonious, except for one,[221] he rushed into the blacksmith shop and began testing the hammers.[221] 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.[220][221]

In astronomy

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,[222] the first to divide the globe into five climatic zones,[222] and the first to identify the morning star and the evening star as the same celestial object (now known as Venus).[223] Of the two philosophers, Parmenides has a much stronger claim to having been the first[224] and the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem.[223] Empedocles, who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical.[225] By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals.[226] The identity of the morning star and evening star was known to the Babylonians over a thousand years earlier.[227]

Later influence in antiquity

On Greek philosophy

 
Medieval manuscript of Calcidius's Latin translation of Plato's Timaeus, which is one of the Platonic dialogues with the most overt Pythagorean influences[228]
See also: Timaeus (dialogue)

Sizeable Pythagorean communities existed in Magna Graecia, Phlius, and Thebes during the early fourth century BC.[229] Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia.[230] According to later tradition, Archytas was elected as strategos ("general") seven times, even though others were prohibited from serving more than a year.[230] Archytas was also a renowned mathematician and musician.[231] He was a close friend of Plato[232] and he is quoted in Plato's Republic.[233][234] Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans.[235][236] Cicero repeats this statement, remarking that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean").[237] According to Charles H. Kahn, Plato's middle dialogues, including Meno, Phaedo, and The Republic, have a strong "Pythagorean coloring",[238] and his last few dialogues (particularly Philebus and Timaeus)[228] are extremely Pythagorean in character.[228]

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.[239] Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy, science, and morality.[239] Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world"[239] and it is probable that both were influenced by Orphism.[239] The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans.[240] 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.[241] He concludes that "I do not know of any other man who has been as influential as he was in the school of thought."[242]

A revival of Pythagorean teachings occurred in the first century BC[243] when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed the rise of a "new" Pythagoreanism in Alexandria.[244] At around the same time, Neopythagoreanism became prominent.[245] The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings.[246] The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy[246] and probably understood the soul as a "kind of mathematical harmony."[246] The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory.[245] Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines.[247]

On art and architecture

 
Hadrian's Pantheon in Rome, depicted in this eighteenth-century painting by Giovanni Paolo Panini, was built according to Pythagorean teachings.[248]

Greek sculpture sought to represent the permanent reality behind superficial appearances.[249] 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.[250][251] When dimensions changed, architects sought to relay permanence through mathematics.[252][253] Maurice Bowra believes that these ideas influenced the theory of Pythagoras and his students, who believed that "all things are numbers".[253]

During the sixth century BC, the number philosophy of the Pythagoreans triggered a revolution in Greek sculpture.[254] Greek sculptors and architects attempted to find the mathematical relation (canon) behind aesthetic perfection.[251] Possibly drawing on the ideas of Pythagoras,[251] the sculptor Polykleitos wrote 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.[251][h] 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."[251]

The oldest known building designed according to Pythagorean teachings is the Porta Maggiore Basilica,[255] a subterranean basilica which was built during the reign of the Roman emperor Nero as a secret place of worship for Pythagoreans.[256] The basilica was built underground because of the Pythagorean emphasis on secrecy[257] and also because of the legend that Pythagoras had sequestered himself in a cave on Samos.[258] The basilica's apse is in the east and its atrium in the west out of respect for the rising sun.[259] It has a narrow entrance leading to a small pool where the initiates could purify themselves.[260] The building is also designed according to Pythagorean numerology,[261] with each table in the sanctuary providing seats for seven people.[141] Three aisles lead to a single altar, symbolizing the three parts of the soul approaching the unity of Apollo.[141] The apse depicts a scene of the poet 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,[262] symbolizing Pythagorean teachings about the immortality of the soul.[262] The interior of the sanctuary is almost entirely white because the color white was regarded by Pythagoreans as sacred.[263]

The emperor Hadrian's Pantheon in Rome was also built based on Pythagorean numerology.[248] 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.[264] The single oculus at the top of the dome symbolizes the monad and the sun-god Apollo.[265] 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.[266] The five coffered rings beneath the ribs represent the marriage of the sun and moon.[136]

In early Christianity

Many early Christians had a deep respect for Pythagoras.[267] Eusebius (c. 260 – c. 340 AD), bishop of Caesarea, praises Pythagoras in his Against Hierokles for his rule of silence, his frugality, his "extraordinary" morality, and his wise teachings.[268] In another work, Eusebius compares Pythagoras to Moses.[268] In one of his letter, the Church Father Jerome (c. 347 – 420 AD) praises Pythagoras for his wisdom[268] and, in another letter, he credits Pythagoras for his belief in the immortality of the soul, which he suggests Christians inherited from him.[269] Augustine of Hippo (354 – 430 AD) rejected Pythagoras's teaching of metempsychosis without explicitly naming him, but otherwise expressed admiration for him.[270] In On the Trinity, Augustine lauds the fact that Pythagoras was humble enough to call himself a philosophos or "lover of wisdom" rather than a "sage".[271] In another passage, Augustine defends Pythagoras's reputation, arguing that Pythagoras certainly never taught the doctrine of metempsychosis.[271]

Influence after antiquity

In the Middle Ages

 
Pythagoras appears in a relief sculpture on one of the archivolts over the right door of the west portal at Chartres Cathedral.[272]

During the Middle Ages, Pythagoras was revered as the founder of mathematics and music, two of the Seven Liberal Arts.[272] He appears in numerous medieval depictions, in illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres.[272] The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe,[272] which led William of Conches (c. 1080–1160) to declare that Plato was Pythagorean.[272] In the 1430s, the Camaldolese friar Ambrose Traversari translated Diogenes Laërtius's Lives and Opinions of Eminent Philosophers from Greek into Latin[272] and, in the 1460s, the philosopher Marsilio Ficino translated Porphyry and Iamblichus's Lives of Pythagoras into Latin as well,[272] thereby allowing them to be read and studied by western scholars.[272] In 1494, the Greek Neopythagorean scholar Constantine Lascaris published The Golden Verses of Pythagoras, translated into Latin, with a printed edition of his Grammatica,[273] thereby bringing them to a widespread audience.[273] In 1499, he published the first Renaissance biography of Pythagoras in his work Vitae illustrium philosophorum siculorum et calabrorum, issued in Messina.[273]

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,[272][274] 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.[274] Johannes Kepler considered himself to be a Pythagorean.[272][275][276] He believed in the Pythagorean doctrine of musica universalis[277] and it was his search for the mathematical equations behind this doctrine that led to his discovery of the laws of planetary motion.[277] Kepler titled his book on the subject Harmonices Mundi (Harmonics of the World), after the Pythagorean teaching that had inspired him.[272][278] 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."[279] He also called Pythagoras the "grandfather" of all Copernicans.[280]

Isaac Newton firmly believed in the Pythagorean teaching of the mathematical harmony and order of the universe.[281] Though Newton was notorious for rarely giving others credit for their discoveries,[282] he attributed the discovery of the Law of Universal Gravitation to Pythagoras.[282] 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."[283] 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".[284] By this measure, Whitehead declared that Einstein and other modern scientists like him are "following the pure Pythagorean tradition."[283][285]

On vegetarianism

 
Pythagoras Advocating Vegetarianism (1618–1630) by Peter Paul Rubens was inspired by Pythagoras's speech in Ovid's Metamorphoses.[286] The painting portrays the Pythagoreans with corpulent bodies, indicating a belief that vegetarianism was healthful and nutritious.[286]

A fictionalized portrayal of Pythagoras appears in Book XV of Ovid's Metamorphoses,[287] in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet.[288] 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.[288] John Donne's Progress of the Soul discusses the implications of the doctrines expounded in the speech,[289] and Michel de Montaigne quoted the speech no less than three times in his treatise "Of Cruelty" to voice his moral objections against the mistreatment of animals.[289] William Shakespeare references the speech in his play The Merchant of Venice.[290] John Dryden included a translation of the scene with Pythagoras in his 1700 work Fables, Ancient and Modern,[289] and John Gay's 1726 fable "Pythagoras and the Countryman" reiterates its major themes, linking carnivorism with tyranny.[289] Lord Chesterfield records that his conversion to vegetarianism had been motivated by reading Pythagoras's speech in Ovid's Metamorphoses.[289] Until the word vegetarianism was coined in the 1840s, vegetarians were referred to in English as "Pythagoreans".[289] Percy Bysshe Shelley wrote an ode entitled "To the Pythagorean Diet",[291] and Leo Tolstoy adopted the Pythagorean diet himself.[291]

On Western esotericism

Early modern European esotericism drew heavily on the teachings of Pythagoras.[272] The German humanist scholar Johannes Reuchlin (1455–1522) synthesized Pythagoreanism with Christian theology and Jewish Kabbalah,[292] arguing that Kabbalah and Pythagoreanism were both inspired by Mosaic tradition[293] and that Pythagoras was therefore a kabbalist.[293] In his dialogue De verbo mirifico (1494), Reuchlin compared the Pythagorean tetractys to the ineffable divine name YHWH,[292] ascribing each of the four letters of the tetragrammaton a symbolic meaning according to Pythagorean mystical teachings.[293]

Heinrich Cornelius Agrippa's popular and influential three-volume treatise De Occulta Philosophia cites Pythagoras as a "religious magi"[294] and indicates that Pythagoras's mystical numerology operates on a supercelestial level.[294] The freemasons deliberately modeled their society on the community founded by Pythagoras at Croton.[295] Rosicrucianism used Pythagorean symbolism,[272] as did Robert Fludd (1574–1637),[272] who believed his own musical writings to have been inspired by Pythagoras.[272] John Dee was heavily influenced by Pythagorean ideology,[296][294] particularly the teaching that all things are made of numbers.[296][294] Adam Weishaupt, the founder of the Illuminati, was a strong admirer of Pythagoras[297] and, in his book Pythagoras (1787), he advocated that society should be reformed to be more like Pythagoras's commune at Croton.[298] Wolfgang Amadeus Mozart incorporated Masonic and Pythagorean symbolism into his opera The Magic Flute.[299] 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".[300]

On literature

 
Dante Alighieri's description of Heaven in his Paradiso incorporates Pythagorean numerology.[301]

Dante Alighieri was fascinated by Pythagorean numerology[301] and based his descriptions of Hell, Purgatory, and Heaven on Pythagorean numbers.[301] Dante wrote that Pythagoras saw Unity as Good and Plurality as Evil[302] and, in Paradiso XV, 56–57, he declares: "five and six, if understood, ray forth from unity."[303] 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.[304] Dante describes the ninth and tenth bolgias in the Eighth Circle of Hell as being twenty-two miles and eleven miles respectively,[304] which correspond to the fraction 22/7, which was the Pythagorean approximation of pi.[304]

The Transcendentalists read the ancient Lives of Pythagoras as guides on how to live a model life.[305] Henry David Thoreau was impacted by Thomas Taylor's translations of Iamblichus's Life of Pythagoras and Stobaeus's Pythagoric Sayings[305] and his views on nature may have been influenced by the Pythagorean idea of images corresponding to archetypes.[305] The Pythagorean teaching of musica universalis is a recurring theme throughout Thoreau's magnum opus, Walden.[305]

See also

References

Footnotes

  1. ^ US: /pɪˈθæɡərəs/,[2] UK: /paɪ-/;[3]
  2. ^ "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."[4]
  3. ^ 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.
  4. ^ Some writers call him a Tyrrhenian from Lemnos, a Phliasian, or a native Samian, 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; Iamblichus, ii. 4. Due to this obscurity, some modern scholars "accept the simple statement that Pythagoras and his father were pure-blooded Greeks": Felix Jacoby, Jan Bollansée, Guido Schepens (1998) Die Fragmente Der Griechischen Historiker, Continued, BRILL. p. 296, n. 73
  5. ^ as Empedocles did afterwards, Aristotle, Rhet. i. 14. § 2; Sextus Empiricus, ix. 127. This was also one of the Orphic precepts, Aristoph. Ran. 1032
  6. ^ 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).
  7. ^ "For Thales, the origin was water, and for Anaximander the infinite (apeiron), which must be considered a material form"[249]
  8. ^ "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.

Citations

  1. ^ a b c Joost-Gaugier 2006, p. 143.
  2. ^ American: Pythagoras, Collins Dictionary, n.d., retrieved 25 September 2014
  3. ^ British: Pythagoras, Collins Dictionary, n.d., retrieved 25 September 2014
  4. ^ William Keith Chambers Guthrie, (1978), A history of Greek philosophy, Volume 1: The earlier Presocratics and the Pythagoreans, p. 173. Cambridge University Press
  5. ^ a b c d e Joost-Gaugier 2006, p. 11.
  6. ^ Celenza 2010, p. 796.
  7. ^ a b Ferguson 2008, p. 4.
  8. ^ Ferguson 2008, pp. 3–5.
  9. ^ Gregory 2015, pp. 21–23.
  10. ^ a b c Copleston 2003, p. 29.
  11. ^ a b c Kahn 2001, p. 2.
  12. ^ a b Burkert 1985, p. 299.
  13. ^ a b c Joost-Gaugier 2006, p. 12.
  14. ^ Riedweg 2005, p. 62.
  15. ^ Diogenes Laërtius, viii. 36
  16. ^ a b c d e Copleston 2003, p. 31.
  17. ^ a b Joost-Gaugier 2006, pp. 12–13.
  18. ^ a b c Joost-Gaugier 2006, p. 13.
  19. ^ Joost-Gaugier 2006, pp. 14–15.
  20. ^ a b c d e f Joost-Gaugier 2006, p. 16.
  21. ^ 4. 95.
  22. ^ Marincola (2001), p. 59
  23. ^ Roberts (2011), p. 2
  24. ^ Sparks (1998), p. 58
  25. ^ Asheri, Lloyd & Corcella (2007)
  26. ^ Cameron (2004), p. 156
  27. ^ Joost-Gaugier 2006, p. 88.
  28. ^ He alludes to it himself, Met. i. 5. p. 986. 12, ed. Bekker.
  29. ^ a b c d Burkert 1972, p. 109.
  30. ^ a b c d e f g h i j k l Kahn 2001, p. 5.
  31. ^ a b c d e Zhmud 2012, p. 9.
  32. ^ a b c Burkert 1972, p. 106.
  33. ^ Herodotus, Histories, 4.95 (in Greek original text and English transtations: [1] [2])
  34. ^ a b c d e f Kahn 2001, p. 6.
  35. ^ a b Ferguson 2008, p. 12.
  36. ^ Kenny 2004, p. 9.
  37. ^ Ferguson 2008, p. 11.
  38. ^ Porphyry, Vita Pythagorae, Leipzig, 1886; Porphyry, Life of Pythogoras in M. Hadas and M. Smith, Heroes and Gods, London, 1965.
  39. ^ 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 978-90-04-23011-8
  40. ^ Joost-Gaugier 2006, p. 21.
  41. ^ Ferguson 2008, pp. 11–12.
  42. ^ Ferguson 2008, p. 15.
  43. ^ Taub 2017, p. 122.
  44. ^ Apollonius of Tyana ap. Porphyry, Vit. Pyth. 2.
  45. ^ a b c Riedweg 2005, p. 59.
  46. ^ Porphyry, Vit. Pyth. 9
  47. ^ Riedweg 2005, pp. 45–47.
  48. ^ a b Riedweg 2005, pp. 44–45.
  49. ^ a b c Riedweg 2005, p. 7.
  50. ^ a b Riedweg 2005, pp. 7–8.
  51. ^ Gregory 2015, pp. 22–23.
  52. ^ Porphyry, Vit. Pyth. 6.
  53. ^ Plutarch, On Isis And Osiris, ch. 10.
  54. ^ Press 2003, p. 83.
  55. ^ cf. Antiphon. ap. Porphyry, Vit. Pyth. 7; Isocrates, Busiris, 28–9; Cicero, de Finibus, v. 29; Strabo, 14.1.16.
  56. ^ a b Diogenes Laërtius, viii. 1, 3.
  57. ^ a b c d e f g h i j k l Riedweg 2005, p. 8.
  58. ^ Dillon 2005, p. 163.
  59. ^ Porphyry, Vit. Pyth. 2, Diogenes Laërtius, viii. 2.
  60. ^ a b Iamblichus, Vit. Pyth. 9.
  61. ^ Porphyry, Vit. Pyth. 2.
  62. ^ a b Riedweg 2005, pp. 8–9.
  63. ^ a b c d e f g h Riedweg 2005, p. 9.
  64. ^ Aristoxenus and others in Diogenes Laërtius, i. 118, 119; Cicero, de Div. i. 49
  65. ^ a b c Boyer, Carl B. (1968), A History of Mathematics
  66. ^ a b Zhmud 2012, pp. 2, 16.
  67. ^ Diogenes Laërtius, Lives of Eminent Philosophers, viii. 1, 8.
  68. ^ Waithe, M. E. (April 30, 1987), Ancient Women Philosophers: 600 B.C.-500 A. D., Springer Science & Business Media, ISBN 9789024733682 – via Google Books
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  71. ^ 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. 47. "The person who is referred to as Themistoclea in Laërtius and Theoclea in Suidas, Porphyry calls Aristoclea."
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  73. ^ Ariston. ap. Diogenes Laërtius, viii. 8, 21; Porphyry, Vit. Pyth. 41.
  74. ^ a b c d e f g Riedweg 2005, p. 10.
  75. ^ a b c d e Cornelli & McKirahan 2013, p. 64.
  76. ^ a b c Riedweg 2005, p. 11.
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  79. ^ Iamblichus, Vit. Pyth. 28; Porphyry, Vit. Pyth. 9
  80. ^ Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism. Assen 1966, pp. 21ff. Cfr. Cicero, De re publica 2, 28–30.
  81. ^ Riedweg 2005, pp. 11–12.
  82. ^ Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism, Assen 1966, S. 148–150.
  83. ^ Riedweg 2005, pp. 12–13.
  84. ^ Riedweg 2005, pp. 12–18.
  85. ^ Porphyry, Vit. Pyth. 18; Iamblichus, Vit. Pyth. 37, etc.
  86. ^ Riedweg 2005, pp. 13–18.
  87. ^ a b c d Kahn 2001, p. 8.
  88. ^ a b c Pomeroy 2013, p. 1.
  89. ^ a b c Pomeroy 2013, p. xvi.
  90. ^ Ferguson 2008, p. 58.
  91. ^ a b c d e f g h i j k l m n o p q Ferguson 2008, p. 59.
  92. ^ Suda Encyclopedia, th.84
  93. ^ a b Riedweg 2005, pp. 5–6, 59, 73.
  94. ^ a b Kahn 2001, pp. 6–7.
  95. ^ a b Riedweg 2005, p. 19.
  96. ^ a b c d Kahn 2001, p. 7.
  97. ^ a b c Riedweg 2005, pp. 19–20.
  98. ^ Iamblichus, Vit. Pyth. 255–259; Porphyry, Vit. Pyth. 54–57; Diogenes Laërtius, viii. 39; comp. Plutarch, de Gen. Socr. p. 583
  99. ^ a b c d e f g Riedweg 2005, p. 20.
  100. ^ Grant 1989, p. 278.
  101. ^ Simoons 1998, pp. 225–228.
  102. ^ a b Bruhn 2005, p. 66.
  103. ^ a b Burkert 1972, pp. 106–109.
  104. ^ Kahn 2001, pp. 5–6.
  105. ^ Kahn 2001, pp. 9–11.
  106. ^ a b Burkert 1972, pp. 29–30.
  107. ^ a b c Kahn 2001, p. 11.
  108. ^ a b Zhmud 2012, p. 232.
  109. ^ Burkert 1985, pp. 300–301.
  110. ^ a b Gregory 2015, pp. 24–25.
  111. ^ a b c Copleston 2003, pp. 30–31.
  112. ^ Diogenes Laërtius, viii. 36, comp. Aristotle, de Anima, i. 3; Herodotus, ii. 123.
  113. ^ Gregory 2015, p. 25.
  114. ^ Kahn 2001, p. 12.
  115. ^ Diogenes Laërtius, viii. 3–4
  116. ^ Cornelli & McKirahan 2013, pp. 164–167.
  117. ^ Porphyry, Vit. Pyth. 26; Pausanias, ii. 17; Diogenes Laërtius, viii. 5; Horace, Od. i. 28,1. 10
  118. ^ Cornelli & McKirahan 2013, pp. 164–165.
  119. ^ Cornelli & McKirahan 2013, pp. 165–166.
  120. ^ a b c Cornelli & McKirahan 2013, p. 167.
  121. ^ Aulus Gellius, iv. 11
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  149. ^ Plato, Republic, 600a, Isocrates, Busiris, 28
  150. ^ a b c d Cornelli & McKirahan 2013, p. 168.
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  155. ^ comp. Cicero, de Leg. i. 12, de Off. i. 7; Diogenes Laërtius, viii. 10
  156. ^ a b Cornelli & McKirahan 2013, p. 65.
  157. ^ 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.
  158. ^ Cornelli & McKirahan 2013, pp. 68–69.
  159. ^ Iamblichus, Vit. Pyth. 98; Strabo, vi.
  160. ^ a b c d e f Kenny 2004, p. 10.
  161. ^ 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.
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  180. ^ Plutarch, de Esu Carn. pp. 993, 996, 997
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  183. ^ Eudoxus, frg. 325
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  188. ^ a b Riedweg 2005, p. 1.
  189. ^ a b c d e f g Riedweg 2005, p. 2.
  190. ^ Gregory 2015, pp. 30–31.
  191. ^ a b c d Gregory 2015, p. 30.
  192. ^ a b c Kenny 2004, p. 11.
  193. ^ a b c d e Ferguson 2008, p. 60.
  194. ^ Porphyry, Vit. Pyth. 20; Iamblichus, Vit. Pyth. 31, 140; Aelian, Varia Historia, ii. 26; Diogenes Laërtius, viii. 36.
  195. ^ a b McKeown 2013, p. 155.
  196. ^ Comp. Herodian, iv. 94, etc.
  197. ^ Burkert 1972, p. 144.
  198. ^ Ferguson 2008, p. 10.
  199. ^ See Antoine Faivre, in The Eternal Hermes (1995)
  200. ^ Joost-Gaugier 2006, p. 47.
  201. ^ a b Ferguson 2008, pp. 58–59.
  202. ^ a b c Cornelli & McKirahan 2013, p. 160.
  203. ^ Ferguson 2008, pp. 60–61.
  204. ^ a b c d e Ferguson 2008, p. 61.
  205. ^ Gregory 2015, pp. 21–22.
  206. ^ Diogenes Laërtius, viii. 12; Plutarch, Non posse suav. vivi sec. Ep. p. 1094
  207. ^ Porphyry, in Ptol. Harm. p. 213; Diogenes Laërtius, viii. 12.
  208. ^ Diogenes Laërtius, viii. 14; Pliny, Hist. Nat. ii. 8.
  209. ^ Diogenes Laërtius, viii. 12, 14, 32.
  210. ^ Kahn 2001, pp. 32–33.
  211. ^ Riedweg 2005, pp. 26–27.
  212. ^ a b c d e f Riedweg 2005, p. 27.
  213. ^ Burkert 1972, p. 428.
  214. ^ Burkert 1972, pp. 429, 462.
  215. ^ a b Kahn 2001, p. 32.
  216. ^ Ferguson 2008, pp. 6–7.
  217. ^ a b c Burkert 1972, p. 429.
  218. ^ Kahn 2001, p. 33.
  219. ^ Riedweg 2005, pp. 27–28.
  220. ^ a b Gregory 2015, p. 27.
  221. ^ a b c Riedweg 2005, p. 28.
  222. ^ a b Burkert 1972, p. 306.
  223. ^ a b Burkert 1972, pp. 307–308.
  224. ^ Burkert 1972, pp. 306–308.
  225. ^ Kahn 2001, p. 53.
  226. ^ Dicks 1970, p. 68.
  227. ^ Langdon & Fotheringham 1928.
  228. ^ a b c Kahn 2001, pp. 55–62.
  229. ^ Kahn 2001, pp. 48–49.
  230. ^ a b Kahn 2001, p. 39.
  231. ^ Kahn 2001, pp. 39–43.
  232. ^ Kahn 2001, pp. 39–40.
  233. ^ Kahn 2001, pp. 40, 44–45.
  234. ^ Plato, Republic VII, 530d
  235. ^ Metaphysics, 1.6.1 (987a)
  236. ^ Kahn 2001, p. 1.
  237. ^ Tusc. Disput. 1.17.39.
  238. ^ Kahn 2001, p. 55.
  239. ^ a b c d Hare 1999, pp. 117–119.
  240. ^ Copleston 2003, p. 37.
  241. ^ Russell 2008, pp. 33–37.
  242. ^ Russell 2008, p. 37.
  243. ^ Riedweg 2005, pp. 123–124.
  244. ^ Riedweg 2005, p. 124.
  245. ^ a b Riedweg 2005, pp. 125–126.
  246. ^ a b c Riedweg 2005, p. 125.
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  248. ^ a b Joost-Gaugier 2006, pp. 166–181.
  249. ^ a b Homann-Wedeking 1968, p. 63.
  250. ^ Homann-Wedeking 1968, p. 62.
  251. ^ a b c d e Carpenter 1921, pp. 107, 122, 128.
  252. ^ Homann-Wedeking 1968, pp. 62–63.
  253. ^ a b Bowra 1994, p. 166.
  254. ^ Homann-Wedeking 1968, pp. 62–65.
  255. ^ Joost-Gaugier 2006, p. 154.
  256. ^ Joost-Gaugier 2006, pp. 154–156.
  257. ^ Joost-Gaugier 2006, pp. 157–158.
  258. ^ Joost-Gaugier 2006, p. 158.
  259. ^ Joost-Gaugier 2006, pp. 158–159.
  260. ^ Joost-Gaugier 2006, p. 159.
  261. ^ Joost-Gaugier 2006, pp. 159–161.
  262. ^ a b Joost-Gaugier 2006, p. 162.
  263. ^ Joost-Gaugier 2006, pp. 162–164.
  264. ^ Joost-Gaugier 2006, pp. 167–168.
  265. ^ Joost-Gaugier 2006, p. 168.
  266. ^ Joost-Gaugier 2006, pp. 169–170.
  267. ^ Joost-Gaugier 2006, pp. 57–65.
  268. ^ a b c Joost-Gaugier 2006, p. 57.
  269. ^ Joost-Gaugier 2006, pp. 57–58.
  270. ^ Joost-Gaugier 2006, pp. 58–59.
  271. ^ a b Joost-Gaugier 2006, p. 59.
  272. ^ a b c d e f g h i j k l m n o Celenza 2010, p. 798.
  273. ^ a b c Russo 2004, pp. 5–87, especially 51–53.
  274. ^ a b Kahn 2001, p. 160.
  275. ^ Kahn 2001, pp. 161–171.
  276. ^ Ferguson 2008, p. 265.
  277. ^ a b Ferguson 2008, pp. 264–274.
  278. ^ Kahn 2001, p. 162.
  279. ^ Ferguson 2008, p. 274.
  280. ^ Jamie James, The Music of the Spheres: Music, Science, and the Natural Order of the Universe, p 142.
  281. ^ Ferguson 2008, p. 279.
  282. ^ a b Ferguson 2008, pp. 279–280.
  283. ^ a b Kahn 2001, p. 172.
  284. ^ Whitehead 1953, pp. 36–37.
  285. ^ Whitehead 1953, p. 36.
  286. ^ a b Borlik 2011, p. 192.
  287. ^ Borlik 2011, p. 189.
  288. ^ a b Borlik 2011, pp. 189–190.
  289. ^ a b c d e f Borlik 2011, p. 190.
  290. ^ Ferguson 2008, p. 282.
  291. ^ a b Ferguson 2008, p. 294.
  292. ^ a b Riedweg 2005, pp. 127–128.
  293. ^ a b c Riedweg 2005, p. 128.
  294. ^ a b c d French 2002, p. 30.
  295. ^ Riedweg 2005, p. 133.
  296. ^ a b Sherman 1995, p. 15.
  297. ^ Ferguson 2008, pp. 284–288.
  298. ^ Ferguson 2008, pp. 287–288.
  299. ^ Ferguson 2008, pp. 286–287.
  300. ^ Ferguson 2008, p. 288.
  301. ^ a b c Haag 2013, p. 89.
  302. ^ Haag 2013, p. 90.
  303. ^ Haag 2013, pp. 90–91.
  304. ^ a b c Haag 2013, p. 91.
  305. ^ a b c d Bregman 2002, p. 186.

Works cited

Only a few relevant source texts deal with Pythagoras and the Pythagoreans; most are available in different translations. Later texts usually build solely upon information in these works.

Classical sources

Modern secondary sources

  • Asheri, David; Lloyd, Alan; Corcella, Aldo (2007), A Commentary on Herodotus, Books 1–4, Oxford University Press, ISBN 978-0-19-814956-9
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  • Burkert, Walter (1 June 1972), Lore and Science in Ancient Pythagoreanism, Cambridge, Massachusetts: Harvard University Press, ISBN 978-0-674-53918-1
  • Burkert, Walter (1985), Greek Religion, Cambridge, Massachusetts: Harvard University Press, ISBN 978-0-674-36281-9
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  • 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) [1946], "The Pythagorean Society", A History of Philosophy, vol. 1 Greece and Rome, London, England and New York City, New York: Continuum, ISBN 978-0-8264-6947-2
  • 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) [1972], John Dee: The World of the Elizabethan Magus, New York City, New York and London, England: Routledge, ISBN 978-0-7448-0079-1
  • Celenza, Christopher (2010), "Pythagoras and Pythagoreanism", in Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.), The Classical Tradition, Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press, pp. 796–799, 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 978-0-684-19126-3
  • Gregory, Andrew (2015), "The Pythagoreans: Number and Numerology", in Lawrence, Snezana; McCartney, Mark (eds.), Mathematicians and their Gods: Interactions between Mathematics and Religious Beliefs, Oxford, England: Oxford University Press, pp. 21–50, ISBN 978-0-19-870305-1
  • Guthrie, W. K. (1979), A History of Greek Philosophy: Earlier Presocratics and the Pythagoreans, Cambridge, England: Cambridge University Press, ISBN 978-0-521-29420-1
  • 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) [1982], "Plato", in Taylor, C. C. W.; Hare, R. M.; Barnes, Jonathan (eds.), 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
  • Kenny, Anthony (2004), Ancient Philosophy, A New History of Western Philosophy, vol. 1, Oxford, England: Oxford University Press, ISBN 978-0-19-875273-8
  • Kingsley, Peter (1995), Ancient Philosophy, Mystery, and Magic: Empedocles and the Pythagorean Tradition, Oxford, England: Oxford University Press
  • Langdon, Stephen; Fotheringham, John (1928), The Venus Tablets of Ammizaduga: A solution of Babylonian chronology by means of the Venus observations of the First Dynasty, Oxford University Press, ISBN 978-9-33-362298-1
  • Marincola, John (2001), Greek Historians, Oxford University Press, ISBN 978-0-19-922501-9
  • 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 978-0-19-823913-0
  • Press, Gerald A. (2003) [1982], Development of the Idea of History in Antiquity, Montreal, Canada and Kingston, New York: McGill-Queen's University Press, ISBN 978-0-7735-1002-9
  • 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) [2002], Pythagoras: His Life, Teachings, and Influence, Ithaca, New York: Cornell University Press, ISBN 978-0-8014-7452-1
  • Roberts, Jennifer T. (2011), Herodotus: a Very Short Introduction, OXford University Press, ISBN 978-0-19-957599-2
  • Russell, Bertrand (2008) [1945], 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, 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 978-1-55849-070-3
  • Simoons, Frederick J. (1998), Plants of Life, Plants of Death, Madison, Wisconsin: University of Wisconsin Press, ISBN 978-0-299-15904-7
  • Sparks, Kenton L. (1998), Ethnicity and Identity in Ancient Israel: Prolegomena to the Study of Ethnic Sentiments and their Expression in the Hebrew Bible, Winona Lake, IN: Eisenbrauns, ISBN 978-1-57506-033-0
  • Taub, Liba (2017), Science Writing in Greco-Roman Antiquity, Cambridge University Press, ISBN 978-0-521-11370-0
  • Vasunia, Phiroze (2007), "The Philosopher's Zarathushtra", in Tuplin, Christopher (ed.), Persian Responses: Political and Cultural Interaction with(in) the Achaemenid Empire, Swansea: The Classical Press of Wales, ISBN 978-1-910589-46-5
  • Whitehead, Afred North (1953) [1926], 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

External links

 
Wikisource has the text of the 1911 Encyclopædia Britannica article "Pythagoras".

January 16, 2023
pythagoras, samos, redirects, here, samian, statuary, sculptor, other, uses, disambiguation, samos, ancient, greek, Πυθαγόρας, Σάμιος, romanized, pythagóras, sámios, samian, simply, Πυθαγόρας, Πυθαγόρης, ionian, greek, ancient, ionian, greek, philosopher, epon. Pythagoras of Samos redirects here For the Samian statuary see Pythagoras sculptor For other uses see Pythagoras disambiguation Pythagoras of Samos a Ancient Greek Py8agoras ὁ Samios romanized Pythagoras ho Samios lit Pythagoras the Samian or simply Py8agoras Py8agorhs in Ionian Greek c 570 c 495 BC b was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato Aristotle and through them the West in general Knowledge of his life is clouded by legend but he appears to have been the son of Mnesarchus a gem engraver on the island of Samos Modern scholars disagree regarding Pythagoras s education and influences but they do agree that around 530 BC he travelled to Croton in southern Italy where he founded a school in which initiates were sworn to secrecy and lived a communal ascetic lifestyle This lifestyle entailed a number of dietary prohibitions traditionally said to have included vegetarianism although modern scholars doubt that he ever advocated complete vegetarianism PythagorasBust of Pythagoras of Samos in theCapitoline Museums Rome 1 Bornc 570 BC SamosDiedc 495 BC aged around 75 either Croton or MetapontumEraPre Socratic philosophyRegionWestern philosophySchoolPythagoreanismMain interestsEthicsMathematicsMetaphysicsMusic theoryMysticismPoliticsReligionNotable ideasCommunalismMetempsychosisMusica universalisAttributed ideas Five climatic zonesFive regular solidsProportionsPythagorean theoremPythagorean tuningSphericity of the EarthVegetarianismInfluences ThalesAnaximanderPherecydesThemistocleaOrphismInfluenced PythagoreanismXenophanesEmpedoclesPlatoAristotleThe 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 developed the numerological and musical teachings attributed to him or if those teachings were developed by his later followers particularly Philolaus of Croton 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 and died there 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 on 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 modern vegetarian movement Contents 1 Biographical sources 2 Life 2 1 Early life 2 2 Reputed travels 2 3 Alleged Greek teachers 2 4 In Croton 2 5 Family and friends 2 6 Death 3 Teachings 3 1 Metempsychosis 3 2 Mysticism 3 3 Numerology 4 Pythagoreanism 4 1 Communal lifestyle 4 2 Prohibitions and regulations 5 Legends 6 Attributed discoveries 6 1 In mathematics 6 2 In music 6 3 In astronomy 7 Later influence in antiquity 7 1 On Greek philosophy 7 2 On art and architecture 7 3 In early Christianity 8 Influence after antiquity 8 1 In the Middle Ages 8 2 On modern science 8 3 On vegetarianism 8 4 On Western esotericism 8 5 On literature 9 See also 10 References 10 1 Footnotes 10 2 Citations 10 3 Works cited 11 External linksBiographical sources Fictionalized portrait of Pythagoras from a 17th century engraving No authentic writings of Pythagoras have survived 5 6 7 and almost nothing is known for certain about his life 8 9 10 The earliest sources on Pythagoras s life are brief ambiguous and often satirical 7 11 12 The earliest source on Pythagoras s teachings is a satirical poem probably written after his death by Xenophanes of Colophon who had been one of his contemporaries 13 14 In the poem Xenophanes describes Pythagoras interceding on behalf of a dog that is being beaten professing to recognize in its cries the voice of a departed friend 12 13 15 16 Alcmaeon of Croton a doctor who lived in Croton at around the same time Pythagoras lived there 13 incorporates many Pythagorean teachings into his writings 17 and alludes to having possibly known Pythagoras personally 17 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 18 mocked Pythagoras as a clever charlatan 11 18 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 11 18 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 19 The first concise description of Pythagoras comes from the historian Herodotus of Halicarnassus c 484 c 420 BC 20 who describes him as not the most insignificant of Greek sages 21 and states that Pythagoras taught his followers how to attain immortality 20 The accuracy of the works of Herodotus is controversial 22 23 24 25 26 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 27 The Athenian rhetorician Isocrates 436 338 BC was the first to describe Pythagoras as having visited Egypt 20 Aristotle wrote a treatise On the Pythagoreans which is no longer extant 28 Some of it may be preserved in the Protrepticus Aristotle s disciples Dicaearchus Aristoxenus and Heraclides Ponticus also wrote on the same subject 29 Most of the major sources on Pythagoras s life are from the Roman period 30 by which point according to the German classicist Walter Burkert the history of Pythagoreanism was already the laborious reconstruction of something lost and gone 29 Three ancient biographies of Pythagoras have survived from late antiquity 10 30 all of which are filled primarily with myths and legends 10 30 31 The earliest and most respectable of these is the one from Diogenes Laertius s Lives and Opinions of Eminent Philosophers 30 31 The two later biographies were written by the Neoplatonist philosophers Porphyry and Iamblichus 30 31 and were partially intended as polemics against the rise of Christianity 31 The later sources are much lengthier than the earlier ones 30 and even more fantastic in their descriptions of Pythagoras s achievements 30 31 Porphyry and Iamblichus used material from the lost writings of Aristotle s disciples 29 and material taken from these sources is generally considered to be the most reliable 29 LifeEarly life 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 32 Herodotus 33 Isocrates and other early writers agree that Pythagoras was the son of Mnesarchus 20 34 and that he was born on the Greek island of Samos in the eastern Aegean 5 34 35 36 According to these biographers Pythagoras father wasn t born on the island although he got naturalized there 35 but according to Iamblichus he was a native of the island 37 He is said to have been a gem engraver or a wealthy merchant 38 39 40 but his ancestry is disputed and unclear 41 d His mother was a native of Samos descending from a geomoroi family 42 Apollonius of Tyana gives her name as Pythais 43 44 Iamblichus tells the story that the Pythia prophesied to her while she was pregnant with him that she would give birth to a man supremely beautiful wise and beneficial to humankind 45 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 46 Pythagoras s name led him to be associated with Pythian Apollo Puthia Aristippus of Cyrene in the 4th century BC explained his name by saying He spoke ἀgoreyw agoreuō the truth no less than did the Pythian py8ikos puthikos 45 During Pythagoras s formative years Samos was a thriving cultural hub known for its feats of advanced architectural engineering including the building of the Tunnel of Eupalinos and for its riotous festival culture 47 It was a major center of trade in the Aegean where traders brought goods from the Near East 5 According to Christiane L Joost Gaugier these traders almost certainly brought with them Near Eastern ideas and traditions 5 Pythagoras s early life also coincided with the flowering of early Ionian natural philosophy 34 48 He was a contemporary of the philosophers Anaximander Anaximenes and the historian Hecataeus all of whom lived in Miletus across the sea from Samos 48 Reputed travels Pythagoras is traditionally thought to have received most of his education in the Near East 49 Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures 49 Like many other important Greek thinkers Pythagoras was said to have studied in Egypt 20 50 51 By the time of Isocrates in the fourth century BC Pythagoras s reputed studies in Egypt were already taken as fact 20 45 The writer Antiphon who may have lived during the Hellenistic Era claimed in his lost work On Men of Outstanding Merit used as a source by Porphyry that Pythagoras learned to speak Egyptian from the Pharaoh Amasis II himself that he studied with the Egyptian priests at Diospolis Thebes and that he was the only foreigner ever to be granted the privilege of taking part in their worship 49 52 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 53 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 54 Some ancient writers claimed that Pythagoras learned geometry and the doctrine of metempsychosis from the Egyptians 50 55 Other ancient writers however claimed that Pythagoras had learned these teachings from the Magi in Persia or even from Zoroaster himself 56 57 Diogenes Laertius asserts that Pythagoras later visited Crete where he went to the Cave of Ida with Epimenides 56 The Phoenicians are reputed to have taught Pythagoras arithmetic and the Chaldeans to have taught him astronomy 57 By the third century BC Pythagoras was already reported to have studied under the Jews as well 57 Contradicting all these reports the novelist Antonius Diogenes writing in the second century BC reports that Pythagoras discovered all his doctrines himself by interpreting dreams 57 The third century AD Sophist Philostratus claims that in addition to the Egyptians Pythagoras also studied under sages or gymnosophists in India 57 Iamblichus expands this list even further by claiming that Pythagoras also studied with the Celts and Iberians 57 Alleged Greek teachers Bust of Pythagoras in the Vatican Museums Vatican City showing him as a tired looking older man 1 Bronze bust of a philosopher wearing a tainia from Villa of the Papyri Herculaneum possibly a fictional bust of Pythagoras 58 1 Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers 57 Some identify Hermodamas of Samos as a possible tutor 57 59 Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer 57 Others credit Bias of Priene Thales 60 or Anaximander a pupil of Thales 57 60 61 Other traditions claim the mythic bard Orpheus as Pythagoras s teacher thus representing the Orphic Mysteries 57 The Neoplatonists wrote of a sacred discourse Pythagoras had written on the gods in the Doric Greek dialect which they believed had been dictated to Pythagoras by the Orphic priest Aglaophamus upon his initiation to the orphic Mysteries at Leibethra 57 Iamblichus credited Orpheus with having been the model for Pythagoras s manner of speech his spiritual attitude and his manner of worship 62 Iamblichus describes Pythagoreanism as a synthesis of everything Pythagoras had learned from Orpheus from the Egyptian priests from the Eleusinian Mysteries and from other religious and philosophical traditions 62 Riedweg states that although these stories are fanciful Pythagoras s teachings were definitely influenced by Orphism to a noteworthy extent 63 Of the various Greek sages claimed to have taught Pythagoras Pherecydes of Syros is mentioned most often 63 64 Similar miracle stories were told about both Pythagoras and Pherecydes including one in which the hero predicts a shipwreck one in which he predicts the conquest of Messina and one in which he drinks from a well and predicts an earthquake 63 Apollonius Paradoxographus a paradoxographer who may have lived in the second century BC identified Pythagoras s thaumaturgic ideas as a result of Pherecydes s influence 63 Another story which may be traced to the Neopythagorean philosopher Nicomachus tells that when Pherecydes was old and dying on the island of Delos Pythagoras returned to care for him and pay his respects 63 Duris the historian and tyrant of Samos is reported to have patriotically boasted of an epitaph supposedly penned by Pherecydes which declared that Pythagoras s wisdom exceeded his own 63 On the grounds of all these references connecting Pythagoras with Pherecydes Riedweg concludes that there may well be some historical foundation to the tradition that Pherecydes was Pythagoras s teacher 63 Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis 63 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 65 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 66 Diogenes Laertius cites a statement from Aristoxenus fourth century BC stating that Pythagoras learned most of his moral doctrines from the Delphic priestess Themistoclea 67 68 69 Porphyry agrees with this assertion 70 but calls the priestess Aristoclea Aristokleia 71 Ancient authorities furthermore note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphic or Cretan mysteries 72 or the Delphic oracle 73 In Croton Croton Metapontum Sybaris Tarentum Acragasclass notpageimage Map of Italy showing locations associated with Pythagoras Porphyry repeats an account from Antiphon who reported that while he was still on Samos Pythagoras founded a school known as the semicircle 74 75 Here Samians debated matters of public concern 74 75 Supposedly the school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach 74 Pythagoras himself dwelled in a secret cave where he studied in private and occasionally held discourses with a few of his close friends 74 75 Christoph Riedweg a German scholar of early Pythagoreanism states that it is entirely possible Pythagoras may have taught on Samos 74 but cautions that Antiphon s account which makes reference to a specific building that was still in use during his own time appears to be motivated by Samian patriotic interest 74 Around 530 BC when Pythagoras was about forty years old he left Samos 5 34 76 77 78 His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos 65 76 Riedweg notes that this explanation closely aligns with Nicomachus s emphasis on Pythagoras s purported love of freedom but that Pythagoras s enemies portrayed him as having a proclivity towards tyranny 76 Other accounts claim that Pythagoras left Samos because he was so overburdened with public duties in Samos because of the high estimation in which he was held by his fellow citizens 79 He arrived in the Greek colony of Croton today s Crotone in Calabria in what was then Magna Graecia 34 78 80 81 All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment 34 82 83 He served as an advisor to the elites in Croton and gave them frequent advice 84 Later biographers tell fantastical stories of the effects of his eloquent speeches 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 85 86 Family and friends Illustration from 1913 showing Pythagoras teaching a class of women Many prominent members of his school were women 87 88 and some modern scholars think that he may have believed that women should be taught philosophy as well as men 89 Diogenes Laertius states that Pythagoras did not indulge in the pleasures of love 90 and that he cautioned others to only have sex whenever you are willing to be weaker than yourself 91 According to Porphyry Pythagoras married Theano a lady of Crete and the daughter of Pythenax 91 and had several children with her 91 Porphyry writes that Pythagoras had two sons named Telauges and Arignote 91 and a daughter named Myia 91 who took precedence among the maidens in Croton and when a wife among married women 91 Iamblichus mentions none of these children 91 and instead only mentions a son named Mnesarchus after his grandfather 91 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 91 Suda writes that Pythagoras had 4 children Telauges Mnesarchus Myia and Arignote 92 The wrestler Milo of Croton was said to have been a close associate of Pythagoras 93 and was credited with having saved the philosopher s life when a roof was about to collapse 93 This association may been the result of confusion with a different man named Pythagoras who was an athletics trainer 74 Diogenes Laertius records Milo s wife s name as Myia 91 Iamblichus mentions Theano as the wife of Brontinus of Croton 91 Diogenes Laertius states that the same Theano was Pythagoras s pupil 91 and that Pythagoras s wife Theano was her daughter 91 Diogenes Laertius also records that works supposedly written by Theano were still extant during his own lifetime 91 and quotes several opinions attributed to her 91 These writings are now known to be pseudepigraphical 91 Death Pythagoras s emphasis on dedication and asceticism are credited with aiding in Croton s decisive victory over the neighboring colony of Sybaris in 510 BC 94 After the victory some prominent citizens of Croton proposed a democratic constitution which the Pythagoreans rejected 94 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 95 Followers of Cylon and Ninon attacked the Pythagoreans during one of their meetings either in the house of Milo or in some other meeting place 96 97 Accounts of the attack are often contradictory and many probably confused it with later anti Pythagorean rebellions 95 The building was apparently set on fire 96 and many of the assembled members perished 96 only the younger and more active members managed to escape 98 Sources disagree regarding whether Pythagoras was present when the attack occurred and if he was whether or not he managed to escape 32 97 In some accounts Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes 97 According to another account from Dicaearchus Pythagoras was at the meeting and managed to escape 99 leading a small group of followers to the nearby city of Locris where they pleaded for sanctuary but were denied 99 They reached the city of Metapontum where they took shelter in the temple of the Muses and died there of starvation after forty days without food 32 96 99 100 Another tale recorded by Porphyry claims that as Pythagoras s enemies were burning the house his devoted students laid down on the ground to make a path for him to escape by walking over their bodies across the flames like a bridge 99 Pythagoras managed to escape but was so despondent at the deaths of his beloved students that he committed suicide 99 A different legend reported by both Diogenes Laertius and Iamblichus states that Pythagoras almost managed to escape but that he came to a fava bean field and refused to run through it since doing so would violate his teachings so he stopped instead and was killed 99 101 This story seems to have originated from the writer Neanthes who told it about later Pythagoreans not about Pythagoras himself 99 TeachingsMetempsychosis In Raphael s fresco The School of Athens Pythagoras is shown writing in a book as a young man presents him with a tablet showing a diagrammatic representation of a lyre above a drawing of the sacred tetractys 102 Although the exact details of Pythagoras s teachings are uncertain 103 104 it is possible to reconstruct a general outline of his main ideas 103 105 Aristotle writes at length about the teachings of the Pythagoreans 16 106 but without mentioning Pythagoras directly 16 106 One of Pythagoras s main doctrines appears to have been metempsychosis 77 107 108 109 110 111 the belief that all souls are immortal and that after death a soul is transferred into a new body 107 110 This teaching is referenced by Xenophanes Ion of Chios and Herodotus 107 112 Nothing whatsoever however is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur 113 Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations 114 Diogenes Laertius reports an account from Heraclides Ponticus that Pythagoras told people that he had lived four previous lives that he could remember in detail 115 116 117 The first of these lives was as Aethalides the son of Hermes who granted him the ability to remember all his past incarnations 118 Next he was incarnated as Euphorbus a minor hero from the Trojan War briefly mentioned in the Iliad 119 He then became the philosopher Hermotimus 120 who recognized the shield of Euphorbus in the temple of Apollo 120 His final incarnation was as Pyrrhus a fisherman from Delos 120 One of his past lives as reported by Dicaearchus was as a beautiful courtesan 108 121 Mysticism Another belief attributed to Pythagoras was that of the harmony of the spheres 122 123 which maintained that the planets and stars move according to mathematical equations which correspond to musical notes and thus produce an inaudible symphony 122 123 According to Porphyry Pythagoras taught that the seven Muses were actually the seven planets singing together 124 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 125 Pythagoras was said to have practiced divination and prophecy 126 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 127 Numerology 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 Pythagoras is credited with having devised the tetractys 128 129 an important sacred symbol in later Pythagoreanism 130 131 According to Aristotle the Pythagoreans used mathematics for solely mystical reasons devoid of practical application 132 They believed that all things were made of numbers 133 134 The number one the monad represented the origin of all things 135 and the number two the dyad represented matter 135 The number three was an ideal number because it had a beginning middle and end 136 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 136 The number four signified the four seasons and the four elements 137 The number seven was also sacred because it was the number of planets and the number of strings on a lyre 137 and because Apollo s birthday was celebrated on the seventh day of each month 137 They believed that odd numbers were masculine 138 that even numbers were feminine 138 and that the number five represented marriage because it was the sum of two and three 139 140 Ten was regarded as the perfect number 132 and the Pythagoreans honored it by never gathering in groups larger than ten 141 Pythagoras was credited with devising the tetractys the triangular figure of four rows which add up to the perfect number ten 128 129 The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance 128 129 130 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 102 129 130 142 Andrew Gregory concludes that the tradition linking Pythagoras to the tetractys is probably genuine 143 Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton 144 In his landmark study Lore and Science in Ancient Pythagoreanism Walter Burkert argues that Pythagoras was a charismatic political and religious teacher 145 but that the number philosophy attributed to him was really an innovation by Philolaus 146 According to Burkert Pythagoras never dealt with numbers at all let alone made any noteworthy contribution to mathematics 145 Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple proofless arithmetic 147 but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics 148 PythagoreanismCommunal lifestyle Pythagoreans Celebrate the Sunrise 1869 by Fyodor Bronnikov Main article Pythagoreanism Both Plato and Isocrates state that above all else Pythagoras was known as the founder of a new way of life 149 150 151 The organization Pythagoras founded at Croton was called a school 152 153 65 but in many ways resembled a monastery 154 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 155 The members of the sect shared all their possessions in common 156 and were devoted to each other to the exclusion of outsiders 157 158 Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans 159 160 One Pythagorean maxim was koina ta philōn All things in common among friends 156 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 161 Iamblichus in particular presents the Pythagorean Way of Life as a pagan alternative to the Christian monastic communities of his own time 154 Two groups existed within early Pythagoreanism the mathematikoi learners and the akousmatikoi listeners 66 162 The akousmatikoi are traditionally identified by scholars as old believers in mysticism numerology and religious teachings 162 whereas the mathematikoi are traditionally identified as a more intellectual modernist faction who were more rationalist and scientific 162 Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed the two approaches were compatible 162 The study of mathematics and music may have been connected to the worship of Apollo 163 The Pythagoreans believed that music was a purification for the soul just as medicine was a purification for the body 124 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 124 The Pythagoreans also placed particular emphasis on the importance of physical exercise 154 therapeutic dancing daily morning walks along scenic routes and athletics were major components of the Pythagorean lifestyle 154 Moments of contemplation at the beginning and end of each day were also advised 164 Prohibitions and regulations French manuscript from 1512 1514 showing Pythagoras turning his face away from fava beans in revulsion Pythagorean teachings were known as symbols symbola 87 and members took a vow of silence that they would not reveal these symbols to non members 87 150 165 Those who did not obey the laws of the community were expelled 166 and the remaining members would erect tombstones for them as though they had died 166 A number of oral sayings akousmata attributed to Pythagoras have survived 16 167 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 168 Many of these sayings emphasize the importance of ritual purity and avoiding defilement 169 111 For instance a saying which Leonid Zhmud concludes can probably be genuinely traced back to Pythagoras himself forbids his followers from wearing woolen garments 170 Other extant oral sayings forbid Pythagoreans from breaking bread poking fires with swords or picking up crumbs 160 and teach that a person should always put the right sandal on before the left 160 The exact meanings of these sayings however are frequently obscure 171 Iamblichus preserves Aristotle s descriptions of the original ritualistic intentions behind a few of these sayings 172 but these apparently later fell out of fashion because Porphyry provides markedly different ethical philosophical interpretations of them 173 Pythagorean saying Original ritual purpose according to Aristotle Iamblichus Porphyry s philosophical interpretation Do not take roads traveled by the public 174 16 Fear of being defiled by the impure 174 with this he forbade following the opinions of the masses yet to follow the ones of the few and the educated 174 and do not wear images of the gods on rings 174 Fear of defiling them by wearing them 174 One should not have the teaching and knowledge of the gods quickly at hand and visible for everyone nor communicate them to the masses 174 and pour libations for the gods from a drinking cup s handle the ear 174 Efforts to keep the divine and the human strictly separate 174 thereby he enigmatically hints that the gods should be honored and praised with music for it goes through the ears 174 New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five year initiation period 75 during which they were required to remain silent 75 Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women 89 and female members of Pythagoras s school appear to have played an active role in its operations 87 89 Iamblichus provides a list of 235 famous Pythagoreans 88 seventeen of whom are women 88 In later times many prominent female philosophers contributed to the development of Neopythagoreanism 175 Pythagoreanism also entailed a number of dietary prohibitions 111 160 176 It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beans 177 160 and the meat of non sacrificial animals such as fish and poultry 170 160 Both of these assumptions however have been contradicted 178 179 Pythagorean dietary restrictions may have been motivated by belief in the doctrine of metempsychosis 150 180 181 182 Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet e 150 181 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 183 184 Other authorities contradict this statement 185 According to Aristoxenus 186 Pythagoras allowed the use of all kinds of animal food except the flesh of oxen used for ploughing and rams 184 187 According to Heraclides Ponticus Pythagoras ate the meat from sacrifices 184 and established a diet for athletes dependent on meat 184 Legends Pythagoras Emerging from the Underworld 1662 by Salvator Rosa Within his own lifetime Pythagoras was already the subject of elaborate hagiographic legends 30 188 Aristotle described Pythagoras as a wonder worker and somewhat of a supernatural figure 189 190 In a fragment Aristotle writes that Pythagoras had a golden thigh 189 191 192 which he publicly exhibited at the Olympic Games 189 193 and showed to Abaris the Hyperborean as proof of his identity as the Hyperborean Apollo 189 194 Supposedly the priest of Apollo gave Pythagoras a magic arrow which he used to fly over long distances and perform ritual purifications 195 He was supposedly once seen at both Metapontum and Croton at the same time 196 30 193 191 192 When Pythagoras crossed the river Kosas the modern day Basento several witnesses reported that they heard it greet him by name 197 193 191 In Roman times a legend claimed that Pythagoras was the son of Apollo 198 192 According to Muslim tradition Pythagoras was said to have been initiated by Hermes Egyptian Thoth 199 Pythagoras was said to have dressed all in white 189 200 He is also said to have borne a golden wreath atop his head 189 and to have worn trousers after the fashion of the Thracians 189 Diogenes Laertius presents Pythagoras as having exercised remarkable self control 201 he was always cheerful 201 but abstained wholly from laughter and from all such indulgences as jests and idle stories 91 Pythagoras was said to have had extraordinary success in dealing with animals 30 202 193 A fragment from Aristotle records that when a deadly snake bit Pythagoras he bit it back and killed it 195 193 191 Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans 30 202 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 30 202 Riedweg suggests that Pythagoras may have personally encouraged these legends 188 but Gregory states that there is no direct evidence of this 162 Anti Pythagorean legends were also circulated 203 Diogenes Laertes 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 204 He stayed in this room for months while his mother secretly recorded everything that happened during his absence 204 After he returned from this room Pythagoras recounted everything that had happened while he was gone 204 convincing everyone that he had really been in the underworld 204 and leading them to trust him with their wives 204 Attributed discoveriesIn mathematics The Pythagorean theorem The sum of the areas of the two squares on the legs a and b equals the area of the square on the hypotenuse c Although Pythagoras is most famous today for his alleged mathematical discoveries 131 205 classical historians dispute whether he himself ever actually made any significant contributions to the field 147 145 Many mathematical and scientific discoveries were attributed to Pythagoras including his famous theorem 206 as well as discoveries in the fields of music 207 astronomy 208 and medicine 209 Since at least the first century BC Pythagoras has commonly been given credit for discovering the Pythagorean theorem 210 211 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 212 that is a 2 b 2 c 2 displaystyle a 2 b 2 c 2 According to a popular legend after he discovered this theorem Pythagoras sacrificed an ox or possibly even a whole hecatomb to the gods 212 213 Cicero rejected this story as spurious 212 because of the much more widely held belief that Pythagoras forbade blood sacrifices 212 Porphyry attempted to explain the story by asserting that the ox was actually made of dough 212 The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras 214 212 215 216 but he may have been the first to introduce it to the Greeks 217 215 Some historians of mathematics have even suggested that he or his students may have constructed the first proof 218 Burkert rejects this suggestion as implausible 217 noting that Pythagoras was never credited with having proved any theorem in antiquity 217 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 131 and that he was the first to discover the Theory of Proportions 131 In music Late medieval woodcut from Franchino Gafurio s Theoria musice 1492 showing Pythagoras with bells and other instruments in Pythagorean tuning 143 See also Pythagorean tuning and Pythagorean hammers 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 219 220 Thinking that the sounds of the hammers were beautiful and harmonious except for one 221 he rushed into the blacksmith shop and began testing the hammers 221 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 220 221 In astronomy 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 222 the first to divide the globe into five climatic zones 222 and the first to identify the morning star and the evening star as the same celestial object now known as Venus 223 Of the two philosophers Parmenides has a much stronger claim to having been the first 224 and the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem 223 Empedocles who lived in Magna Graecia shortly after Pythagoras and Parmenides knew that the earth was spherical 225 By the end of the fifth century BC this fact was universally accepted among Greek intellectuals 226 The identity of the morning star and evening star was known to the Babylonians over a thousand years earlier 227 Later influence in antiquityOn Greek philosophy Medieval manuscript of Calcidius s Latin translation of Plato s Timaeus which is one of the Platonic dialogues with the most overt Pythagorean influences 228 See also Timaeus dialogue Sizeable Pythagorean communities existed in Magna Graecia Phlius and Thebes during the early fourth century BC 229 Around the same time the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia 230 According to later tradition Archytas was elected as strategos general seven times even though others were prohibited from serving more than a year 230 Archytas was also a renowned mathematician and musician 231 He was a close friend of Plato 232 and he is quoted in Plato s Republic 233 234 Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans 235 236 Cicero repeats this statement remarking that Platonem ferunt didicisse Pythagorea omnia They say Plato learned all things Pythagorean 237 According to Charles H Kahn Plato s middle dialogues including Meno Phaedo and The Republic have a strong Pythagorean coloring 238 and his last few dialogues particularly Philebus and Timaeus 228 are extremely Pythagorean in character 228 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 239 Additionally Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy science and morality 239 Plato and Pythagoras shared a mystical approach to the soul and its place in the material world 239 and it is probable that both were influenced by Orphism 239 The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans 240 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 241 He concludes that I do not know of any other man who has been as influential as he was in the school of thought 242 A revival of Pythagorean teachings occurred in the first century BC 243 when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed the rise of a new Pythagoreanism in Alexandria 244 At around the same time Neopythagoreanism became prominent 245 The first century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings 246 The later first century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy 246 and probably understood the soul as a kind of mathematical harmony 246 The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory 245 Numenius of Apamea interpreted Plato s teachings in light of Pythagorean doctrines 247 On art and architecture Hadrian s Pantheon in Rome depicted in this eighteenth century painting by Giovanni Paolo Panini was built according to Pythagorean teachings 248 Greek sculpture sought to represent the permanent reality behind superficial appearances 249 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 eἶdos which was mathematically calculated 250 251 When dimensions changed architects sought to relay permanence through mathematics 252 253 Maurice Bowra believes that these ideas influenced the theory of Pythagoras and his students who believed that all things are numbers 253 During the sixth century BC the number philosophy of the Pythagoreans triggered a revolution in Greek sculpture 254 Greek sculptors and architects attempted to find the mathematical relation canon behind aesthetic perfection 251 Possibly drawing on the ideas of Pythagoras 251 the sculptor Polykleitos wrote 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 251 h 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 251 The oldest known building designed according to Pythagorean teachings is the Porta Maggiore Basilica 255 a subterranean basilica which was built during the reign of the Roman emperor Nero as a secret place of worship for Pythagoreans 256 The basilica was built underground because of the Pythagorean emphasis on secrecy 257 and also because of the legend that Pythagoras had sequestered himself in a cave on Samos 258 The basilica s apse is in the east and its atrium in the west out of respect for the rising sun 259 It has a narrow entrance leading to a small pool where the initiates could purify themselves 260 The building is also designed according to Pythagorean numerology 261 with each table in the sanctuary providing seats for seven people 141 Three aisles lead to a single altar symbolizing the three parts of the soul approaching the unity of Apollo 141 The apse depicts a scene of the poet 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 262 symbolizing Pythagorean teachings about the immortality of the soul 262 The interior of the sanctuary is almost entirely white because the color white was regarded by Pythagoreans as sacred 263 The emperor Hadrian s Pantheon in Rome was also built based on Pythagorean numerology 248 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 264 The single oculus at the top of the dome symbolizes the monad and the sun god Apollo 265 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 266 The five coffered rings beneath the ribs represent the marriage of the sun and moon 136 In early Christianity Many early Christians had a deep respect for Pythagoras 267 Eusebius c 260 c 340 AD bishop of Caesarea praises Pythagoras in his Against Hierokles for his rule of silence his frugality his extraordinary morality and his wise teachings 268 In another work Eusebius compares Pythagoras to Moses 268 In one of his letter the Church Father Jerome c 347 420 AD praises Pythagoras for his wisdom 268 and in another letter he credits Pythagoras for his belief in the immortality of the soul which he suggests Christians inherited from him 269 Augustine of Hippo 354 430 AD rejected Pythagoras s teaching of metempsychosis without explicitly naming him but otherwise expressed admiration for him 270 In On the Trinity Augustine lauds the fact that Pythagoras was humble enough to call himself a philosophos or lover of wisdom rather than a sage 271 In another passage Augustine defends Pythagoras s reputation arguing that Pythagoras certainly never taught the doctrine of metempsychosis 271 Influence after antiquityIn the Middle Ages Pythagoras appears in a relief sculpture on one of the archivolts over the right door of the west portal at Chartres Cathedral 272 During the Middle Ages Pythagoras was revered as the founder of mathematics and music two of the Seven Liberal Arts 272 He appears in numerous medieval depictions in illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres 272 The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe 272 which led William of Conches c 1080 1160 to declare that Plato was Pythagorean 272 In the 1430s the Camaldolese friar Ambrose Traversari translated Diogenes Laertius s Lives and Opinions of Eminent Philosophers from Greek into Latin 272 and in the 1460s the philosopher Marsilio Ficino translated Porphyry and Iamblichus s Lives of Pythagoras into Latin as well 272 thereby allowing them to be read and studied by western scholars 272 In 1494 the Greek Neopythagorean scholar Constantine Lascaris published The Golden Verses of Pythagoras translated into Latin with a printed edition of his Grammatica 273 thereby bringing them to a widespread audience 273 In 1499 he published the first Renaissance biography of Pythagoras in his work Vitae illustrium philosophorum siculorum et calabrorum issued in Messina 273 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 272 274 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 274 Johannes Kepler considered himself to be a Pythagorean 272 275 276 He believed in the Pythagorean doctrine of musica universalis 277 and it was his search for the mathematical equations behind this doctrine that led to his discovery of the laws of planetary motion 277 Kepler titled his book on the subject Harmonices Mundi Harmonics of the World after the Pythagorean teaching that had inspired him 272 278 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 279 He also called Pythagoras the grandfather of all Copernicans 280 Isaac Newton firmly believed in the Pythagorean teaching of the mathematical harmony and order of the universe 281 Though Newton was notorious for rarely giving others credit for their discoveries 282 he attributed the discovery of the Law of Universal Gravitation to Pythagoras 282 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 283 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 284 By this measure Whitehead declared that Einstein and other modern scientists like him are following the pure Pythagorean tradition 283 285 On vegetarianism Pythagoras Advocating Vegetarianism 1618 1630 by Peter Paul Rubens was inspired by Pythagoras s speech in Ovid s Metamorphoses 286 The painting portrays the Pythagoreans with corpulent bodies indicating a belief that vegetarianism was healthful and nutritious 286 A fictionalized portrayal of Pythagoras appears in Book XV of Ovid s Metamorphoses 287 in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet 288 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 288 John Donne s Progress of the Soul discusses the implications of the doctrines expounded in the speech 289 and Michel de Montaigne quoted the speech no less than three times in his treatise Of Cruelty to voice his moral objections against the mistreatment of animals 289 William Shakespeare references the speech in his play The Merchant of Venice 290 John Dryden included a translation of the scene with Pythagoras in his 1700 work Fables Ancient and Modern 289 and John Gay s 1726 fable Pythagoras and the Countryman reiterates its major themes linking carnivorism with tyranny 289 Lord Chesterfield records that his conversion to vegetarianism had been motivated by reading Pythagoras s speech in Ovid s Metamorphoses 289 Until the word vegetarianism was coined in the 1840s vegetarians were referred to in English as Pythagoreans 289 Percy Bysshe Shelley wrote an ode entitled To the Pythagorean Diet 291 and Leo Tolstoy adopted the Pythagorean diet himself 291 On Western esotericism Early modern European esotericism drew heavily on the teachings of Pythagoras 272 The German humanist scholar Johannes Reuchlin 1455 1522 synthesized Pythagoreanism with Christian theology and Jewish Kabbalah 292 arguing that Kabbalah and Pythagoreanism were both inspired by Mosaic tradition 293 and that Pythagoras was therefore a kabbalist 293 In his dialogue De verbo mirifico 1494 Reuchlin compared the Pythagorean tetractys to the ineffable divine name YHWH 292 ascribing each of the four letters of the tetragrammaton a symbolic meaning according to Pythagorean mystical teachings 293 Heinrich Cornelius Agrippa s popular and influential three volume treatise De Occulta Philosophia cites Pythagoras as a religious magi 294 and indicates that Pythagoras s mystical numerology operates on a supercelestial level 294 The freemasons deliberately modeled their society on the community founded by Pythagoras at Croton 295 Rosicrucianism used Pythagorean symbolism 272 as did Robert Fludd 1574 1637 272 who believed his own musical writings to have been inspired by Pythagoras 272 John Dee was heavily influenced by Pythagorean ideology 296 294 particularly the teaching that all things are made of numbers 296 294 Adam Weishaupt the founder of the Illuminati was a strong admirer of Pythagoras 297 and in his book Pythagoras 1787 he advocated that society should be reformed to be more like Pythagoras s commune at Croton 298 Wolfgang Amadeus Mozart incorporated Masonic and Pythagorean symbolism into his opera The Magic Flute 299 Sylvain Marechal in his six volume 1799 biography The Voyages of Pythagoras declared that all revolutionaries in all time periods are the heirs of Pythagoras 300 On literature Dante Alighieri s description of Heaven in his Paradiso incorporates Pythagorean numerology 301 Dante Alighieri was fascinated by Pythagorean numerology 301 and based his descriptions of Hell Purgatory and Heaven on Pythagorean numbers 301 Dante wrote that Pythagoras saw Unity as Good and Plurality as Evil 302 and in Paradiso XV 56 57 he declares five and six if understood ray forth from unity 303 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 304 Dante describes the ninth and tenth bolgias in the Eighth Circle of Hell as being twenty two miles and eleven miles respectively 304 which correspond to the fraction 22 7 which was the Pythagorean approximation of pi 304 The Transcendentalists read the ancient Lives of Pythagoras as guides on how to live a model life 305 Henry David Thoreau was impacted by Thomas Taylor s translations of Iamblichus s Life of Pythagoras and Stobaeus s Pythagoric Sayings 305 and his views on nature may have been influenced by the Pythagorean idea of images corresponding to archetypes 305 The Pythagorean teaching of musica universalis is a recurring theme throughout Thoreau s magnum opus Walden 305 See alsoCosmos Ex pede Herculem Isopsephy gematria List of things named after Pythagoras Lute of Pythagoras Pythagoras tree fractal Pythagorean comma Pythagorean cup Pythagorean triple Pythagoras sculptor Sacred geometryReferencesFootnotes US p ɪ ˈ 8 ae ɡ er e s 2 UK p aɪ 3 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 4 Cicero Tusculan Disputations 5 3 8 9 citing Heraclides Ponticus fr 88 Wehrli Diogenes Laertius 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 from Lemnos a Phliasian or a native Samian and give Marmacus or Demaratus as the name of his father Diogenes Laertius viii 1 Porphyry Vit Pyth 1 2 Justin xx 4 Pausanias ii 13 Iamblichus ii 4 Due to this obscurity some modern scholars accept the simple statement that Pythagoras and his father were pure blooded Greeks Felix Jacoby Jan Bollansee Guido Schepens 1998 Die Fragmente Der Griechischen Historiker Continued BRILL p 296 n 73 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 Hoyrup The Pythagorean Rule and Theorem Mirror of the Relation between Babylonian and Greek Mathematics in J Renger red Babylon Focus mesopotamischer Geschichte Wiege fruher 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 249 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 Citations a b c 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 William Keith Chambers Guthrie 1978 A history of Greek philosophy Volume 1 The earlier Presocratics and the Pythagoreans p 173 Cambridge University Press a b c d e Joost Gaugier 2006 p 11 Celenza 2010 p 796 a b Ferguson 2008 p 4 Ferguson 2008 pp 3 5 Gregory 2015 pp 21 23 a b c Copleston 2003 p 29 a b c Kahn 2001 p 2 a b Burkert 1985 p 299 a b c Joost Gaugier 2006 p 12 Riedweg 2005 p 62 Diogenes Laertius viii 36 a b c d e Copleston 2003 p 31 a b Joost Gaugier 2006 pp 12 13 a b c Joost Gaugier 2006 p 13 Joost Gaugier 2006 pp 14 15 a b c d e f Joost Gaugier 2006 p 16 4 95 Marincola 2001 p 59 Roberts 2011 p 2 Sparks 1998 p 58 Asheri Lloyd amp Corcella 2007 Cameron 2004 p 156 Joost Gaugier 2006 p 88 He alludes to it himself Met i 5 p 986 12 ed Bekker a b c d Burkert 1972 p 109 a b c d e f g h i j k l Kahn 2001 p 5 a b c d e Zhmud 2012 p 9 a b c Burkert 1972 p 106 Herodotus Histories 4 95 in Greek original text and English transtations 1 2 a b c d e f Kahn 2001 p 6 a b Ferguson 2008 p 12 Kenny 2004 p 9 Ferguson 2008 p 11 Porphyry Vita Pythagorae Leipzig 1886 Porphyry Life of Pythogoras in M Hadas and M Smith Heroes and Gods London 1965 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 978 90 04 23011 8 Joost Gaugier 2006 p 21 Ferguson 2008 pp 11 12 Ferguson 2008 p 15 Taub 2017 p 122 Apollonius of Tyana ap Porphyry Vit Pyth 2 a b c Riedweg 2005 p 59 Porphyry Vit Pyth 9 Riedweg 2005 pp 45 47 a b Riedweg 2005 pp 44 45 a b c Riedweg 2005 p 7 a b Riedweg 2005 pp 7 8 Gregory 2015 pp 22 23 Porphyry Vit Pyth 6 Plutarch On Isis And Osiris ch 10 Press 2003 p 83 cf Antiphon ap Porphyry Vit Pyth 7 Isocrates Busiris 28 9 Cicero de Finibus v 29 Strabo 14 1 16 a b Diogenes Laertius viii 1 3 a b c d e f g h i j k l Riedweg 2005 p 8 Dillon 2005 p 163 Porphyry Vit Pyth 2 Diogenes Laertius viii 2 a b Iamblichus Vit Pyth 9 Porphyry Vit Pyth 2 a b Riedweg 2005 pp 8 9 a b c d e f g h Riedweg 2005 p 9 Aristoxenus and others in Diogenes Laertius i 118 119 Cicero de Div i 49 a b c Boyer Carl B 1968 A History of Mathematics a b Zhmud 2012 pp 2 16 Diogenes Laertius Lives of Eminent Philosophers viii 1 8 Waithe M E April 30 1987 Ancient Women Philosophers 600 B C 500 A D Springer Science amp Business Media ISBN 9789024733682 via Google Books Malone John C 30 June 2009 Psychology Pythagoras to present MIT Press p 22 ISBN 978 0 262 01296 6 retrieved 25 October 2010 Porphyry Life of Pythagoras 41 Gilles Menage The history of women philosophers Translated from the Latin with an introduction by Beatrice H Zedler University Press of America Lanham 1984 p 47 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 Laertius viii 3 Ariston ap Diogenes Laertius viii 8 21 Porphyry Vit Pyth 41 a b c d e f g Riedweg 2005 p 10 a b c d e Cornelli amp McKirahan 2013 p 64 a b c Riedweg 2005 p 11 a b Ferguson 2008 p 5 a b Gregory 2015 p 22 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 Riedweg 2005 pp 11 12 Cornelia J de Vogel Pythagoras and Early Pythagoreanism Assen 1966 S 148 150 Riedweg 2005 pp 12 13 Riedweg 2005 pp 12 18 Porphyry Vit Pyth 18 Iamblichus Vit Pyth 37 etc Riedweg 2005 pp 13 18 a b c d Kahn 2001 p 8 a b c Pomeroy 2013 p 1 a b c Pomeroy 2013 p xvi Ferguson 2008 p 58 a b c d e f g h i j k l m n o p q Ferguson 2008 p 59 Suda Encyclopedia th 84 a b Riedweg 2005 pp 5 6 59 73 a b Kahn 2001 pp 6 7 a b Riedweg 2005 p 19 a b c d Kahn 2001 p 7 a b c Riedweg 2005 pp 19 20 Iamblichus Vit Pyth 255 259 Porphyry Vit Pyth 54 57 Diogenes Laertius viii 39 comp Plutarch de Gen Socr p 583 a b c d e f g Riedweg 2005 p 20 Grant 1989 p 278 Simoons 1998 pp 225 228 a b Bruhn 2005 p 66 a b Burkert 1972 pp 106 109 Kahn 2001 pp 5 6 Kahn 2001 pp 9 11 a b Burkert 1972 pp 29 30 a b c Kahn 2001 p 11 a b Zhmud 2012 p 232 Burkert 1985 pp 300 301 a b Gregory 2015 pp 24 25 a b c Copleston 2003 pp 30 31 Diogenes Laertius viii 36 comp Aristotle de Anima i 3 Herodotus ii 123 Gregory 2015 p 25 Kahn 2001 p 12 Diogenes Laertius viii 3 4 Cornelli amp McKirahan 2013 pp 164 167 Porphyry Vit Pyth 26 Pausanias ii 17 Diogenes Laertius viii 5 Horace Od i 28 1 10 Cornelli amp McKirahan 2013 pp 164 165 Cornelli amp McKirahan 2013 pp 165 166 a b c Cornelli amp McKirahan 2013 p 167 Aulus Gellius iv 11 a b Riedweg 2005 pp 29 30 a b Gregory 2015 pp 38 39 a b c 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 Laertius viii 3 13 Cicero Tusc Qu v 3 a b c Bruhn 2005 pp 65 66 a b c d Gregory 2015 pp 28 29 a b c Riedweg 2005 p 29 a b c d Kahn 2001 pp 1 2 a b Burkert 1972 pp 467 468 Burkert 1972 p 265 Kahn 2001 p 27 a b Riedweg 2005 p 23 a b c Joost Gaugier 2006 pp 170 172 a b c Joost Gaugier 2006 p 172 a b Burkert 1972 p 433 Burkert 1972 p 467 Joost Gaugier 2006 p 170 a b c Joost Gaugier 2006 p 161 Iamblichus Vit Pyth 29 a b Gregory 2015 p 28 Joost Gaugier 2006 pp 87 88 a b c Kahn 2001 pp 2 3 Kahn 2001 p 3 a b Burkert 1972 pp 428 433 Burkert 1972 p 465 Plato Republic 600a Isocrates Busiris 28 a b c d Cornelli amp McKirahan 2013 p 168 Grant 1989 p 277 Porphyry Vit Pyth 19 Thirlwall Hist of Greece vol ii p 148 a b c d Riedweg 2005 p 31 comp Cicero de Leg i 12 de Off i 7 Diogenes Laertius viii 10 a b Cornelli amp 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 amp McKirahan 2013 pp 68 69 Iamblichus Vit Pyth 98 Strabo vi a b c d e f Kenny 2004 p 10 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 a b c d e Gregory 2015 p 31 Aelian Varia Historia ii 26 Diogenes Laertius viii 13 Iamblichus Vit Pyth 8 91 141 Riedweg 2005 pp 33 34 Scholion ad Aristophanes Nub 611 Iamblichus Vit Pyth 237 238 a b Cornelli amp McKirahan 2013 p 69 Riedweg 2005 pp 64 67 Riedweg 2005 p 64 Riedweg 2005 p 65 a b Zhmud 2012 p 200 Riedweg 2005 pp 65 67 Riedweg 2005 pp 65 66 Riedweg 2005 pp 66 67 a b c d e f g h i Riedweg 2005 p 66 Pomeroy 2013 pp xvi xvii comp Porphyry Vit Pyth 32 Iamblichus Vit Pyth 96 etc Zhmud 2012 pp 137 200 Copleston 2003 p 30 Diogenes Laertius viii 19 34 Aulus Gellius iv 11 Porphyry Vit Pyth 34 de Abst i 26 Iamblichus Vit Pyth 98 Plutarch de Esu Carn pp 993 996 997 a b Kahn 2001 p 9 Kenny 2004 pp 10 11 Eudoxus frg 325 a b c d Zhmud 2012 p 235 Aristo ap Diogenes Laertius viii 20 comp Porphyry Vit Pyth 7 Iamblichus Vit Pyth 85 108 Aristoxenus ap Diogenes Laertius viii 20 comp Porphyry Vit Pyth 7 Iamblichus Vit Pyth 85 108 a b Riedweg 2005 p 1 a b c d e f g Riedweg 2005 p 2 Gregory 2015 pp 30 31 a b c d Gregory 2015 p 30 a b c Kenny 2004 p 11 a b c d e Ferguson 2008 p 60 Porphyry Vit Pyth 20 Iamblichus Vit Pyth 31 140 Aelian Varia Historia ii 26 Diogenes Laertius viii 36 a b McKeown 2013 p 155 Comp Herodian iv 94 etc Burkert 1972 p 144 Ferguson 2008 p 10 See Antoine Faivre in The Eternal Hermes 1995 Joost Gaugier 2006 p 47 a b Ferguson 2008 pp 58 59 a b c Cornelli amp McKirahan 2013 p 160 Ferguson 2008 pp 60 61 a b c d e Ferguson 2008 p 61 Gregory 2015 pp 21 22 Diogenes Laertius viii 12 Plutarch Non posse suav vivi sec Ep p 1094 Porphyry in Ptol Harm p 213 Diogenes Laertius viii 12 Diogenes Laertius viii 14 Pliny Hist Nat ii 8 Diogenes Laertius viii 12 14 32 Kahn 2001 pp 32 33 Riedweg 2005 pp 26 27 a b c d e f Riedweg 2005 p 27 Burkert 1972 p 428 Burkert 1972 pp 429 462 a b Kahn 2001 p 32 Ferguson 2008 pp 6 7 a b c Burkert 1972 p 429 Kahn 2001 p 33 Riedweg 2005 pp 27 28 a b Gregory 2015 p 27 a b c Riedweg 2005 p 28 a b Burkert 1972 p 306 a b Burkert 1972 pp 307 308 Burkert 1972 pp 306 308 Kahn 2001 p 53 Dicks 1970 p 68 Langdon amp Fotheringham 1928 a b c Kahn 2001 pp 55 62 Kahn 2001 pp 48 49 a b 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 a b c d 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 a b Riedweg 2005 pp 125 126 a b c Riedweg 2005 p 125 Riedweg 2005 pp 126 127 a b Joost Gaugier 2006 pp 166 181 a b Homann Wedeking 1968 p 63 Homann Wedeking 1968 p 62 a b c d e Carpenter 1921 pp 107 122 128 Homann Wedeking 1968 pp 62 63 a b Bowra 1994 p 166 Homann Wedeking 1968 pp 62 65 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 a b 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 Joost Gaugier 2006 pp 57 65 a b c Joost Gaugier 2006 p 57 Joost Gaugier 2006 pp 57 58 Joost Gaugier 2006 pp 58 59 a b Joost Gaugier 2006 p 59 a b c d e f g h i j k l m n o Celenza 2010 p 798 a b c Russo 2004 pp 5 87 especially 51 53 a b Kahn 2001 p 160 Kahn 2001 pp 161 171 Ferguson 2008 p 265 a b Ferguson 2008 pp 264 274 Kahn 2001 p 162 Ferguson 2008 p 274 Jamie James The Music of the Spheres Music Science and the Natural Order of the Universe p 142 Ferguson 2008 p 279 a b Ferguson 2008 pp 279 280 a b Kahn 2001 p 172 Whitehead 1953 pp 36 37 Whitehead 1953 p 36 a b Borlik 2011 p 192 Borlik 2011 p 189 a b Borlik 2011 pp 189 190 a b c d e f Borlik 2011 p 190 Ferguson 2008 p 282 a b Ferguson 2008 p 294 a b Riedweg 2005 pp 127 128 a b c Riedweg 2005 p 128 a b c d French 2002 p 30 Riedweg 2005 p 133 a b Sherman 1995 p 15 Ferguson 2008 pp 284 288 Ferguson 2008 pp 287 288 Ferguson 2008 pp 286 287 Ferguson 2008 p 288 a b c Haag 2013 p 89 Haag 2013 p 90 Haag 2013 pp 90 91 a b c Haag 2013 p 91 a b c d Bregman 2002 p 186 Works cited Only a few relevant source texts deal with Pythagoras and the Pythagoreans most are available in different translations Later texts usually build solely upon information in these works Classical sources Diogenes Laertius Vitae philosophorum VIII Lives of Eminent Philosophers c 200 AD which in turn references the lost doxography by Alexander Polyhistor Laertius Diogenes 1925 Pythagoreans Pythagoras Lives of the Eminent Philosophers vol 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 Vasunia 2007 p 246 Hierocles of Alexandria Golden Verses of Pythagoras c 430 AD Modern secondary sources Asheri David Lloyd Alan Corcella Aldo 2007 A Commentary on Herodotus Books 1 4 Oxford University Press ISBN 978 0 19 814956 9 Bowra C M 1994 1957 The Greek Experience London England Weidenfeld amp Nicolson History ISBN 978 1 85799 122 2 Bregman Jay 2002 Neoplatonism and American Aesthetics in Alexandrakis Aphrodite Moulafakis Nicholas J eds Neoplatonism and Western Aesthetics Studies in Neoplatonism Ancient and Modern vol 12 Albany New York State University of New York Press ISBN 978 0 7914 5280 6 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 978 0 674 53918 1 Burkert Walter 1985 Greek Religion Cambridge Massachusetts Harvard University Press ISBN 978 0 674 36281 9 Cameron Alan 2004 Greek Mythography in the Roman World Oxford University Press ISBN 978 0 19 803821 4 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 1946 The Pythagorean Society A History of Philosophy vol 1 Greece and Rome London England and New York City New York Continuum ISBN 978 0 8264 6947 2 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 amp Company ISBN 978 0 8027 1631 6 French Peter J 2002 1972 John Dee The World of the Elizabethan Magus New York City New York and London England Routledge ISBN 978 0 7448 0079 1 Celenza Christopher 2010 Pythagoras and Pythagoreanism in Grafton Anthony Most Glenn W Settis Salvatore eds The Classical Tradition Cambridge Massachusetts and London England The Belknap Press of Harvard University Press pp 796 799 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 978 0 684 19126 3 Gregory Andrew 2015 The Pythagoreans Number and Numerology in Lawrence Snezana McCartney Mark eds Mathematicians and their Gods Interactions between Mathematics and Religious Beliefs Oxford England Oxford University Press pp 21 50 ISBN 978 0 19 870305 1 Guthrie W K 1979 A History of Greek Philosophy Earlier Presocratics and the Pythagoreans Cambridge England Cambridge University Press ISBN 978 0 521 29420 1 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 1982 Plato in Taylor C C W Hare R M Barnes Jonathan eds 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 Kenny Anthony 2004 Ancient Philosophy A New History of Western Philosophy vol 1 Oxford England Oxford University Press ISBN 978 0 19 875273 8 Kingsley Peter 1995 Ancient Philosophy Mystery and Magic Empedocles and the Pythagorean Tradition Oxford England Oxford University Press Langdon Stephen Fotheringham John 1928 The Venus Tablets of Ammizaduga A solution of Babylonian chronology by means of the Venus observations of the First Dynasty Oxford University Press ISBN 978 9 33 362298 1 Marincola John 2001 Greek Historians Oxford University Press ISBN 978 0 19 922501 9 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 978 0 19 823913 0 Press Gerald A 2003 1982 Development of the Idea of History in Antiquity Montreal Canada and Kingston New York McGill Queen s University Press ISBN 978 0 7735 1002 9 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 2002 Pythagoras His Life Teachings and Influence Ithaca New York Cornell University Press ISBN 978 0 8014 7452 1 Roberts Jennifer T 2011 Herodotus a Very Short Introduction OXford University Press ISBN 978 0 19 957599 2 Russell Bertrand 2008 1945 A History of Western Philosophy A Touchstone Book New York City New York Simon amp Schuster ISBN 978 0 671 31400 2 Russo Attilio 2004 Costantino Lascaris tra fama e oblio nel Cinquecento messinese Archivio Storico Messinese 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 978 1 55849 070 3 Simoons Frederick J 1998 Plants of Life Plants of Death Madison Wisconsin University of Wisconsin Press ISBN 978 0 299 15904 7 Sparks Kenton L 1998 Ethnicity and Identity in Ancient Israel Prolegomena to the Study of Ethnic Sentiments and their Expression in the Hebrew Bible Winona Lake IN Eisenbrauns ISBN 978 1 57506 033 0 Taub Liba 2017 Science Writing in Greco Roman Antiquity Cambridge University Press ISBN 978 0 521 11370 0 Vasunia Phiroze 2007 The Philosopher s Zarathushtra in Tuplin Christopher ed Persian Responses Political and Cultural Interaction with in the Achaemenid Empire Swansea The Classical Press of Wales ISBN 978 1 910589 46 5 Whitehead Afred North 1953 1926 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 8External linksPythagoras at Wikipedia s sister projects Definitions from Wiktionary Media from Commons News from Wikinews Quotations from Wikiquote Texts from Wikisource Textbooks from Wikibooks Resources from Wikiversity Wikisource has the text of the 1911 Encyclopaedia Britannica article Pythagoras Pythagoras on In Our Time at the BBC Huffman Carl Pythagoras in Zalta Edward N ed 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 amp M University Pythagoras and Pythagoreanism The Catholic Encyclopedia Works by or about Pythagoras at Internet Archive Works by Pythagoras at LibriVox public domain audiobooks Portals Mathematics Music Astronomy Stars Society Philosophy Retrieved from https en wikipedia org w index php title Pythagoras amp oldid 1132210440, wikipedia, wiki, book, books, library,

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