Pythagoras of Samos (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC) was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism.
Pythagoras of Samos1 (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC)2 was an ancient IonianGreek philosopher, polymath, 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, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle.
In antiquity, Pythagoras was credited with mathematical and scientific discoveries, such as the Pythagorean theorem, Pythagorean tuning, the five regular solids, the theory of proportions, the sphericity of the Earth, the identity of the morning and evening stars as the planet Venus, and the division of the globe into five climatic zones. He was reputedly the first man to call himself a philosopher ("lover of wisdom").3 Historians debate whether Pythagoras made these discoveries and pronouncements, as some of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors, such as and .
This page is based on “Pythagoras” from English Wikipedia, (r1379710816) CC BY-SA 4.0 used under the license. The original authors are listed in its page history.
The teaching most securely identified with Pythagoras is the "transmigration of souls" or metempsychosis, 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 ratios and thus resonate to produce an inaudible symphony of music. Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy, and their meeting houses were burned. Pythagoras may have been killed during this persecution, or he may have escaped to Metapontum and died there.
Pythagoras influenced Plato whose dialogues (especially Timaeus) exhibit Pythagorean ideas. A major revival of his teachings occurred 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 Pythagoreanism had an influence on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was also used throughout early modern European esotericism, and his teachings as portrayed in Ovid's Metamorphoses would later influence the modern vegetarian movement.
Life
No authentic writings of Pythagoras have survived,45 and almost nothing is known for certain about his life.67 The earliest sources on Pythagoras's life, from Xenophanes, Heraclitus, Empedocles, Ion of Chios, and Herodotus8 are brief, ambiguous, and often satirical.910 The major sources on Pythagoras's life are three biographies from late antiquity written by Diogenes Laërtius, Porphyry, and Iamblichus, all of which are filled primarily with myths and legends71112 and which become longer and more fantastic in their descriptions of Pythagoras's achievements the more removed they are from Pythagoras's times.1112 However, Porphyry and Iamblichus also used some material taken from earlier writings in the 4th century BC by Aristotle's students Dicaearchus, Aristoxenus, and Heraclides Ponticus,13 which, when it can be identified, is generally considered to be the most reliable.13
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.
Herodotus15 and Isocrates agree that Pythagoras was the son of Mnesarchus1617 and that he was born on the Greek island of Samos in the eastern Aegean.41718 Mnesarchus is said to have been a gem-engraver or a wealthy merchant,192021 but his ancestry is disputed and unclear.22Apollonius of Tyana writes that Pythagoras's mother was Pythaïs, a woman who was said to be a descendant of Ancaeus, the mythical founder of Samos.2324Iamblichus 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, and Iamblichus also held to the belief that his mother descended from Ancaeus.25 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.26 Pythagoras's name led him to be associated with PythianApollo (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]".25
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.27 It was a major center of trade in the Aegean where traders brought goods from the Near East.4 According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions.4 Pythagoras's early life also coincided with the flowering of early Ionian natural philosophy.1728 He was a contemporary of the philosophers Anaximander and Anaximenes and of the historian Hecataeus, all of whom lived in Miletus, across the sea from Samos.28
Reputed travels
Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures, which appears to have been recognized by authors later in the Classical and Hellenistic periods, who attributed many of Pythagoras's unusual and unconventional beliefs to travels to far off lands, where he learned from those people himself.29 The doctrine of metempsychosis, or reincarnation of the soul after death, which Herodotus and Diogenes Laertius had attributed to the Egyptians, led to an elaborate tale30 where Pythagoras learned the Egyptian language from the PharaohAmasis II himself, and then traveled to study with the Egyptian priests at Diospolis (Thebes), where he was the only foreigner ever to be granted the privilege of taking part in their worship.29 Other ancient writers, however, claimed that Pythagoras had learned these teachings from the Magi in Persia or even from Zoroaster himself.3129 The Phoenicians are also reputed to have taught Pythagoras arithmetic and the Chaldeans to have taught him astronomy.29 By the third century BC, Pythagoras was also reported to have studied under the Jews as well.29 By the third century AD, Pythagoras was also reported by Philostratus to have studied under sages or gymnosophists in India and, according to Iamblichus, also with the Celts and Iberians.29
Alleged Greek teachers
Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers.32 Diogenes Laërtius asserts that Pythagoras later visited Crete, where he went to the Cave of Ida with Epimenides.33 Some identify Hermodamas of Samos as a possible tutor.3234 Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer.32 Others credit Bias of Priene, Thales,35 or Anaximander (a pupil of Thales).323536 Other traditions claim the mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphic Mysteries.32 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.32 Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship.37 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.37 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.32 Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent.38
Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros is mentioned most often.3839 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.38Apollonius Paradoxographus, a paradoxographer who may have lived in the second century BC, identified Pythagoras's thaumaturgic ideas as a result of Pherecydes's influence.38 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.38Duris, 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.38 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.38 Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis.38
In Croton
Porphyry repeats an account from Antiphon, who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle".4041 Here, Samians debated matters of public concern.4041 Supposedly, the school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach.40 Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends.4041 Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos,40 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.40
Around 530 BC, when Pythagoras was about forty years old, he left Samos.4174243 His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos;42 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.42 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.44 He arrived in the Greek colony of Croton (today's Crotone, in Calabria) in what was then Magna Graecia.1743454647 All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment.174849 He served as an advisor to the elites in Croton and gave them frequent advice.50 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.5152
Family and friends
Suda writes that Pythagoras had four children (Telauges, Mnesarchus, Myia and Arignote), and Diogenes Laertius records him as having had two brothers, Eunomus the elder and Tyrrhenus the second.5354 The wrestler Milo of Croton was said to have been a close associate of Pythagoras55 and was credited with having saved the philosopher's life when a roof was about to collapse.55 This association may have been the result of confusion with a different man named Pythagoras, who was an athletics trainer.40
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.56 After the victory, some prominent citizens of Croton proposed a democratic constitution, which the Pythagoreans rejected.56 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.57 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.5859 Accounts of the attack are often contradictory and many probably confused it with the later anti-Pythagorean rebellions, such as the one in Metapontum in 454 BC.5760 The building was apparently set on fire,58 and many of the assembled members perished;58 only the younger and more active members managed to escape.61
Sources disagree regarding whether Pythagoras was present when the attack occurred and, if he was, whether or not he managed to escape.1459 In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes.59 According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape,62 leading a small group of followers to the nearby city of Locris, where they pleaded for sanctuary, but were denied.62 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.14586263 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.62 Pythagoras managed to escape, but was so despondent at the deaths of his beloved students that he committed suicide.62 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.62 This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself.62
Teachings
Metempsychosis
Although the exact details of Pythagoras's teachings are uncertain,6465 it is possible to reconstruct a general outline of his main ideas.6466 Aristotle writes at length about the teachings of the Pythagoreans,6768 but without mentioning Pythagoras directly.6768 One of Pythagoras's main doctrines appears to have been metempsychosis,6970717273 the belief that all souls are immortal and that, after death, a soul is transferred into a new body.6972 This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus.6974 The earliest source on Pythagoras's metempsychosis is a satirical poem probably written after his death by the Greek philosopher Xenophanes of Colophon (c. 570 – c. 478 BC), who had been one of his contemporaries,7576 in which 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.77107567 Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur.78
Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations.79 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.808182 The first of these lives was as Aethalides the son of Hermes, who granted him the ability to remember all his past incarnations.83 Next, he was incarnated as Euphorbus, a minor hero from the Trojan War briefly mentioned in the Iliad.84 He then became the philosopher Hermotimus,85 who recognized the shield of Euphorbus in the temple of Apollo.85 His final incarnation was as Pyrrhus, a fisherman from Delos.85 One of his past lives, as reported by Dicaearchus, was as a beautiful courtesan.7086
Numerology
Another belief attributed to Pythagoras was that of the "harmony of the spheres",8788 which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony.8788 According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together.89
The so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything.
Modern scholars typically ascribe these discoveries to the later Pythagorean philosopher Philolaus of Croton (c. 470 – c. 385 BC), whose extant fragments are the earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras.90 In his landmark study Lore and Science in Ancient Pythagoreanism, Walter Burkert argues that Pythagoras was a charismatic political and religious teacher,91 but that the number philosophy attributed to him was really an innovation by Philolaus.92 According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics.91 Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, prooflessarithmetic,93 but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics.94 For the later Pythagoreans, Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the "perfect" number, ten.9596 The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance.97 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.9798
This shouldn't be confused with a simplified version known today as "Pythagorean numerology", involving a variant of an isopsephic technique known – among other names – as pythmenes 'roots'99 or 'base numbers',100 by means of which the base values of letters in a word were mathematically reduced by addition or division, in order to obtain a single value from one to nine for the whole name or word.99
Pythagoreanism
Communal lifestyle
Both Plato and Isocrates state that, above all else, Pythagoras was known as the founder of a new way of life.101102103 The organization Pythagoras founded at Croton was called a "school",104105 but, in many ways, resembled a monastery.106 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.107 The members of the sect shared all their possessions in common108 and were devoted to each other to the exclusion of outsiders.109110 Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans.111112 One Pythagorean maxim was "koinà tà phílōn" ("All things in common among friends").108 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 mankind.113 Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time.106 For Pythagoreans, the highest reward humans could attain was for their soul to join in the life of the gods and thus escape the cycle of reincarnation.114
Two groups existed within early Pythagoreanism: the mathematikoi ("learners") and the akousmatikoi ("listeners").115116 The akousmatikoi are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings;116 whereas the mathematikoi are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific.116 Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed the two approaches were compatible.116 The study of mathematics and music may have been connected to the worship of Apollo.117 The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body.89 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.89 The Pythagoreans also placed particular emphasis on the importance of physical exercise;106 therapeutic dancing, daily morning walks along scenic routes, and athletics were major components of the Pythagorean lifestyle.106 Moments of contemplation at the beginning and end of each day were also advised.118
Prohibitions and regulations
Pythagorean teachings were known as "symbols" (symbola)119 and members took a vow of silence that they would not reveal these symbols to non-members.119102120 Those who did not obey the laws of the community were expelled121 and the remaining members would erect tombstones for them as though they had died.121 A number of "oral sayings" (akoúsmata) attributed to Pythagoras have survived,67122 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.123 Many of these sayings emphasize the importance of ritual purity and avoiding defilement.12473 Other extant oral sayings forbid Pythagoreans from breaking bread, poking fires with swords, or picking up crumbs112 and teach that a person should always put the right sandal on before the left.112 The exact meanings of these sayings, however, are frequently obscure.125 Iamblichus preserves Aristotle's descriptions of the original, ritualistic intentions behind a few of these sayings,126 but these apparently later fell out of fashion, because Porphyry provides markedly different ethical-philosophical interpretations of them:127
New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five-year initiation period,41 during which they were required to remain silent.41 Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women128 and female members of Pythagoras's school appear to have played an active role in its operations.119128 Iamblichus provides a list of 235 famous Pythagoreans,129 seventeen of whom are women.129 In later times, many prominent female philosophers contributed to the development of Neopythagoreanism.130
Pythagoreanism also entailed a number of dietary prohibitions.73112131 It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beans132112 and the meat of non-sacrificial animals such as fish and poultry.133112 Both of these assumptions, however, have been contradicted.134135 Pythagorean dietary restrictions may have been motivated by belief in the doctrine of metempsychosis;102136137138 alternatively, they may be based on the genetic prevalence of favism, a type of enzyme deficiency anemia, in the Mediterranean.139 Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet.140102137Eudoxus 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."141142 Other authorities contradict this statement.143 According to Aristoxenus,144 Pythagoras allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and rams.142145 According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices142 and established a diet for athletes dependent on meat.142
Legends
Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends.11146 Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure.147148 In a fragment, Aristotle writes that Pythagoras had a golden thigh,147149150 which he publicly exhibited at the Olympic Games147 and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo".147151 Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications.152 He was supposedly once seen at both Metapontum and Croton at the same time.15311149150 When Pythagoras crossed the river Kosas (the modern-day Basento), "several witnesses" reported that they heard it greet him by name.154149 In Roman times, a legend claimed that Pythagoras was the son of Apollo.150
Pythagoras was said to have dressed all in white.147155 He is also said to have borne a golden wreath atop his head147 and to have worn trousers after the fashion of the Thracians.147 Pythagoras was said to have had extraordinary success in dealing with animals.11156 A fragment from Aristotle records that, when a deadly snake bit Pythagoras, he bit it back and killed it.152149 Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans11156 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.11156 Riedweg suggests that Pythagoras may have personally encouraged these legends,146 but Gregory states that there is no direct evidence of this.116
Attributed discoveries
In mathematics
Although Pythagoras is most famous today for his alleged mathematical discoveries,157158 classical historians dispute whether he himself ever actually made any significant contributions to the field.9391 Many mathematical and scientific discoveries were attributed to Pythagoras, including the famous theorem named for him,159 as well as discoveries in the fields of music,160astronomy,161 and medicine.162 Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides"163—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.163164 Cicero rejected this story as spurious163 because of the much more widely held belief that Pythagoras forbade blood sacrifices.163 Porphyry attempted to explain the story by asserting that the ox was actually made of dough.163
The geometric principles underlying the Pythagorean theorem were known and used in earlier traditions. They appear in Babylonian mathematics, such as the Plimpton 322 tablet, and were explicitly formulated in ancient India by Baudhayana as the bhujā-koṭi-karṇa-nyāya 'rule of the diagonal', in the Baudhayana Sulbsutra (c. 800–500 BC).165166167163168 Burkert rejects the suggestion that Pythagoras had anything to do with the theorem,169 noting that Pythagoras was never credited with having proved any theorem in antiquity.169 Riedweg stresses that "there is certainly no reason to suppose that either Pythagoras himself or any early Pythagorean could have provided a deductive proof of the theorem".168 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.170
In music
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.171172 Thinking that the sounds of the hammers were beautiful and harmonious, except for one,173 he rushed into the blacksmith shop and began testing the hammers.173 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.172173
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,174 the first to divide the globe into five climatic zones,174 and the first to identify the morning star and the evening star as the same celestial object (now known as Venus).175 Of the two philosophers, Parmenides has a much stronger claim to having been the first176 and the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem.175Empedocles, who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical.177 By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals.178
Later influence in antiquity
On Greek philosophy
Sizeable Pythagorean communities existed in Magna Graecia, Phlius, and Thebes during the early fourth century BC.179 Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia.180 According to later tradition, Archytas was elected as strategos ("general") seven times, even though others were prohibited from serving more than a year.180 Archytas was also a renowned mathematician and musician.181 He was a close friend of Plato182 and he is quoted in Plato's Republic.183184 Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans.185186187 Cicero repeats this statement, remarking that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean").188 According to Charles H. Kahn, Plato's middle dialogues, including Meno, Phaedo, and The Republic, have a strong "Pythagorean coloring",189 and his last few dialogues (particularly Philebus and Timaeus)190 are extremely Pythagorean in character.190
The poet Heraclitus of Ephesus (fl. c. 500 BC), who was born a few miles across the sea from Samos and may have lived within Pythagoras's lifetime,191 mocked Pythagoras as a clever charlatan,9191 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."9191Alcmaeon of Croton (fl. c. 450 BC), a doctor who lived in Croton at around the same time Pythagoras lived there,75 incorporates many Pythagorean teachings into his writings192 and alludes to having possibly known Pythagoras personally.192 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.193
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.194 Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy, science, and morality.194 Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world"194 and both were probably influenced by Orphism.194 The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans.195
A revival of Pythagorean teachings occurred in the first century BC196 when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed the rise of a "new" Pythagoreanism in Alexandria.197 At around the same time, Neopythagoreanism became prominent.198 The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings.199 The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy199 and probably understood the soul as a "kind of mathematical harmony".199 The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory.198Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines.200
On art and architecture
The oldest known building designed according to Pythagorean teachings is the Porta Maggiore Basilica,201 a subterranean basilica which was built during the reign of the Roman emperor Nero as a secret place of worship for Pythagoreans.202 The basilica was built underground because of the Pythagorean emphasis on secrecy203 and also because of the legend that Pythagoras had sequestered himself in a cave on Samos.204 The basilica's apse is in the east and its atrium in the west out of respect for the rising sun.205 It has a narrow entrance leading to a small pool where the initiates could purify themselves.206 The building is also designed according to Pythagorean numerology,207 with each table in the sanctuary providing seats for seven people.208 Three aisles lead to a single altar, symbolizing the three parts of the soul approaching the unity of Apollo.208 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,209 symbolizing Pythagorean teachings about the immortality of the soul.209 The interior of the sanctuary is almost entirely white because the color white was regarded by Pythagoreans as sacred.210
The emperor Hadrian's Pantheon in Rome was also built based on Pythagorean numerology.211 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.212 The single oculus at the top of the dome symbolizes the monad and the sun-god Apollo.213 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.214 The five coffered rings beneath the ribs represent the marriage of the sun and moon.215
In early Christianity
Many early Christians had a deep respect for Pythagoras.216Eusebius (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.217 In another work, Eusebius compares Pythagoras to Moses.217 In one of his letters, the Church FatherJerome (c. 347 – c. 420 AD) praises Pythagoras for his wisdom217 and, in another letter, he credits Pythagoras for his belief in the immortality of the soul, which he suggests Christians inherited from him.218Augustine of Hippo (354–430 AD) rejected Pythagoras's teaching of metempsychosis without explicitly naming him, but otherwise expressed admiration for him.219 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".220 In another passage, Augustine defends Pythagoras's reputation, arguing that Pythagoras certainly never taught the doctrine of metempsychosis.220
Influence after antiquity
In the Middle Ages
During the Middle Ages, Pythagoras was revered as the founder of mathematics and music, two of the Seven Liberal Arts.221 He appears in numerous medieval depictions, in illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres.221 The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe,221 which led William of Conches (c. 1080–1160) to declare that Plato was Pythagorean.221 In the 1430s, the Camaldolese friar Ambrose Traversari translated Diogenes Laërtius's Lives and Opinions of Eminent Philosophers from Greek into Latin221 and, in the 1460s, the philosopher Marsilio Ficino translated Porphyry and Iamblichus's Lives of Pythagoras into Latin as well,221 thereby allowing them to be read and studied by western scholars.221 In 1494, the Greek Neopythagorean scholar Constantine Lascaris published The Golden Verses of Pythagoras, translated into Latin, with a printed edition of his Grammatica,222 thereby bringing them to a widespread audience.222 In 1499, he published the first Renaissance biography of Pythagoras in his work Vitae illustrium philosophorum siculorum et calabrorum, issued in Messina.222
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,221223 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.223Johannes Kepler considered himself to be a Pythagorean.221224 He believed in the Pythagorean doctrine of musica universalis and it was his search for the mathematical equations behind this doctrine that led to his discovery of the laws of planetary motion. Kepler titled his book on the subject Harmonices Mundi (Harmonics of the World), after the Pythagorean teaching that had inspired him.221225 He also called Pythagoras the "grandfather" of all Copernicans.226
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."227 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".228 By this measure, Whitehead declared that Einstein and other modern scientists like him are "following the pure Pythagorean tradition."227229
On vegetarianism
A fictionalized portrayal of Pythagoras appears in Book XV of Ovid's Metamorphoses,230 in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet.231 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.231John Donne's Progress of the Soul discusses the implications of the doctrines expounded in the speech,232 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.232John Dryden included a translation of the scene with Pythagoras in his 1700 work Fables, Ancient and Modern,232 and John Gay's 1726 fable "Pythagoras and the Countryman" reiterates its major themes, linking carnivorism with tyranny.232Lord Chesterfield records that his conversion to vegetarianism had been motivated by reading Pythagoras's speech in Ovid's Metamorphoses.232 Until the word vegetarianism was coined in the 1840s, vegetarians were referred to in English as "Pythagoreans".232
On Western esotericism
Early modern European esotericism drew heavily on the teachings of Pythagoras.221 The German humanist scholar Johannes Reuchlin (1455–1522) synthesized Pythagoreanism with Christian theology and Jewish Kabbalah,233 arguing that Kabbalah and Pythagoreanism were both inspired by Mosaic tradition234 and that Pythagoras was therefore a kabbalist.234 In his dialogue De verbo mirifico (1494), Reuchlin compared the Pythagorean tetractys to the ineffable divine name YHWH,233 ascribing each of the four letters of the tetragrammaton a symbolic meaning according to Pythagorean mystical teachings.234
Heinrich Cornelius Agrippa's popular and influential three-volume treatise De Occulta Philosophia cites Pythagoras as a "religious magi"235 and advances the idea that Pythagoras's mystical numerology operates on a supercelestial level,235 a religious term used to describe a high heavenly realm used during his time. The freemasons deliberately modeled their society on the community founded by Pythagoras at Croton.236Rosicrucianism used Pythagorean symbolism,221 as did Robert Fludd (1574–1637),221 who believed his own musical writings to have been inspired by Pythagoras.221John Dee was heavily influenced by Pythagorean ideology,237235 particularly the teaching that all things are made of numbers.237235
On literature
The Transcendentalists read the ancient Lives of Pythagoras as guides on how to live a model life.238Henry David Thoreau was impacted by Thomas Taylor's translations of Iamblichus's Life of Pythagoras and Stobaeus's Pythagoric Sayings238 and his views on nature may have been influenced by the Pythagorean idea of images corresponding to archetypes.238 The Pythagorean teaching of musica universalis is a recurring theme throughout Thoreau's magnum opus, Walden.238
Bibliography
Classical sources
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Herodotus (1920) [c. 430 BC]. "Book II". The Persian Wars. Vol. I. Translated by Godley, A. D. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC966656476 – via Perseus Digital Library (perseus.tufts.edu).
——— (1920) [c. 430 BC]. "Book IV". The Persian Wars. Vol. II. Translated by Godley, A. D. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC966656315 – via Perseus Digital Library (perseus.tufts.edu).
——— (1931) [c. 350 BC]. "De Anima". In Ross, W.D. (ed.). The Works of Aristotle Translated into English. Vol. 3. Translated by Smith, J. A. Oxford: Oxford University Press. OCLC237147799 – via The Internet Classics Archive (classics.mit.edu).
——— (1933) [c. 350 BC]. "Book I". Metaphysics Books I–IX. Vol. XVII. Translated by Tredennick, Hugh. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC958278244 – via Perseus Digital Library (perseus.tufts.edu).
Cicero (1928) [c. 52 BC]. "De Re Publica". On the Republic. On the Laws (De Re Publica. De Legibus). Vol. XVI. Translated by Keyes, Clinton W. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC298443420 – via Internet Archive.
——— (1928) [c. 52 BC]. "De Legibus". On the Republic. On the Laws (De Re Publica. De Legibus). Vol. XVI. Translated by Keyes, Clinton W. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC298443420 – via Internet Archive.
——— (1927) [c. 44 BC]. "De Divinatione I". On Old Age. On Friendship. On Divination (De Senectute, De Amicitia, De Divinatione). Vol. XX. Translated by W. A., Falconer. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC298443420 – via Internet Archive.
——— (1913) [c. 44 BC]. On Duties (De officiis). Vol. XXI. Translated by Miller, Walter. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC298443420 – via Internet Archive.
——— (1968) [c. 100 AD]. "On the Signs of Socrates (De Genio Socratis)". Plutarch's Moralia. Vol. VII. Translated by De Lacy, Phillip H.; Einarson, Benedict. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC938641243 – via Internet Archive.
——— (1957) [c. 100 AD]. "On the Eating of Flesh (Du Esu Carnium)". Plutarch's Moralia. Vol. XII. Translated by Helmbold, William C.; Cherniss, Harold. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd – via Internet Archive.
——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC758307224 – via Wikisource.
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.
Burkert, Walter (May 1960). "Platon oder Pythagoras?: Zum Ursprung des Wortes 'Philosophie'". Hermes (in German). 88 (2): 159–177. JSTOR4475110.
——— (1985). Greek Religion. Translated by Raffan, John. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-36281-9.
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.
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.
De Vogel, Cornelia J. (1966). Pythagoras and Early Pythagoreanism: An Interpretation of Neglected Evidence on the Philosopher Pythagoras. Assen: Van Gorcum. OCLC513833.
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.
Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8.
Lloyd, Geoffrey (24 April 2014). "Pythagoras". In Huffman, Carl A. (ed.). A History of Pythagoreanism. Cambridge University Press. pp. 24–45. ISBN 978-1-139-91598-4. Retrieved 18 May 2025.
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.
Russo, Attilio (2004). "Costantino Lascaris tra fama e oblio nel Cinquecento messinese". Archivio Storico Messinese. LXXXIV–LXXXV: 5–87, especially 51–53. ISSN0392-0240.
Horky, Philip Sydney (2013). Plato and Pythagoreanism. Oxford, England: Oxford University Press. ISBN 978-0-19-989822-0.
Kingsley, Peter (1995). Ancient Philosophy, Mystery, and Magic: Empedocles and the Pythagorean Tradition. Oxford, England: Oxford University Press.
Scharinger, Stephan (2017). Die Wunder des Pythagoras: Überlieferungen im Vergleich [The miracles of Pythagoras: A comparison of traditions]. Philippika, vol. 107. Wiesbaden: Harrassowitz. ISBN 978-3-447-10787-7.
/paɪˈθæɡərəs/ py-THAG-ər-əs,2 also US: /pɪˈθæɡərəs/ pih-;3Ancient Greek: Πυθαγόρας ὁ Σάμιος, romanized: Pythagóras ho Sámios, lit. 'Pythagoras the Samian', or Πυθαγόρης, Pythagórēs in Ionian Greek. ↩
"The dates of his life cannot be fixed exactly, but assuming the approximate correctness of the statement of Aristoxenus (Porphyry, Vit. Pyth, §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." Guthrie (1967), p. 173 ↩
Some writers call him a native Samian, a Tyrrhenian from Lemnos, or a Phliasian from Peloponnesus, and give Marmacus or Demaratus as his name (see Diog VIII, §1.1; Porphyry, Vit. Pyth, §1, §2; Justin, xx. 4; Pausanias, ii. 13; Iamblichus, Vit. Pyth, §2.4). Porphyry, in particular, presents a conflicting report by Neanthes, that Mnesarchus was born in Tyre (in Lebanon), or that he was a Tyrrhenian from Lemnos; however, the confusion was possibly due to the similarity of the names "Tyre" and "Tyrrhenian", while it has also been suggested that Porphyry's own background from Tyre, could explain why his work was the only one, out of the three biographies of Pythagoras that have survived from late antiquity, to have linked Pythagoras's father with it.22 Due to the obscurity surrounding his background, some modern scholars deem it safer to accept "that Pythagoras and his father were pure-blooded Greeks, of undiluted Samian stock".23↩
Xenophanes's Poem (or Elegies) on Pythagorus is provided below, which was preserved in Diog VIII, §1.36: - Greek: περὶ δὲ τοῦ ἄλλοτε ἄλλον γεγενῆσθαι (Pythagoras) Ζενοφάνης ἐν ἐλεγείαι προσμαρτυρεῖ, ἧς ἀρχή 'νῦν ... κέλενθον'. ὃ δὲ περὶ αὐτοῦ (Pythagoras) φησιν, οὕτως ἔχει καί ... αἰών'. νῦν αὖτ' ἄλλον ἔπειμι λόγον, δείξω δὲ κέλευθον. καί ποτέ μιν στυφελιζομένου σκύλακος παριόντα φασὶν ἐποικτῖραι καὶ τόδε φάσθαι ἔπος "παῦσαι μηδὲ ῥάπιζε, ἐπεὶ ἡ φίλου ἀνέρος ἐστὶν ψυχή, τὴν ἔγνων φθεγξαμένης αὐδῆς." DK 21B7, p. 130 - English: "And now I will turn to another tale and point the way. ... Once they say that he (Pythagoras) was passing by when a dog was being beaten and spoke this word: "Stop! don't beat it! For it is the soul of a friend that I recognised when I heard its voice." Burnet (1920), p. 118 ↩
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). ↩
Pythagoras of Samos1 (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC)2 was an ancient IonianGreek philosopher, polymath, 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, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle.
In antiquity, Pythagoras was credited with mathematical and scientific discoveries, such as the Pythagorean theorem, Pythagorean tuning, the five regular solids, the theory of proportions, the sphericity of the Earth, the identity of the morning and evening stars as the planet Venus, and the division of the globe into five climatic zones. He was reputedly the first man to call himself a philosopher ("lover of wisdom"). Historians debate whether Pythagoras made these discoveries and pronouncements, as some of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors, such as and .
The teaching most securely identified with Pythagoras is the "transmigration of souls" or metempsychosis, 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 ratios and thus resonate to produce an inaudible symphony of music. Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy, and their meeting houses were burned. Pythagoras may have been killed during this persecution, or he may have escaped to Metapontum and died there.
Pythagoras influenced Plato whose dialogues (especially Timaeus) exhibit Pythagorean ideas. A major revival of his teachings occurred 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 Pythagoreanism had an influence on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was also used throughout early modern European esotericism, and his teachings as portrayed in Ovid's Metamorphoses would later influence the modern vegetarian movement.
Life
No authentic writings of Pythagoras have survived,45 and almost nothing is known for certain about his life.67 The earliest sources on Pythagoras's life, from Xenophanes, Heraclitus, Empedocles, Ion of Chios, and Herodotus8 are brief, ambiguous, and often satirical.910 The major sources on Pythagoras's life are three biographies from late antiquity written by Diogenes Laërtius, Porphyry, and Iamblichus, all of which are filled primarily with myths and legends71112 and which become longer and more fantastic in their descriptions of Pythagoras's achievements the more removed they are from Pythagoras's times.1112 However, Porphyry and Iamblichus also used some material taken from earlier writings in the 4th century BC by Aristotle's students Dicaearchus, Aristoxenus, and Heraclides Ponticus,13 which, when it can be identified, is generally considered to be the most reliable.13
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.
Herodotus15 and Isocrates agree that Pythagoras was the son of Mnesarchus1617 and that he was born on the Greek island of Samos in the eastern Aegean.41718 Mnesarchus is said to have been a gem-engraver or a wealthy merchant,192021 but his ancestry is disputed and unclear.22Apollonius of Tyana writes that Pythagoras's mother was Pythaïs, a woman who was said to be a descendant of Ancaeus, the mythical founder of Samos.2324Iamblichus 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, and Iamblichus also held to the belief that his mother descended from Ancaeus.25 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.26 Pythagoras's name led him to be associated with PythianApollo (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]".25
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.27 It was a major center of trade in the Aegean where traders brought goods from the Near East.4 According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions.4 Pythagoras's early life also coincided with the flowering of early Ionian natural philosophy.1728 He was a contemporary of the philosophers Anaximander and Anaximenes and of the historian Hecataeus, all of whom lived in Miletus, across the sea from Samos.28
Reputed travels
Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures, which appears to have been recognized by authors later in the Classical and Hellenistic periods, who attributed many of Pythagoras's unusual and unconventional beliefs to travels to far off lands, where he learned from those people himself.29 The doctrine of metempsychosis, or reincarnation of the soul after death, which Herodotus and Diogenes Laertius had attributed to the Egyptians, led to an elaborate tale30 where Pythagoras learned the Egyptian language from the PharaohAmasis II himself, and then traveled to study with the Egyptian priests at Diospolis (Thebes), where he was the only foreigner ever to be granted the privilege of taking part in their worship.29 Other ancient writers, however, claimed that Pythagoras had learned these teachings from the Magi in Persia or even from Zoroaster himself.3129 The Phoenicians are also reputed to have taught Pythagoras arithmetic and the Chaldeans to have taught him astronomy.29 By the third century BC, Pythagoras was also reported to have studied under the Jews as well.29 By the third century AD, Pythagoras was also reported by Philostratus to have studied under sages or gymnosophists in India and, according to Iamblichus, also with the Celts and Iberians.29
Alleged Greek teachers
Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers.32 Diogenes Laërtius asserts that Pythagoras later visited Crete, where he went to the Cave of Ida with Epimenides.33 Some identify Hermodamas of Samos as a possible tutor.3234 Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer.32 Others credit Bias of Priene, Thales,35 or Anaximander (a pupil of Thales).323536 Other traditions claim the mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphic Mysteries.32 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.32 Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship.37 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.37 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.32 Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent.38
Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros is mentioned most often.3839 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.38Apollonius Paradoxographus, a paradoxographer who may have lived in the second century BC, identified Pythagoras's thaumaturgic ideas as a result of Pherecydes's influence.38 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.38Duris, 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.38 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.38 Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis.38
In Croton
Porphyry repeats an account from Antiphon, who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle".4041 Here, Samians debated matters of public concern.4041 Supposedly, the school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach.40 Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends.4041 Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos,40 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.40
Around 530 BC, when Pythagoras was about forty years old, he left Samos.4174243 His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos;42 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.42 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.44 He arrived in the Greek colony of Croton (today's Crotone, in Calabria) in what was then Magna Graecia.1743454647 All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment.174849 He served as an advisor to the elites in Croton and gave them frequent advice.50 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.5152
Family and friends
Suda writes that Pythagoras had four children (Telauges, Mnesarchus, Myia and Arignote), and Diogenes Laertius records him as having had two brothers, Eunomus the elder and Tyrrhenus the second.5354 The wrestler Milo of Croton was said to have been a close associate of Pythagoras55 and was credited with having saved the philosopher's life when a roof was about to collapse.55 This association may have been the result of confusion with a different man named Pythagoras, who was an athletics trainer.40
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.56 After the victory, some prominent citizens of Croton proposed a democratic constitution, which the Pythagoreans rejected.56 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.57 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.5859 Accounts of the attack are often contradictory and many probably confused it with the later anti-Pythagorean rebellions, such as the one in Metapontum in 454 BC.5760 The building was apparently set on fire,58 and many of the assembled members perished;58 only the younger and more active members managed to escape.61
Sources disagree regarding whether Pythagoras was present when the attack occurred and, if he was, whether or not he managed to escape.1459 In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes.59 According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape,62 leading a small group of followers to the nearby city of Locris, where they pleaded for sanctuary, but were denied.62 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.14586263 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.62 Pythagoras managed to escape, but was so despondent at the deaths of his beloved students that he committed suicide.62 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.62 This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself.62
Teachings
Metempsychosis
Although the exact details of Pythagoras's teachings are uncertain,6465 it is possible to reconstruct a general outline of his main ideas.6466 Aristotle writes at length about the teachings of the Pythagoreans,6768 but without mentioning Pythagoras directly.6768 One of Pythagoras's main doctrines appears to have been metempsychosis,6970717273 the belief that all souls are immortal and that, after death, a soul is transferred into a new body.6972 This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus.6974 The earliest source on Pythagoras's metempsychosis is a satirical poem probably written after his death by the Greek philosopher Xenophanes of Colophon (c. 570 – c. 478 BC), who had been one of his contemporaries,7576 in which 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.77107567 Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur.78
Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations.79 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.808182 The first of these lives was as Aethalides the son of Hermes, who granted him the ability to remember all his past incarnations.83 Next, he was incarnated as Euphorbus, a minor hero from the Trojan War briefly mentioned in the Iliad.84 He then became the philosopher Hermotimus,85 who recognized the shield of Euphorbus in the temple of Apollo.85 His final incarnation was as Pyrrhus, a fisherman from Delos.85 One of his past lives, as reported by Dicaearchus, was as a beautiful courtesan.7086
Numerology
Another belief attributed to Pythagoras was that of the "harmony of the spheres",8788 which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony.8788 According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together.89
The so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything.
Modern scholars typically ascribe these discoveries to the later Pythagorean philosopher Philolaus of Croton (c. 470 – c. 385 BC), whose extant fragments are the earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras.90 In his landmark study Lore and Science in Ancient Pythagoreanism, Walter Burkert argues that Pythagoras was a charismatic political and religious teacher,91 but that the number philosophy attributed to him was really an innovation by Philolaus.92 According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics.91 Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, prooflessarithmetic,93 but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics.94 For the later Pythagoreans, Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the "perfect" number, ten.9596 The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance.97 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.9798
This shouldn't be confused with a simplified version known today as "Pythagorean numerology", involving a variant of an isopsephic technique known – among other names – as pythmenes 'roots'99 or 'base numbers',100 by means of which the base values of letters in a word were mathematically reduced by addition or division, in order to obtain a single value from one to nine for the whole name or word.99
Pythagoreanism
Communal lifestyle
Both Plato and Isocrates state that, above all else, Pythagoras was known as the founder of a new way of life.101102103 The organization Pythagoras founded at Croton was called a "school",104105 but, in many ways, resembled a monastery.106 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.107 The members of the sect shared all their possessions in common108 and were devoted to each other to the exclusion of outsiders.109110 Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans.111112 One Pythagorean maxim was "koinà tà phílōn" ("All things in common among friends").108 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 mankind.113 Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time.106 For Pythagoreans, the highest reward humans could attain was for their soul to join in the life of the gods and thus escape the cycle of reincarnation.114
Two groups existed within early Pythagoreanism: the mathematikoi ("learners") and the akousmatikoi ("listeners").115116 The akousmatikoi are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings;116 whereas the mathematikoi are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific.116 Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed the two approaches were compatible.116 The study of mathematics and music may have been connected to the worship of Apollo.117 The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body.89 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.89 The Pythagoreans also placed particular emphasis on the importance of physical exercise;106 therapeutic dancing, daily morning walks along scenic routes, and athletics were major components of the Pythagorean lifestyle.106 Moments of contemplation at the beginning and end of each day were also advised.118
Prohibitions and regulations
Pythagorean teachings were known as "symbols" (symbola)119 and members took a vow of silence that they would not reveal these symbols to non-members.119102120 Those who did not obey the laws of the community were expelled121 and the remaining members would erect tombstones for them as though they had died.121 A number of "oral sayings" (akoúsmata) attributed to Pythagoras have survived,67122 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.123 Many of these sayings emphasize the importance of ritual purity and avoiding defilement.12473 Other extant oral sayings forbid Pythagoreans from breaking bread, poking fires with swords, or picking up crumbs112 and teach that a person should always put the right sandal on before the left.112 The exact meanings of these sayings, however, are frequently obscure.125 Iamblichus preserves Aristotle's descriptions of the original, ritualistic intentions behind a few of these sayings,126 but these apparently later fell out of fashion, because Porphyry provides markedly different ethical-philosophical interpretations of them:127
New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five-year initiation period,41 during which they were required to remain silent.41 Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women128 and female members of Pythagoras's school appear to have played an active role in its operations.119128 Iamblichus provides a list of 235 famous Pythagoreans,129 seventeen of whom are women.129 In later times, many prominent female philosophers contributed to the development of Neopythagoreanism.130
Pythagoreanism also entailed a number of dietary prohibitions.73112131 It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beans132112 and the meat of non-sacrificial animals such as fish and poultry.133112 Both of these assumptions, however, have been contradicted.134135 Pythagorean dietary restrictions may have been motivated by belief in the doctrine of metempsychosis;102136137138 alternatively, they may be based on the genetic prevalence of favism, a type of enzyme deficiency anemia, in the Mediterranean.139 Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet.140102137Eudoxus 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."141142 Other authorities contradict this statement.143 According to Aristoxenus,144 Pythagoras allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and rams.142145 According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices142 and established a diet for athletes dependent on meat.142
Legends
Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends.11146 Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure.147148 In a fragment, Aristotle writes that Pythagoras had a golden thigh,147149150 which he publicly exhibited at the Olympic Games147 and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo".147151 Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications.152 He was supposedly once seen at both Metapontum and Croton at the same time.15311149150 When Pythagoras crossed the river Kosas (the modern-day Basento), "several witnesses" reported that they heard it greet him by name.154149 In Roman times, a legend claimed that Pythagoras was the son of Apollo.150
Pythagoras was said to have dressed all in white.147155 He is also said to have borne a golden wreath atop his head147 and to have worn trousers after the fashion of the Thracians.147 Pythagoras was said to have had extraordinary success in dealing with animals.11156 A fragment from Aristotle records that, when a deadly snake bit Pythagoras, he bit it back and killed it.152149 Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans11156 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.11156 Riedweg suggests that Pythagoras may have personally encouraged these legends,146 but Gregory states that there is no direct evidence of this.116
Attributed discoveries
In mathematics
Although Pythagoras is most famous today for his alleged mathematical discoveries,157158 classical historians dispute whether he himself ever actually made any significant contributions to the field.9391 Many mathematical and scientific discoveries were attributed to Pythagoras, including the famous theorem named for him,159 as well as discoveries in the fields of music,160astronomy,161 and medicine.162 Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides"163—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.163164 Cicero rejected this story as spurious163 because of the much more widely held belief that Pythagoras forbade blood sacrifices.163 Porphyry attempted to explain the story by asserting that the ox was actually made of dough.163
The geometric principles underlying the Pythagorean theorem were known and used in earlier traditions. They appear in Babylonian mathematics, such as the Plimpton 322 tablet, and were explicitly formulated in ancient India by Baudhayana as the bhujā-koṭi-karṇa-nyāya 'rule of the diagonal', in the Baudhayana Sulbsutra (c. 800–500 BC).165166167163168 Burkert rejects the suggestion that Pythagoras had anything to do with the theorem,169 noting that Pythagoras was never credited with having proved any theorem in antiquity.169 Riedweg stresses that "there is certainly no reason to suppose that either Pythagoras himself or any early Pythagorean could have provided a deductive proof of the theorem".168 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.170
In music
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.171172 Thinking that the sounds of the hammers were beautiful and harmonious, except for one,173 he rushed into the blacksmith shop and began testing the hammers.173 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.172173
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,174 the first to divide the globe into five climatic zones,174 and the first to identify the morning star and the evening star as the same celestial object (now known as Venus).175 Of the two philosophers, Parmenides has a much stronger claim to having been the first176 and the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem.175Empedocles, who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical.177 By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals.178
Later influence in antiquity
On Greek philosophy
Sizeable Pythagorean communities existed in Magna Graecia, Phlius, and Thebes during the early fourth century BC.179 Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia.180 According to later tradition, Archytas was elected as strategos ("general") seven times, even though others were prohibited from serving more than a year.180 Archytas was also a renowned mathematician and musician.181 He was a close friend of Plato182 and he is quoted in Plato's Republic.183184 Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans.185186187 Cicero repeats this statement, remarking that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean").188 According to Charles H. Kahn, Plato's middle dialogues, including Meno, Phaedo, and The Republic, have a strong "Pythagorean coloring",189 and his last few dialogues (particularly Philebus and Timaeus)190 are extremely Pythagorean in character.190
The poet Heraclitus of Ephesus (fl. c. 500 BC), who was born a few miles across the sea from Samos and may have lived within Pythagoras's lifetime,191 mocked Pythagoras as a clever charlatan,9191 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."9191Alcmaeon of Croton (fl. c. 450 BC), a doctor who lived in Croton at around the same time Pythagoras lived there,75 incorporates many Pythagorean teachings into his writings192 and alludes to having possibly known Pythagoras personally.192 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.193
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.194 Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy, science, and morality.194 Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world"194 and both were probably influenced by Orphism.194 The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans.195
A revival of Pythagorean teachings occurred in the first century BC196 when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed the rise of a "new" Pythagoreanism in Alexandria.197 At around the same time, Neopythagoreanism became prominent.198 The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings.199 The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy199 and probably understood the soul as a "kind of mathematical harmony".199 The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory.198Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines.200
On art and architecture
The oldest known building designed according to Pythagorean teachings is the Porta Maggiore Basilica,201 a subterranean basilica which was built during the reign of the Roman emperor Nero as a secret place of worship for Pythagoreans.202 The basilica was built underground because of the Pythagorean emphasis on secrecy203 and also because of the legend that Pythagoras had sequestered himself in a cave on Samos.204 The basilica's apse is in the east and its atrium in the west out of respect for the rising sun.205 It has a narrow entrance leading to a small pool where the initiates could purify themselves.206 The building is also designed according to Pythagorean numerology,207 with each table in the sanctuary providing seats for seven people.208 Three aisles lead to a single altar, symbolizing the three parts of the soul approaching the unity of Apollo.208 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,209 symbolizing Pythagorean teachings about the immortality of the soul.209 The interior of the sanctuary is almost entirely white because the color white was regarded by Pythagoreans as sacred.210
The emperor Hadrian's Pantheon in Rome was also built based on Pythagorean numerology.211 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.212 The single oculus at the top of the dome symbolizes the monad and the sun-god Apollo.213 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.214 The five coffered rings beneath the ribs represent the marriage of the sun and moon.215
In early Christianity
Many early Christians had a deep respect for Pythagoras.216Eusebius (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.217 In another work, Eusebius compares Pythagoras to Moses.217 In one of his letters, the Church FatherJerome (c. 347 – c. 420 AD) praises Pythagoras for his wisdom217 and, in another letter, he credits Pythagoras for his belief in the immortality of the soul, which he suggests Christians inherited from him.218Augustine of Hippo (354–430 AD) rejected Pythagoras's teaching of metempsychosis without explicitly naming him, but otherwise expressed admiration for him.219 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".220 In another passage, Augustine defends Pythagoras's reputation, arguing that Pythagoras certainly never taught the doctrine of metempsychosis.220
Influence after antiquity
In the Middle Ages
During the Middle Ages, Pythagoras was revered as the founder of mathematics and music, two of the Seven Liberal Arts.221 He appears in numerous medieval depictions, in illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres.221 The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe,221 which led William of Conches (c. 1080–1160) to declare that Plato was Pythagorean.221 In the 1430s, the Camaldolese friar Ambrose Traversari translated Diogenes Laërtius's Lives and Opinions of Eminent Philosophers from Greek into Latin221 and, in the 1460s, the philosopher Marsilio Ficino translated Porphyry and Iamblichus's Lives of Pythagoras into Latin as well,221 thereby allowing them to be read and studied by western scholars.221 In 1494, the Greek Neopythagorean scholar Constantine Lascaris published The Golden Verses of Pythagoras, translated into Latin, with a printed edition of his Grammatica,222 thereby bringing them to a widespread audience.222 In 1499, he published the first Renaissance biography of Pythagoras in his work Vitae illustrium philosophorum siculorum et calabrorum, issued in Messina.222
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,221223 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.223Johannes Kepler considered himself to be a Pythagorean.221224 He believed in the Pythagorean doctrine of musica universalis and it was his search for the mathematical equations behind this doctrine that led to his discovery of the laws of planetary motion. Kepler titled his book on the subject Harmonices Mundi (Harmonics of the World), after the Pythagorean teaching that had inspired him.221225 He also called Pythagoras the "grandfather" of all Copernicans.226
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."227 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".228 By this measure, Whitehead declared that Einstein and other modern scientists like him are "following the pure Pythagorean tradition."227229
On vegetarianism
A fictionalized portrayal of Pythagoras appears in Book XV of Ovid's Metamorphoses,230 in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet.231 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.231John Donne's Progress of the Soul discusses the implications of the doctrines expounded in the speech,232 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.232John Dryden included a translation of the scene with Pythagoras in his 1700 work Fables, Ancient and Modern,232 and John Gay's 1726 fable "Pythagoras and the Countryman" reiterates its major themes, linking carnivorism with tyranny.232Lord Chesterfield records that his conversion to vegetarianism had been motivated by reading Pythagoras's speech in Ovid's Metamorphoses.232 Until the word vegetarianism was coined in the 1840s, vegetarians were referred to in English as "Pythagoreans".232
On Western esotericism
Early modern European esotericism drew heavily on the teachings of Pythagoras.221 The German humanist scholar Johannes Reuchlin (1455–1522) synthesized Pythagoreanism with Christian theology and Jewish Kabbalah,233 arguing that Kabbalah and Pythagoreanism were both inspired by Mosaic tradition234 and that Pythagoras was therefore a kabbalist.234 In his dialogue De verbo mirifico (1494), Reuchlin compared the Pythagorean tetractys to the ineffable divine name YHWH,233 ascribing each of the four letters of the tetragrammaton a symbolic meaning according to Pythagorean mystical teachings.234
Heinrich Cornelius Agrippa's popular and influential three-volume treatise De Occulta Philosophia cites Pythagoras as a "religious magi"235 and advances the idea that Pythagoras's mystical numerology operates on a supercelestial level,235 a religious term used to describe a high heavenly realm used during his time. The freemasons deliberately modeled their society on the community founded by Pythagoras at Croton.236Rosicrucianism used Pythagorean symbolism,221 as did Robert Fludd (1574–1637),221 who believed his own musical writings to have been inspired by Pythagoras.221John Dee was heavily influenced by Pythagorean ideology,237235 particularly the teaching that all things are made of numbers.237235
On literature
The Transcendentalists read the ancient Lives of Pythagoras as guides on how to live a model life.238Henry David Thoreau was impacted by Thomas Taylor's translations of Iamblichus's Life of Pythagoras and Stobaeus's Pythagoric Sayings238 and his views on nature may have been influenced by the Pythagorean idea of images corresponding to archetypes.238 The Pythagorean teaching of musica universalis is a recurring theme throughout Thoreau's magnum opus, Walden.238
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/paɪˈθæɡərəs/ py-THAG-ər-əs,2 also US: /pɪˈθæɡərəs/ pih-;3Ancient Greek: Πυθαγόρας ὁ Σάμιος, romanized: Pythagóras ho Sámios, lit. 'Pythagoras the Samian', or Πυθαγόρης, Pythagórēs in Ionian Greek. ↩
"The dates of his life cannot be fixed exactly, but assuming the approximate correctness of the statement of Aristoxenus (Porphyry, Vit. Pyth, §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." Guthrie (1967), p. 173 ↩
Some writers call him a native Samian, a Tyrrhenian from Lemnos, or a Phliasian from Peloponnesus, and give Marmacus or Demaratus as his name (see Diog VIII, §1.1; Porphyry, Vit. Pyth, §1, §2; Justin, xx. 4; Pausanias, ii. 13; Iamblichus, Vit. Pyth, §2.4). Porphyry, in particular, presents a conflicting report by Neanthes, that Mnesarchus was born in Tyre (in Lebanon), or that he was a Tyrrhenian from Lemnos; however, the confusion was possibly due to the similarity of the names "Tyre" and "Tyrrhenian", while it has also been suggested that Porphyry's own background from Tyre, could explain why his work was the only one, out of the three biographies of Pythagoras that have survived from late antiquity, to have linked Pythagoras's father with it.22 Due to the obscurity surrounding his background, some modern scholars deem it safer to accept "that Pythagoras and his father were pure-blooded Greeks, of undiluted Samian stock".23↩
Xenophanes's Poem (or Elegies) on Pythagorus is provided below, which was preserved in Diog VIII, §1.36: - Greek: περὶ δὲ τοῦ ἄλλοτε ἄλλον γεγενῆσθαι (Pythagoras) Ζενοφάνης ἐν ἐλεγείαι προσμαρτυρεῖ, ἧς ἀρχή 'νῦν ... κέλενθον'. ὃ δὲ περὶ αὐτοῦ (Pythagoras) φησιν, οὕτως ἔχει καί ... αἰών'. νῦν αὖτ' ἄλλον ἔπειμι λόγον, δείξω δὲ κέλευθον. καί ποτέ μιν στυφελιζομένου σκύλακος παριόντα φασὶν ἐποικτῖραι καὶ τόδε φάσθαι ἔπος "παῦσαι μηδὲ ῥάπιζε, ἐπεὶ ἡ φίλου ἀνέρος ἐστὶν ψυχή, τὴν ἔγνων φθεγξαμένης αὐδῆς." DK 21B7, p. 130 - English: "And now I will turn to another tale and point the way. ... Once they say that he (Pythagoras) was passing by when a dog was being beaten and spoke this word: "Stop! don't beat it! For it is the soul of a friend that I recognised when I heard its voice." Burnet (1920), p. 118 ↩
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). ↩