Samos (US: /pɪˈθæɡərəs/, UK:
/paɪˈθæɡərəs/; Ancient Greek: Πυθαγόρας ὁ
Σάμιος, translit. Pythagóras ho Sámios,
Pythagoras the Samian', or simply Πυθαγόρας;
Πυθαγόρης in Ionian Greek; c. 570 –
c. 495 BC)[Notes 1] was an
Ionian Greek philosopher and the
eponymous founder of the
Pythagoreanism movement. His political and
religious teachings were well-known in
Magna Graecia and influenced
the philosophies of Plato, Aristotle, and, through them, Western
Knowledge of Pythagoras's life is largely clouded by legend and
obfuscation, but he appears to have been the son of Mnesarchus, a seal
engraver on the island of Samos. Modern scholars disagree regarding
Pythagoras's education and influences, but they do agree that, in
around 530 BC, he travelled to Croton, where he founded a school in
which initiates were sworn to secrecy and lived a communal, ascetic
lifestyle. Following Croton's decisive victory over
Sybaris in around
510 BC, Pythagoras's followers came into conflict with supporters of
democracy and Pythagorean meeting houses were burned.
have been killed during this persecution, or he may have escaped to
Metapontum, where he eventually died. The teaching most securely
Pythagoras is metempsychosis, or the "transmigration
of souls", which holds that every soul is immortal and, upon death,
enters into a new body. He may have also devised the doctrine of
musica universalis, which holds that the planets move according to
mathematical equations and thus resonate to produce an inaudible
symphony of music. Scholars debate whether
developed the numerological and musical teachings attributed to him,
or if those teachings were developed by his later followers,
Philolaus of Croton. He probably prohibited his followers
from eating beans, but he may or may not have advocated a strictly
Pythagoras was credited with many mathematical and
scientific discoveries, including the Pythagorean theorem, Pythagorean
tuning, the five regular solids, the Theory of Proportions, the
sphericity of the Earth, and the identity of the morning and evening
stars as the planet Venus. It was said that he was the first man to
call himself a philosopher ("lover of wisdom")[Notes 2] and that he
was the first to divide the globe into five climatic zones. Classical
historians debate whether
Pythagoras made these discoveries, and many
of the accomplishments credited to him likely originated earlier or
were made by his colleagues or successors. Some accounts mention that
the philosophy associated with
Pythagoras was related to mathematics
and that numbers were important, but it is debated to what extent, if
at all, he actually contributed to mathematics or natural philosophy.
Pythagoras influenced Plato, whose dialogues, especially his Timaeus,
exhibit Pythagorean teachings. Pythagorean ideas about mathematical
perfection also impacted ancient Greek art. His teachings underwent a
major revival in the first century BC among Middle Platonists,
coinciding with the rise of Neopythagoreanism.
Pythagoras continued to
be regarded as a great philosopher throughout the
Middle Ages and his
philosophy had a major impact on scientists such as Nicolaus
Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism
was used throughout early modern European esotericism and his
teachings as portrayed in Ovid's
Metamorphoses influenced the growth
of the vegetarian movement.
1 Biographical sources
3.1 Mathematical discoveries
3.2 Musical theories and investigations
3.3 Scientific discoveries
5.1 Communal lifestyle
Music and athletics
Asceticism and possible vegetarianism
6.1 Influence on philosophy
Archytas and Plato
Middle Platonism and Neopythagoreanism
6.2 Influence on art and architecture
6.3 Later influence
6.3.1 Middle Ages
6.3.2 Modern science
6.3.4 Western esotericism
7 See also
10.1 Classical secondary sources
10.2 Modern secondary sources
11 External links
Pythagoras in the Vatican Museum, Vatican City, showing him as
a "tired-looking older man"
Bronze bust of a philosopher wearing a tainia from Villa of the
Papyri, Herculaneum, possibly a fictional bust of Pythagoras
No authentic writings of
Pythagoras have survived to the present
day and almost nothing is known for certain about his
life. The earliest sources on Pythagoras's life are brief,
ambiguous, and often satirical. The earliest source on
Pythagoras's teachings is a satirical poem written by
Colophon, a contemporary of Pythagoras, which describes
Pythagoras interceding on behalf of a dog that is being beaten,
professing to recognize in its cries the voice of a departed
Alcmaeon of Croton, a doctor who lived in Croton at around the same
Pythagoras lived there, incorporates many Pythagorean
teachings into his writings and alludes to having possibly known
Pythagoras personally. The poet
Heraclitus of Ephesus, who was
born across a few miles of sea away from
Samos and may have lived
within Pythagoras's lifetime, pegged
Pythagoras as a clever
charlatan, remarking that "Pythagoras, son of Mnesarchus,
practiced inquiry more than any other man, and selecting from these
writings he manufactured a wisdom for himself—much learning, artful
The Greek poets
Ion of Chios (c. 480 – c. 421 BC) and
Empedocles of Acragas (c. 493 – c. 432 BC) both
express admiration for
Pythagoras in their poems. The first
concise early description of
Pythagoras comes from the historian
Herodotus of Halicarnassus
Herodotus of Halicarnassus (c. 484 – c. 420 BC),
Pythagoras as "not the most insignificant" of Greek
sages and states that
Pythagoras taught his followers how to
attain immortality. The writings attributed to the Pythagorean
Philolaus of Croton, who lived in the late fifth century
BC, are the earliest texts to describe the numerological and musical
theories that were later ascribed to Pythagoras. The Athenian
Isocrates (436–338 BC) was the first to describe
Pythagoras as having visited Egypt.
Aristotle wrote a treatise On
the Pythagoreans, which is no longer extant. Some of it may be
preserved in the Protrepticus. Aristotle's disciples Dicaearchus,
Heraclides Ponticus also wrote on the same
Most of the major sources on Pythagoras's life are from the Roman
period, by which point "the history of
already... the laborious reconstruction of something lost and
gone." Three lives of
Pythagoras have survived from late
antiquity, all of which are filled primarily with myths and
legends. The earliest and most respectable of these is the one
Diogenes Laërtius's Lives and Opinions of Eminent
Philosophers. The two later lives were written by the
Neoplatonist philosophers Porphyry and Iamblichus and were
partially intended as polemics against the rise of Christianity.
The later sources are much lengthier than the earlier ones, and
even more fantastic in their descriptions of Pythagoras's
achievements. Porphyry and
Iamblichus did use some material
from the lost writings of Aristotle's disciples and material taken
from these sources is generally considered to be the most
There is not a single detail in the life of
Pythagoras that stands
uncontradicted. But it is possible, from a more or less critical
selection of the data, to construct a plausible account.
— Walter Burkert, 1972
Herodotus, Isocrates, and other early writers agree that Pythagoras
was the son of Mnesarchus and that he was born on the Greek island
of Samos, situated in the eastern Aegean. His father is said
to have been a gem-engraver or a wealthy merchant, but his
ancestry is disputed and unclear.[Notes 3] Pythagoras's name led
him to be associated with Pythian Apollo;
Aristippus of Cyrene
explained his name by saying, "He spoke (ἀγορεύω, agoreúō)
the truth no less than did the Pythian [sic] (Πῡθῐ́ᾱ,
Iamblichus tells the story that the
that his pregnant mother would give birth to a man supremely
beautiful, wise, and beneficial to humankind. A late source gives
his mother's name as Pythais. As to the date of his birth,
Aristoxenus stated that
Samos in the reign of
Polycrates, at the age of 40, which would give a date of birth around
According to Antiphon, while he was still on Samos,
a school known as the "semicircle", where prominent Samians
could discuss matters of public concern.
dwelled in a secret cave, where he studied in private.
Map of Italy showing locations associated with Pythagoras
Around 530 BC, he left Samos, possibly because he disagreed
with the tyranny of
Polycrates in Samos. His later admirers state
that it was because
Pythagoras was so overburdened with public duties
in Samos, because of the high estimation in which he was held by his
fellow-citizens. He arrived in the Greek colony of Croton (today's
Crotone, in Calabria) in what was then Magna Graecia. At
Croton, he founded the philosophical school of Pythagoreanism,
whose practitioners adhered to a strict, disciplined way of life.
Pythagoras acquired great political influence in Magna
Graecia; later biographers tell fantastical stories of the
effects of his eloquent speech in leading the people of Croton to
abandon their luxurious and corrupt way of life and devote themselves
to the purer system which he came to introduce.
Pythagoras's teachings of dedication and asceticism are credited with
aiding in Croton's decisive victory over the neighboring colony of
Sybaris in 510 BC. The forces of Croton were headed by the
Pythagorean Milo, and it is likely that the members of the brotherhood
took a prominent part. After the victory, a democratic constitution
was proposed, but the Pythagoreans rejected it. The supporters
of democracy, headed by Cylon and Ninon, the former of whom is said to
have been irritated by his exclusion from Pythagoras's brotherhood,
roused the populace against them. An attack was made upon them while
assembled either in the house of Milo, or in some other
meeting-place. The building was set on fire, and many of the
assembled members perished; only the younger and more active
members managed to escape. Sources disagree regarding whether
Pythagoras was killed, or if he managed to flee to Metapontum,
where he lived out the rest of his life. One legend
reported by both
Diogenes Laërtius and
Iamblichus states that
Pythagoras almost managed to escape his pursuers, but that he came to
a bean field and refused to run through it because doing so would
violate his own teachings, so instead he stopped and was killed as
Illustration from 1913 showing
Pythagoras teaching a class of women.
Pythagoras believed that women should be taught philosophy as well as
men and many prominent members of his school were women.
Diogenes Laërtius states that
Pythagoras "did not indulge in the
pleasures of love" and that he cautioned others to only have sex
"whenever you are willing to be weaker than yourself". According
Pythagoras married Theano, a lady of
Crete and the
daughter of Pythenax and had several children with her.
Porphyry writes that
Pythagoras had two sons named
Arignote, and a daughter named Myia, who "took precedence
among the maidens in Croton and, when a wife, among married
Iamblichus mentions none of these children and instead
only mentions a son named Mnesarchus after his grandfather. This
son was raised by Pythagoras's appointed successor Aristaeus and
eventually took over the school when Aristaeus was too old to continue
Milo of Croton
Milo of Croton was said to have been a close associate of
Pythagoras and was credited with having saved the philosopher's
life when a roof was about to collapse. This association may been
the result of confusion with a different man named Pythagoras, who was
an athletics trainer.
Diogenes Laërtius records Milo's wife's
name as Myia.
Iamblichus mentions Theano as the wife of Brontinus
Diogenes Laërtius states that the same Theano was
Pythagoras's pupil and that Pythagoras's wife Theano was her
Diogenes Laërtius also records that works supposedly
written by Theano were still extant during his own lifetime and
quotes several opinions attributed to her. These writings are now
known to be pseudepigraphical.
Paestan red-figure bell-krater depicting the Delphic priestess sitting
atop her tripod, (c. 330 BC). According to one tradition, Pythagoras
learned most of his moral teachings from the Delphic priestess
Scholars disagree regarding who Pythagoras's teacher was because
reliable information on the subject is lacking. Some say his
training was almost entirely Greek, others exclusively Egyptian and
Oriental. Each of Pythagoras's alleged tutors seems to call
attention to a different aspect of Pythagoras's own teachings.
Various ancient sources list Hermodamas of Samos, or his father
Samos (who both stand for the domestic rhapsodic
tradition of Samos) among his possible tutors; whereas other
traditions credit Bias of Priene, Thales,
Anaximander (a pupil of
Pherecydes of Syros
Pherecydes of Syros (all exponents of the Greek
philosophical tradition). Of the various attributions regarding
his Greek teachers,
Pherecydes of Syros
Pherecydes of Syros is mentioned most often.
Before 520 BC, on one of his visits to Egypt or Greece, Pythagoras
might have met
Thales of Miletus, who would have been around
fifty-four years older than him.
Thales was a philosopher,
scientist, mathematician, and engineer, also known for a special
case of the inscribed angle theorem. Pythagoras's birthplace, the
island of Samos, is situated in the Northeast
Aegean Sea not far from
Diogenes Laërtius cites a statement from Aristoxenus
(fourth century BC) stating that
Pythagoras learned most of his moral
doctrines from the Delphic priestess Themistoclea.
Porphyry affirms this assertion, but calls the priestess
Aristoclea (Aristokleia). Ancient authorities furthermore note the
similarities between the religious and ascetic peculiarities of
Pythagoras with the Orphic or Cretan mysteries, or the Delphic
Following a similar logic, the Egyptians are said to have taught him
geometry, the Phoenicians arithmetic, the Chaldeans astronomy, and the
Magi the principles of religion and practical maxims for the conduct
of life. According to
Pythagoras not only
visited Egypt and learnt the Egyptian language (as reported by
Antiphon in his On Men of Outstanding Merit), but also "journeyed
among the Chaldaeans and Magi." Later in Crete, he went to the Cave of
Ida with Epimenides, and entered Egyptian sanctuaries for the purpose
to learn information concerning the secret lore of the different
Middle Platonist biographer
Plutarch (c. 46 –
c. 120 AD) writes in his treatise On Isis and Osiris that,
during his visit to Egypt,
Pythagoras received instruction from the
Egyptian priest Oenuphis of Heliopolis (meanwhile
lectures from a Sonchis of Sais). Other ancient writers also
mention Pythagoras's visit to Egypt. According to the Christian
Clement of Alexandria
Clement of Alexandria (c. 150 – c. 215 AD),
Pythagoras was a disciple of Soches, an Egyptian archprophet, as well
Plato of Sechnuphis of Heliopolis."
In Raphael's fresco The School of Athens,
Pythagoras is shown writing
in a book as a young man presents him with a tablet showing a
diagrammatic representation of a lyre above a drawing of the sacred
Although the exact details of Pythagoras's teachings are
uncertain, it is possible to reconstruct a general outline of
his main ideas.
Aristotle writes at length about the teachings
of the Pythagoreans, but without mentioning Pythagoras
directly. One of Pythagoras's main doctrines appears to have been
metempsychosis, the belief that all souls are immortal
and that, after death, a soul is transferred into a new body. This
teaching is referenced by Xenophanes, Ion of Chios, and
Empedocles alludes in one of his poems that
Pythagoras may have
claimed to possess the ability to recall his former incarnations.
Diogenes Laërtius reports an account from
Heraclides Ponticus that
Pythagoras told people that he had lived four previous lives that he
could remember in detail. The first of these lives was as
Aethalides the son of Hermes, who granted him the ability to remember
all his past incarnations. Next, he was incarnated as Euphorbus, a
minor hero from the
Trojan War briefly mentioned in the Iliad. He
then became the philosopher Hermotimus, who recognized the shield
Euphorbus in the temple of Apollo. His final incarnation was as
Pyrrhus, a fisherman from Delos. One of his past lives, as
reported by Dicaearchus, was as a beautiful courtesan.
Another belief attributed to
Pythagoras was that of the "harmony of
the spheres", which maintained that the planets and stars move
according to mathematical equations, which correspond to musical notes
and thus produce an inaudible symphony. According to Porphyry,
Pythagoras taught that the seven Muses were actually the seven planets
singing together. In his philosophical dialogue Protrepticus,
Aristotle has his literary double say:
Pythagoras was asked [why humans exist], he said, "to observe the
heavens," and he used to claim that he himself was an observer of
nature, and it was for the sake of this that he had passed over into
Pythagoras was said to have practised divination and prophecy. In
the visits to various places in Greece—Delos, Sparta, Phlius, Crete,
etc.—which are ascribed to him, he usually appears either in his
religious or priestly guise, or else as a lawgiver.
The so-called Pythagoreans, who were the first to take up mathematics,
not only advanced this subject, but saturated with it, they fancied
that the principles of mathematics were the principles of all things.
Metaphysics 1–5, c. 350 BC
Pythagoras is credited with having devised the tetractys, an
important sacred symbol in later Pythagoreanism.
According to Aristotle, the Pythagoreans used mathematics for solely
mystical reasons, devoid of practical application. They believed
that all things were made of numbers. The number one (the
monad) represented the origin of all things and the number two
(the dyad) represented matter. The number three was an "ideal
number" because it had a beginning, middle, and end and was the
smallest number of points that could be used to define a plane
triangle, which they revered as a symbol of the god Apollo. The
number four signified the four seasons and the four elements. The
number seven was also sacred because it was the number of planets and
the number of strings on a lyre, and because Apollo's birthday
was celebrated on the seventh day of each month. They believed
that odd numbers were masculine, that even numbers were
feminine, and that the number five represented marriage, because
it was the sum of two and three.
Ten was regarded as the "perfect number" and the Pythagoreans
honored it by never gathering in groups larger than ten.
Pythagoras was credited with devising the tetractys, the triangular
figure of four rows which add up to the perfect number, ten. The
Pythagoreans regarded the tetractys as a symbol of utmost mystical
importance. Iamblichus, in his Life of Pythagoras, states that
the tetractys was "so admirable, and so divinised by those who
understood [it]," that Pythagoras's students would swear oaths by
Modern scholars debate whether these numerological teachings were
Pythagoras himself or by the later Pythagorean
Philolaus of Croton. In his landmark study Lore and
Science in Ancient Pythagoreanism,
Walter Burkert argues that
Pythagoras was a charismatic political and religious teacher, but
that the number philosophy attributed to him was really an innovation
by Philolaus. According to Burkert,
Pythagoras never dealt with
numbers at all, let alone made any noteworthy contribution to
mathematics. Burkert argues that the only mathematics the
Pythagoreans ever actually engaged in was simple, proofless
arithmetic, but that these arithmetic discoveries did contribute
significantly to the beginnings of mathematics.
The Pythagorean theorem: The sum of the areas of the two squares on
the legs (a and b) equals the area of the square on the hypotenuse
A visual proof of the Pythagorean theorem
Pythagoras is most famous today for his alleged mathematical
discoveries, classical historians dispute whether he himself ever
actually made any significant contributions to the field.
Many mathematical and scientific discoveries were attributed to
Pythagoras, including his famous theorem, as well as discoveries
in the fields of music, astronomy, and medicine.
Since at least the first century BC,
Pythagoras has commonly been
given credit for discovering the Pythagorean theorem, a
theorem in geometry that states that "in a right-angled triangle the
square of the hypotenuse is equal [to the sum of] the squares of the
two other sides"—that is,
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
Cicero rejected this story as spurious because of
the much more widely held belief that
Pythagoras forbade blood
sacrifices. Porphyry attempted to explain the story by asserting
that the ox was actually made of dough.
Pythagorean theorem was known and used by the Babylonians and
Indians centuries before Pythagoras, but it is
possible that he may have been the first one to introduce it to the
Greeks. Some historians of mathematics have even suggested
that he—or his students—may have constructed the first proof.
Burkert rejects this suggestion as implausible, noting that
Pythagoras was never credited with having proved any theorem in
antiquity. Furthermore, the manner in which the Babylonians
employed Pythagorean numbers implies that they knew that the principle
was generally applicable, and knew some kind of proof, which has not
yet been found in the (still largely unpublished) cuneiform
sources.[Notes 4] Pythagoras's biographers state that he also was the
first to identify the five regular solids and that he was the
first to discover the Theory of Proportions.
Musical theories and investigations
Medieval woodcut showing
Pythagoras with bells and other instruments
in Pythagorean tuning
Pythagorean tuning and Pythagorean hammers
According to legend,
Pythagoras discovered that musical notes could be
translated into mathematical equations when he passed blacksmiths at
work one day and heard the sound of their hammers clanging
against the anvils. Thinking that the sounds of the hammers were
beautiful and harmonious, except for one, he rushed into the
blacksmith shop and began testing the hammers. He then realized
that the tune played when the hammer struck was directly proportional
to the size of the hammer and therefore concluded that music was
mathematical. However, this legend is demonstrably
false, as these ratios are only relevant to string length
(such as the string of a monochord), and not to hammer weight.
In ancient times,
Pythagoras and his contemporary
Parmenides of Elea
were both credited with having been the first to teach that the Earth
was spherical, the first to divide the globe into five climactic
zones, and the first to identify the morning star and the evening
star as the same celestial object. Of the two philosophers,
Parmenides has a much stronger claim to having been the first and
the attribution of these discoveries to
Pythagoras seems to have
possibly originated from a pseudepigraphal poem. Empedocles, who
Magna Graecia shortly after
Pythagoras and Parmenides, knew
that the earth was spherical. By the end of the fifth century BC,
this fact was universally accepted among Greek intellectuals.
Pythagoras Emerging from the Underworld (1662) by Salvator Rosa
Within his own lifetime,
Pythagoras was already the subject of
elaborate hagiographic legends, which he may have personally
Pythagoras as a wonder-worker and
somewhat of a supernatural figure. In a fragment, Aristotle
Pythagoras had a golden thigh, which he publicly
exhibited at the Olympic Games and showed to Abaris the
Hyperborean as proof of his identity as the "Hyperborean
Supposedly, the priest of
Pythagoras a magic arrow,
which he used to fly over long distances and perform ritual
purifications. He was once seen at both
Metapontum and Croton at
the same time. When
Pythagoras crossed the river Casas,
"several witnesses" reported that they heard it greet him by
name. In Roman times, a legend claimed that
Pythagoras was the
son of Apollo. According to Muslim tradition,
Pythagoras was said
to have been initiated by
Hermes (Egyptian Thoth).
Pythagoras was said to have dressed all in white with a
golden wreath atop his head and to have worn trousers after the
fashion of the Thracians.
Diogenes Laërtius presents Pythagoras
as having exercised remarkable self-control; he was always
cheerful, but "abstained wholly from laughter, and from all such
indulgences as jests and idle stories".
Pythagoras was said to have had extraordinary success in dealing with
animals. A fragment from
Aristotle records that, when a
deadly snake bit Pythagoras, he bit it back and killed it.
Both Porphyry and
Iamblichus report that
Pythagoras once persuaded a
bull not to eat beans and that he once convinced a
notoriously destructive bear to swear that it would never harm a
living thing again, and that the bear kept its word.
Anti-Pythagorean legends were also circulated.
retells a story told by Hermippus of Samos, which states that
Pythagoras had once gone into an underground room, telling everyone
that he was descending to the underworld. He stayed in this room
for months, while his mother secretly recorded everything that
happened during his absence. After he returned from this room,
Pythagoras recounted everything that had happened while he was
gone, convincing everyone that he had really been in the
underworld and leading them to trust him with their wives.
Pythagoreans Celebrate the Sunrise (1869) by Fyodor Bronnikov
Main article: Pythagoreanism
Isocrates affirm that, above all else,
famous for leaving behind him a way of life. Carl B.
Boyer (1968) characterizes the Pythagorean school as "politically
conservative and with a strict code of conduct." Leonid Zhmud
(2012) identifies two camps within the early Pythagoreans: the
scientific mathematikoi and the religious akousmatikoi, who engaged in
politics. The study of mathematics and music may have been
connected to the worship of Apollo.
Pythagoras founded at Croton was called a
"school", but, in many ways, resembled a monastery. The
adherents were bound by a vow to
Pythagoras and each other, for the
purpose of pursuing the religious and ascetic observances, and of
studying his religious and philosophical theories. The members of
the sect shared all their possessions in common and were devoted
to each other to the exclusion of outsiders. One Pythagorean
maxim was "koinà tà phílōn" ("All things in common among
Iamblichus and Porphyry provide detailed accounts
of the organization of the school, although the primary interest of
both writers is not historical accuracy, but rather to present
Pythagoras as a divine figure, sent by the gods to benefit
humankind. Iamblichus, in particular, presents the "Pythagorean
Way of Life" as a pagan alternative to the Christian monastic
communities of his own time.
Pythagorean teachings were known as "symbols" (symbolon) and
members took a vow of silence that they would not reveal these symbols
to non-members. Those who did not obey the laws of the
community were expelled and the remaining members would erect
tombstones for them as though they had died. A number of "oral
sayings" (akoúsmata) attributed to
Pythagoras have survived,
dealing with how members of the Pythagorean community should perform
sacrifices, how they should honor the gods, how they should "move from
here", and how they should be buried. Many of these sayings
emphasize the importance of ritual purity and avoiding
defilement, but their exact meanings are frequently obscure.
Iamblichus preserves Aristotle's descriptions of the original,
ritualistic intentions behind a few of these sayings, but these
apparently later fell out of fashion, because Porphyry provides
markedly different ethical-philosophical interpretations of them:
Original ritual purpose according to Aristotle/Iamblichus
Porphyry's philosophical interpretation
"Do not take roads traveled by the public."
"Fear of being defiled by the impure"
"with this he forbade following the opinions of the masses, yet to
follow the ones of the few and the educated."
"and [do] not wear images of the gods on rings"
"Fear of defiling them by wearing them."
"One should not have the teaching and knowledge of the gods quickly at
hand and visible [for everyone], nor communicate them to the
"and pour libations for the gods from a drinking cup's handle [the
"Efforts to keep the divine and the human strictly separate"
"thereby he enigmatically hints that the gods should be honored and
praised with music; for it goes through the ears."
New initiates were allegedly not permitted to meet
after they had completed a five-year initiation period, during
which they were required to remain silent. Sources indicate that
Pythagoras himself was unusually progressive in his attitudes towards
women and female members of Pythagoras's school appear to have
played an active role in its operations.
Iamblichus provides a
list of 235 famous Pythagoreans, seventeen of whom are women.
In later times, many prominent female philosophers contributed to the
development of Neopythagoreanism.
Music and athletics
French manuscript from 1512/1514, showing
Pythagoras turning his face
away from fava beans in revulsion
The Pythagoreans believed that music was a purification for the soul,
just as medicine was a purification for the body. One anecdote of
Pythagoras reports that when he encountered some drunken youths trying
to break into the home of a virtuous woman, he sang a solemn tune with
long spondees and the boys' "raging willfulness" was quelled. The
Pythagoreans also placed particular emphasis on the importance of
physical exercise; therapeutic dancing, daily morning walks along
scenic routes, and athletics were major components of the Pythagorean
lifestyle. Moments of contemplation at the beginning and end of
each day were also advised.
Asceticism and possible vegetarianism
Pythagoreanism entailed a number of ascetic practices (many of which
may have had symbolic meanings). It is more or less agreed that
Pythagoras issued a prohibition against the consumption of beans
and the meat of non-sacrificial animals, though both of these
assumptions have been contradicted. It is also likely that he
prohibited his followers from wearing woolen garments. Some
ancient writers present
Pythagoras as enforcing a strictly vegetarian
diet,[Notes 5] which may have been motivated due to the
doctrine of metempsychosis. Eudoxus of Cnidus, a
student of Archytas, writes, "
Pythagoras was distinguished by such
purity and so avoided killing and killers that he not only abstained
from animal foods, but even kept his distance from cooks and
hunters." Other authorities contradict this statement.
According to Aristoxenus,
Pythagoras allowed the use of all kinds
of animal food except the flesh of oxen used for ploughing, and
rams. According to Heraclides Ponticus,
Pythagoras ate the
meat from sacrifices and established a diet for athletes
dependent on meat. Temperance of all kinds seems to have been
urged. It is also stated that they had common meals, resembling the
Spartan system, at which they met in companies of ten.
Influence on philosophy
Archytas and Plato
Medieval manuscript of Calcidius's Latin translation of Plato's
Timaeus, which is one of the Platonic dialogues with the most overt
See also: Timaeus (dialogue)
Sizeable Pythagorean communities existed in Magna Graecia, Phlius, and
Thebes during the early fourth century BC. Around the same time,
the Pythagorean philosopher
Archytas was highly influential on the
politics of the city of Tarentum in Magna Graecia. According to
Archytas was elected as strategos ("general") seven
times, even though others were prohibited from serving for more than a
year, and never lost a single battle.
Archytas was also a
renowned mathematician and musician. He was a close friend of
Plato and he is quoted in Plato's Republic.
Aristotle states that the philosophy of
Plato was heavily dependent on
the teachings of the Pythagoreans.
Cicero repeats this
statement, remarking that Platonem ferunt didicisse Pythagorea omnia
Plato learned all things Pythagorean"). According to
Charles H. Kahn, Plato's middle dialogues, including Meno, Phaedo, and
The Republic, have a strong "Pythagorean coloring", and his last
few dialogues (particularly
Philebus and Timaeus) are extremely
Pythagorean in character.
According to R. M. Hare, Plato's Republic may be partially based on
the "tightly organised community of like-minded thinkers" established
Pythagoras at Croton. Additionally,
Plato may have taken from
Pythagoras the idea that mathematics and abstract thought are a secure
basis for philosophy, as well as "for substantial theses in science
Pythagoras shared a "mystical approach to
the soul and its place in the material world" and it is probable
that both were influenced by Orphism. Bertrand Russell, in his A
History of Western Philosophy, contends that the influence of
Plato and others was so great that he should be
considered the most influential philosopher of all time. He
concludes that "I do not know of any other man who has been as
influential as he was in the school of thought."
Middle Platonism and Neopythagoreanism
A revival of Pythagorean teachings occurred in the first century
Middle Platonist philosophers such as Eudorus and Philo
Alexandria hailed the rise of a "new"
Alexandria. At around the same time,
prominent. The first-century AD philosopher Apollonius of Tyana
sought to emulate
Pythagoras and live by Pythagorean teachings.
The later first-century Neopythagorean philosopher Moderatus of Gades
expanded on Pythagorean number philosophy and probably understood
the soul as a "kind of mathematical harmony." The Neopythagorean
mathematician and musicologist
Nicomachus likewise expanded on
Pythagorean numerology and music theory. Numenius of Apamea
interpreted Plato's teachings in light of Pythagorean doctrines.
Influence on art and architecture
Hadrian's Pantheon in Rome, depicted in this eighteenth-century
painting by Giovanni Paolo Panini, was built according to Pythagorean
Greek sculpture sought to represent the permanent reality behind
superficial appearances. Early Archaic sculpture represents life
in simple forms, and may have been influenced by the earliest Greek
natural philosophies.[Notes 6] The Greeks generally believed that
nature expressed itself in ideal forms and was represented by a type
(εἶδος), which was mathematically calculated. When
dimensions changed, architects sought to relay permanence through
Maurice Bowra believes that these ideas
influenced the theory of
Pythagoras and his students, who believed
that "all things are numbers".
During the sixth century BC, the number philosophy of the Pythagoreans
triggered a revolution in Greek sculpture. Greek sculptors and
architects attempted to find the mathematical relation (canon) behind
aesthetic perfection. Possibly drawing on the ideas of
Pythagoras, the sculptor
Polykleitos writes in his Canon that
beauty consists in the proportion, not of the elements (materials),
but of the interrelation of parts with one another and with the
whole. In the Greek architectural orders, every element was
calculated and constructed by mathematical relations. Rhys Carpenter
states that the ratio 2:1 was "the generative ratio of the Doric
order, and in Hellenistic times an ordinary Doric colonnade, beats out
a rhythm of notes."
The oldest known building designed according to Pythagorean teachings
is the Porta Maggiore Basilica, a subterranean basilica which was
built during the reign of the Roman emperor
Nero as a secret place of
worship for Pythagoreans. The basilica was built underground
because of the Pythagorean emphasis on secrecy and also because
of the legend that
Pythagoras had sequestered himself in an
underground cave on Samos. The basilica's apse is in the east and
its atrium in the west out of respect for the rising sun. It has
a narrow entrance leading to a small pool where the initiates could
purify themselves. The building is also designed according to
Pythagorean numerology, with each table in the sanctuary
providing seats for seven people. Three aisles lead to a single
altar, symbolizing the three parts of the soul approaching the unity
of Apollo. The apse depicts a scene of the poetess
off the Leucadian cliffs, clutching her lyre to her breast, while
Apollo stands beneath her, extending his right hand in a gesture of
protection, symbolizing Pythagorean teachings about the
immortality of the soul. The interior of the sanctuary is almost
entirely white because the color white was regarded by Pythagoreans as
The emperor Hadrian's Pantheon in
Rome was also built based on
Pythagorean numerology. The temple's circular plan, central axis,
hemispherical dome, and alignment with the four cardinal directions
symbolize Pythagorean views on the order of the universe. The
single oculus at the top of the dome symbolizes the monad and the
sun-god Apollo. The twenty-eight ribs extending from the oculus
symbolize the moon, because twenty-eight was the same number of months
on the Pythagorean lunar calendar. The five coffered rings
beneath the ribs represent the marriage of the sun and moon.
Pythagoras appears in a relief sculpture on one of the archivolts over
the right door of the west portal at Chartres Cathedral.
During the Middle Ages,
Pythagoras was revered as the founder of
mathematics and music, two of the Seven Liberal Arts. He appears
in numerous medieval depictions, in illuminated manuscripts and in the
relief sculptures on the portal of the Cathedral of Chartres. The
Timaeus was the only dialogue of
Plato to survive in Latin translation
in western Europe, which led
William of Conches (c. 1080-1160) to
Plato was Pythagorean. In the 1430s, the Camaldolese
Ambrose Traversari translated
Diogenes Laërtius's Lives and
Opinions of Eminent Philosophers from Greek into Latin and, in
the 1460s, the philosopher
Marsilio Ficino translated Porphyry and
Iamblichus's Lives of
Pythagoras into Latin as well, thereby
allowing them to be read and studied by western scholars. In
1494, the Greek Neopythagorean scholar
Constantine Lascaris published
the Golden Verses of Pythagoras, translated into Latin, with a printed
edition of his Grammatica, thereby bringing them to a widespread
audience. In 1499, he published the first Renaissance biography
Pythagoras in his work Vitae illustrium philosophorum siculorum et
calabrorum, issued in Messina.
In his preface to his book On the Revolution of the Heavenly Spheres
Nicolaus Copernicus cites various Pythagoreans as the most
important influences on the development of his heliocentric model of
the universe, deliberately omitting mention of Aristarchus
of Samos, a non-Pythagorean astronomer who had developed a fully
heliocentric model in the fourth century BC, in effort to portray his
model as fundamentally Pythagorean.
Johannes Kepler considered
himself to be a Pythagorean. He believed in the
Pythagorean doctrine of musica universalis and it was his search
for the mathematical equations behind this doctrine that led to his
discovery of the laws of planetary motion. Kepler titled his book
on the subject
Harmonices Mundi (Harmonics of the World), after the
Pythagorean teaching that had inspired him. Near the
conclusion of the book, Kepler describes himself falling asleep to the
sound of the heavenly music, "warmed by having drunk a generous
draught... from the cup of Pythagoras."
Isaac Newton firmly believed in the Pythagorean teaching of the
mathematical harmony and order of the universe. Though Newton was
notorious for rarely giving others credit for their discoveries,
he attributed the discovery of the Law of Universal Gravitation to
Albert Einstein believed that a scientist may also be
"a Platonist or a Pythagorean insofar as he considers the viewpoint of
logical simplicity as an indispensable and effective tool of his
research." The English philosopher
Alfred North Whitehead
Alfred North Whitehead argued
that "In a sense,
Pythagoras stand nearer to modern physical
science than does Aristotle. The two former were mathematicians,
Aristotle was the son of a doctor". By this measure,
Whitehead declared that Einstein and other modern scientists like him
are "following the pure Pythagorean tradition."
Vegetarianism (1618-1620) by Peter Paul Rubens
was inspired by Pythagoras's speech in Ovid's Metamorphoses. The
painting portrays the Pythagoreans with corpulent bodies, indicating a
belief that vegetarianism was healthful and nutritious.
A fictionalized portrayal of
Pythagoras appears in Book XV of Ovid's
Metamorphoses, in which he delivers a speech imploring his
followers to adhere to a strictly vegetarian diet. It was through
Arthur Golding's 1567 English translation of Ovid's
Pythagoras was best known to English-speakers throughout the early
modern period. John Donne's Progress of the
Soul discusses the
implications of the doctrines expounded in the speech and Michel
de Montaigne quoted the speech no less than three times in his
treatise Of Cruelty to voice his moral objections against eating
William Shakespeare references the speech in his play The
Merchant of Venice.
John Dryden included a translation of the
Pythagoras in his 1700 work Fables, Ancient and Modern
and John Gay's 1726 fable "
Pythagoras and the Countryman" reiterates
its major themes, linking carnivorism with tyranny. Lord
Chesterfield records that his conversion to vegetarianism had been
motivated by reading Pythagoras's speech in Ovid's Metamorphoses.
Until the word vegetarianism was coined in the 1840s, vegetarians were
referred to in English as "Pythagoreans". Percy Bysshe Shelley
wrote an ode entitled "To the Pythagorean Diet" and Leo Tolstoy
adopted the Pythagorean diet himself.
Early modern European esotericism drew heavily on the teachings of
Pythagoras. The German humanist scholar Johannes Reuchlin
Christian theology and
Jewish Kabbalah, arguing that
both inspired by Mosaic tradition and that
therefore a kabbalist. In his dialogue De verbo mirifico (1494),
Reuchlin compared the Pythagorean tetractys to the ineffable divine
name YHWH, ascribing each of the four letters of the
tetragrammaton a symbolic meaning according to Pythagorean mystical
Heinrich Cornelius Agrippa's popular and influential three-volume
treatise De Occulta Philosophia cites
Pythagoras as a "religious
magi" and indicates that Pythagoras's mystical numerology
operates on a supercelestial level. The freemasons deliberately
modeled their society on the community founded by
Rosicrucianism used Pythagorean symbolism, as did
Robert Fludd (1574–1637), who believed his own musical writings
to have been inspired by Pythagoras.
John Dee was heavily
influenced by Pythagorean ideology, particularly the
teaching that all things are made of numbers. Adam
Weishaupt, the founder of the Illuminati, was a strong admirer of
Pythagoras and, in his book
Pythagoras (1787), he advocated that
society should be reformed to be more like Pythagoras's commune at
Wolfgang Amadeus Mozart
Wolfgang Amadeus Mozart incorporated Masonic and
Pythagorean symbolism into his opera The Magic Flute. Sylvain
Maréchal, in his six-volume 1799 biography The Voyages of Pythagoras,
declared that all revolutionaries in all time periods are the "heirs
Dante Alighieri's description of
Heaven in his Paradiso incorporates
Dante Alighieri was fascinated by Pythagorean numerology and
based his descriptions of Hell, Purgatory, and
Heaven on Pythagorean
numbers. Dante wrote that
Pythagoras saw Unity as Good and
Plurality as Evil and, in Paradiso XV, 56–57, he declares:
"five and six, if understood, ray forth from unity." The number
eleven and its multiples are found throughout the Divine Comedy, each
book of which has thirty-three cantos, except for the Inferno, which
has thirty-four, the first of which serves as a general
introduction. Dante describes the ninth and tenth bolgias in the
Eighth Circle of
Hell as being twenty-two miles and eleven miles
respectively, which correspond to the fraction 22/7, which was
the Pythagorean approximation of pi. Hell, Purgatory, and Heaven
are all described as circular and Dante compares the wonder of
God's majesty to the mathematical puzzle of squaring the circle.
The number three also features prominently: the
Divine Comedy has
three parts and Beatrice is associated with the number nine,
which is equal to three times three.
The Transcendentalists read the ancient Lives of
Pythagoras as guides
on how to live a model life.
Henry David Thoreau
Henry David Thoreau was impacted by
Thomas Taylor's translations of Iamblichus's Life of
Stobaeus's Pythagoric Sayings and his views on nature may have
been influenced by the Pythagorean idea of images corresponding to
archetypes. The Pythagorean teaching of musica universalis is a
recurring theme throughout Thoreau's magnum opus, Walden.
Apollonius of Tyana
Dyad (Greek philosophy)
The golden verses of Pythagoras
List of things named after Pythagoras
Lute of Pythagoras
Pythagoras tree (fractal)
^ "The dates of his life cannot be fixed exactly, but assuming the
approximate correctness of the statement of
Aristoxenus (ap. Porph.
V.P. 9) that he left
Samos to escape the tyranny of
Polycrates at the
age of forty, we may put his birth round about 570 BC, or a few years
earlier. The length of his life was variously estimated in antiquity,
but it is agreed that he lived to a fairly ripe old age, and most
probably he died at about seventy-five or eighty." William Keith
Chambers Guthrie, (1978), A history of Greek philosophy, Volume 1: The
earlier Presocratics and the Pythagoreans, p. 173. Cambridge
^ Cicero, Tusculan Disputations, 5.3.8–9 =
Heraclides Ponticus fr.
Diogenes Laërtius 1.12, 8.8,
Iamblichus VP 58. Burkert
attempted to discredit this ancient tradition, but it has been
defended by C.J. De Vogel,
Pythagoras and Early
pp. 97–102, and C. Riedweg, Pythagoras: His Life, Teaching, And
Influence (2005), p. 92.
^ Some writers call him a Tyrrhenian or Phliasian, and give Marmacus,
or Demaratus, as the name of his father:
Diogenes Laërtius, viii. 1;
Porphyry, Vit. Pyth. 1, 2; Justin, xx. 4; Pausanias, ii. 13.
^ 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).
Empedocles did afterwards, Aristotle, Rhet. i. 14. § 2; Sextus
Empiricus, ix. 127. This was also one of the Orphic precepts,
Aristoph. Ran. 1032
^ "For Thales, the origin was water, and for
Anaximander the infinite
(apeiron), which must be considered a material form"
^ a b c Joost-Gaugier 2006, p. 143.
^ "American: Pythagoras". Collins Dictionary. n.d. Retrieved 25
^ "British: Pythagoras". Collins Dictionary. n.d. Retrieved 25
^ Dillon 2005, p. 163.
^ Joost-Gaugier 2006, p. 11.
^ Grafton, Most & Settis 2010, p. 796.
^ a b Ferguson 2008, p. 4.
^ Ferguson 2008, pp. 3–5.
^ a b c Kahn 2001, p. 2.
^ a b Burkert 1985, p. 299.
^ a b c Joost-Gaugier 2006, p. 12.
^ Riedweg 2005, p. 62.
Diogenes Laërtius, viii. 36
^ a b Joost-Gaugier 2006, pp. 12–13.
^ a b c Joost-Gaugier 2006, p. 13.
^ Joost-Gaugier 2006, pp. 14–15.
^ a b c Joost-Gaugier 2006, p. 16.
^ 4. 95.
^ Joost-Gaugier 2006, p. 88.
^ He alludes to it himself, Met. i. 5. p. 986. 12, ed. Bekker.
^ a b c d Burkert 1972, p. 109.
^ a b c d e f g h i j k l Kahn 2001, p. 5.
^ a b c d e Zhmud 2012, p. 9.
^ a b c Burkert 1972, p. 106.
^ a b c d e f Kahn 2001, p. 6.
^ Ferguson 2008, p. 12.
^ Clemens von Alexandria: Stromata I 62, 2–3, cit. Eugene V.
Afonasin; John M. Dillon; John Finamore, eds. (2012).
the Foundations of Late Platonism. Leiden and Boston: Brill.
p. 15. ISBN 9789004230118.
^ Joost-Gaugier 2006, p. 21.
^ Ferguson 2008, pp. 11–12.
^ a b c d e f Riedweg 2005, pp. 5–6, 59, 73.
Apollonius of Tyana
Apollonius of Tyana ap. Porphyry, Vit. Pyth. 2.
^ Porphyry, Vit. Pyth. 9
^ a b c d e f Cornelli & McKirahan 2013, p. 64.
^ a b Ferguson 2008, p. 5.
^ a b c Boyer, Carl B. (1968). A History of Mathematics.
^ Iamblichus, Vit. Pyth. 28; Porphyry, Vit. Pyth. 9
^ Cornelia J. de Vogel:
Pythagoras and Early Pythagoreanism. Assen
1966, pp. 21ff. Cfr. Cicero, De re publica 2, 28–30.
^ Cornelia J. de Vogel:
Pythagoras and Early Pythagoreanism, Assen
1966, S. 148–150.
^ Porphyry, Vit. Pyth. 18; Iamblichus, Vit. Pyth. 37, etc.
^ a b c Kahn 2001, pp. 6–7.
^ a b c d Kahn 2001, p. 7.
^ Iamblichus, Vit. Pyth. 255–259; Porphyry, Vit. Pyth. 54–57;
Diogenes Laërtius, viii. 39; comp. Plutarch, de Gen. Socr. p. 583
^ Grant 1989, p. 278.
^ Simoons 1998, p. 227.
^ Simoons 1998, pp. 225–228.
^ a b c Pomeroy 2013, p. xvi.
^ a b c d Kahn 2001, p. 8.
^ a b c Pomeroy 2013, p. 1.
^ Ferguson 2008, p. 58.
^ a b c d e f g h i j k l m n o p q Ferguson 2008, p. 59.
^ Riedweg 2005, p. 10.
^ a b
Diogenes Laërtius, Lives of Eminent Philosophers, viii. 1, 8.
^ a b Mary Ellen Waithe, Ancient women philosophers, 600 B.C.–500
A.D., p. 11
^ a b Malone, John C. (30 June 2009). Psychology:
present. MIT Press. p. 22. ISBN 978-0-262-01296-6. Retrieved
25 October 2010.
^ a b c d Riedweg 2005, p. 8.
^ Porphyry, Vit. Pyth. 2,
Diogenes Laërtius, viii. 2.
^ a b Iamblichus, Vit. Pyth. 9.
^ Porphyry, Vit. Pyth. 2.
Aristoxenus and others in
Diogenes Laërtius, i. 118, 119; Cicero,
de Div. i. 49
^ Riedweg 2005, p. 9.
^ C. B. Boyer (1968)
^ a b Zhmud 2012, pp. 2, 16.
^ Porphyry, Life of Pythagoras, 41.
^ Gilles Ménage: The history of women philosophers. Translated from
the Latin with an introduction by Beatrice H. Zedler. University Press
of America, Lanham 1984, p. 48. "The person who is referred to as
Themistoclea in Laertius and Theoclea in Suidas, Porphyry calls
^ Iamblichus, Vit. Pyth. 25; Porphyry, Vit. Pyth. 17; Diogenes
Laërtius, viii. 3.
^ Ariston. ap.
Diogenes Laërtius, viii. 8, 21; Porphyry, Vit. Pyth.
^ Porphyry, Vit. Pyth. 6.
Diogenes Laërtius, viii. 1, 3.
^ Plutarch, On Isis And Osiris, ch. 10.
^ Antiphon. ap. Porphyry, Vit. Pyth. 7; Isocrates, Busiris, 28–9;
Cicero, de Finibus, v. 27; Strabo, xiv.
^ Press 2003, p. 83.
^ a b Bruhn 2005, p. 66.
^ a b Burkert 1972, pp. 106–109.
^ Kahn 2001, pp. 5–6.
^ Kahn 2001, pp. 9–11.
^ a b Burkert 1972, pp. 29–30.
^ a b c Kahn 2001, p. 11.
^ a b Zhmud 2012, p. 232.
^ Burkert 1985, pp. 300–301.
Diogenes Laërtius, viii. 36, comp. Aristotle, de Anima, i. 3;
Herodotus, ii. 123.
^ Kahn 2001, p. 12.
Diogenes Laërtius, viii. 3–4
^ Cornelli & McKirahan 2013, pp. 164–167.
^ Porphyry, Vit. Pyth. 26; Pausanias, ii. 17;
viii. 5; Horace, Od. i. 28,1. 10
^ Cornelli & McKirahan 2013, pp. 164–165.
^ Cornelli & McKirahan 2013, pp. 165–166.
^ a b c Cornelli & McKirahan 2013, p. 167.
^ Aulus Gellius, iv. 11
^ a b Riedweg 2005, pp. 29–30.
^ a b c Riedweg 2005, p. 30.
^ D. S. Hutchinson; Monte Ransome Johnson (25 January 2015). "New
Reconstruction, includes Greek text". p. 48.
^ Cicero, de Divin. i. 3, 46; Porphyry, Vit. Pyth. 29.
^ Iamblichus, Vit. Pyth. 25; Porphyry, Vit. Pyth. 17; Diogenes
Laërtius, viii. 3, 13; Cicero, Tusc. Qu. v. 3.
^ a b c Bruhn 2005, pp. 65–66.
^ a b c d Riedweg 2005, p. 29.
^ a b c d Kahn 2001, pp. 1–2.
^ a b Burkert 1972, pp. 467–468.
^ Burkert 1972, p. 265.
^ Kahn 2001, p. 27.
^ a b Riedweg 2005, p. 23.
^ a b c Joost-Gaugier 2006, pp. 170–172.
^ a b c Joost-Gaugier 2006, p. 172.
^ a b Burkert 1972, p. 433.
^ Burkert 1972, p. 467.
^ Joost-Gaugier 2006, p. 170.
^ a b c Joost-Gaugier 2006, p. 161.
^ Iamblichus, Vit. Pyth., 29
^ Joost-Gaugier 2006, pp. 87–88.
^ a b c Kahn 2001, pp. 2–3.
^ Kahn 2001, p. 3.
^ a b Burkert 1972, pp. 428–433.
^ Burkert 1972, p. 465.
Diogenes Laërtius, viii. 12; Plutarch, Non posse suav. vivi sec.
Ep. p. 1094
^ Porphyry, in Ptol. Harm. p. 213;
Diogenes Laërtius, viii. 12.
Diogenes Laërtius, viii. 14 ; Pliny, Hist. Nat. ii. 8.
Diogenes Laërtius, viii. 12, 14, 32.
^ Kahn 2001, pp. 32–33.
^ Riedweg 2005, pp. 26–27.
^ a b c d e f Riedweg 2005, p. 27.
^ Burkert 1972, p. 428.
^ Burkert 1972, pp. 429, 462.
^ a b Kahn 2001, p. 32.
^ Ferguson 2008, pp. 6–7.
^ a b c Burkert 1972, p. 429.
^ Kahn 2001, p. 33.
^ a b Riedweg 2005, pp. 27–28.
^ a b c d Riedweg 2005, p. 28.
^ a b Christensen 2002, p. 143.
^ a b Burkert 1972, p. 306.
^ a b Burkert 1972, pp. 307–308.
^ Burkert 1972, pp. 306–308.
^ Kahn 2001, p. 53.
^ Dicks 1970, p. 68.
^ a b Riedweg 2005, p. 1.
^ a b c d e f g Riedweg 2005, p. 2.
^ a b c d e Ferguson 2008, p. 60.
^ Porphyry, Vit. Pyth. 20; Iamblichus, Vit. Pyth. 31, 140; Aelian,
Varia Historia, ii. 26;
Diogenes Laërtius, viii. 36.
^ a b c McKeown 2013, p. 155.
^ Comp. Herodian, iv. 94, etc.
^ Ferguson 2008, p. 10.
^ See Antoine Faivre, in The Eternal
^ Joost-Gaugier 2006, p. 47.
^ a b Ferguson 2008, pp. 58–59.
^ a b c Cornelli & McKirahan 2013, p. 160.
^ Ferguson 2008, pp. 60–61.
^ a b c d e Ferguson 2008, p. 61.
^ Plato, Republic, 600a, Isocrates, Busiris, 28
^ a b c d Cornelli & McKirahan 2013, p. 168.
^ Grant 1989, p. 277.
^ Aelian, Varia Historia, ii. 26;
Diogenes Laërtius, viii. 13;
Iamblichus, Vit. Pyth. 8, 91, 141
^ Porphyry, Vit. Pyth. 19
^ Thirlwall, Hist. of Greece, vol. ii. p. 148
^ a b c d Riedweg 2005, p. 31.
^ comp. Cicero, de Leg. i. 12, de Off. i. 7;
Diogenes Laërtius, viii.
^ a b Cornelli & McKirahan 2013, p. 65.
^ Aristonexus ap. Iamblichus, Vit. Pyth. 94, 101, etc., 229, etc.;
comp. the story of Damon and Phintias; Porphyry, Vit. Pyth. 60;
Iamblichus, Vit. Pyth. 233, etc.
^ Cornelli & McKirahan 2013, pp. 68–69.
^ John Dillon and Jackson Hershbell, (1991), Iamblichus, On the
Pythagorean Way of Life, page 14. Scholars Press.; D. J. O'Meara,
Mathematics and Philosophy in Late
Antiquity, pages 35–40. Clarendon Press.
^ Scholion ad Aristophanes, Nub. 611; Iamblichus, Vit. Pyth. 237, 238
^ a b Cornelli & McKirahan 2013, p. 69.
^ Riedweg 2005, pp. 64-67.
^ Riedweg 2005, p. 64.
^ Riedweg 2005, p. 65.
^ Riedweg 2005, pp. 65-67.
^ Riedweg 2005, pp. 65-66.
^ Riedweg 2005, pp. 66-67.
^ a b c d e f g h i Riedweg 2005, p. 66.
^ Pomeroy 2013, pp. xvi–xvii.
^ Riedweg 2005, pp. 33–34.
^ comp. Porphyry, Vit. Pyth. 32; Iamblichus, Vit. Pyth. 96, etc.
^ Zhmud 2012, pp. 137, 200.
^ a b Zhmud 2012, p. 200.
Diogenes Laërtius, viii. 19, 34; Aulus Gellius, iv. 11; Porphyry,
Vit. Pyth. 34, de Abst. i. 26; Iamblichus, Vit. Pyth. 98
^ a b Kahn 2001, p. 9.
^ Plutarch, de Esu Carn. pp. 993, 996, 997
^ Eudoxus, frg. 325
^ a b c d Zhmud 2012, p. 235.
^ Aristo ap.
Diogenes Laërtius, viii. 20; comp. Porphyry, Vit. Pyth.
7; Iamblichus, Vit. Pyth. 85, 108
Diogenes Laërtius, viii. 20
^ comp. Porphyry, Vit. Pyth. 7; Iamblichus, Vit. Pyth. 85, 108
^ Iamblichus, Vit. Pyth. 98; Strabo, vi.
^ a b c Kahn 2001, pp. 55–62.
^ Kahn 2001, pp. 48–49.
^ a b Kahn 2001, p. 39.
^ Kahn 2001, pp. 39–43.
^ Kahn 2001, pp. 39–40.
^ Kahn 2001, pp. 40, 44–45.
^ Plato, Republic VII, 530d
^ Metaphysics, 1.6.1 (987a)
^ Kahn 2001, p. 1.
^ Tusc. Disput. 1.17.39.
^ Kahn 2001, p. 55.
^ a b c d Hare 1999, pp. 117–119.
^ Russell 2008, pp. 33–37.
^ Russell 2008, p. 37.
^ Riedweg 2005, pp. 123–124.
^ Riedweg 2005, p. 124.
^ a b Riedweg 2005, pp. 125–126.
^ a b c Riedweg 2005, p. 125.
^ Riedweg 2005, pp. 126–127.
^ a b Joost-Gaugier 2006, pp. 166–181.
^ Homann-Wedeking 1968, p. 63.
^ Homann-Wedeking 1968, p. 62.
^ a b c d e Carpenter 1921, pp. 107, 122, 128.
^ Homann-Wedeking 1968, pp. 62–63.
^ a b Bowra 1994, p. 166.
^ Homann-Wedeking 1968, pp. 62–65.
^ "Each part (finger, palm, arm, etc) transmitted its individual
existence to the next, and then to the whole": Canon of Polykleitos,
also Plotinus, Ennead I.vi.i: Nigel Spivey, pp. 290–294.
^ Joost-Gaugier 2006, p. 154.
^ Joost-Gaugier 2006, pp. 154–156.
^ Joost-Gaugier 2006, pp. 157–158.
^ Joost-Gaugier 2006, p. 158.
^ Joost-Gaugier 2006, pp. 158–159.
^ Joost-Gaugier 2006, p. 159.
^ Joost-Gaugier 2006, pp. 159–161.
^ a b Joost-Gaugier 2006, p. 162.
^ Joost-Gaugier 2006, pp. 162–164.
^ Joost-Gaugier 2006, pp. 167–168.
^ Joost-Gaugier 2006, p. 168.
^ Joost-Gaugier 2006, pp. 169–170.
^ a b c d e f g h i j k l m n o Grafton, Most & Settis 2010,
^ a b c Russo 2004, pp. 5–87, especially 51–53.
^ a b Kahn 2001, p. 160.
^ Kahn 2001, pp. 161–171.
^ Ferguson 2008, p. 265.
^ a b Ferguson 2008, pp. 264–274.
^ Kahn 2001, p. 162.
^ Ferguson 2008, p. 274.
^ Ferguson 2008, p. 279.
^ a b Ferguson 2008, pp. 279–280.
^ a b Kahn 2001, p. 172.
^ Whitehead 1953, pp. 36–37.
^ Whitehead 1953, p. 36.
^ a b Borlik 2011, p. 192.
^ Borlik 2011, p. 189.
^ a b Borlik 2011, pp. 189–190.
^ a b c d e f Borlik 2011, p. 190.
^ Ferguson 2008, p. 282.
^ a b Ferguson 2008, p. 294.
^ a b Riedweg 2005, pp. 127–128.
^ a b c Riedweg 2005, p. 128.
^ a b c d French 2002, p. 30.
^ Riedweg 2005, p. 133.
^ a b Sherman 1995, p. 15.
^ Ferguson 2008, pp. 284–288.
^ Ferguson 2008, pp. 287–288.
^ Ferguson 2008, pp. 286–287.
^ Ferguson 2008, p. 288.
^ a b c Haag 2013, p. 89.
^ Haag 2013, p. 90.
^ Haag 2013, pp. 90–91.
^ a b c d e f Haag 2013, p. 91.
^ Haag 2013, pp. 91–92.
^ Haag 2013, p. 92.
^ a b c d Bregman 2002, p. 186.
Classical secondary sources
Only a few relevant source texts deal with
Pythagoras and the
Pythagoreans, most are available in different translations. Other
texts usually build solely on information in these works.
Diogenes Laërtius, Vitae philosophorum VIII (Lives of Eminent
Philosophers), c. 200 AD, which in turn references the lost work
Successions of Philosophers
Successions of Philosophers by
Alexander Polyhistor —
Diogenes (1925). "Pythagoreans: Pythagoras". Lives of
the Eminent Philosophers. 2:8. Translated by Hicks, Robert Drew (Two
volume ed.). Loeb Classical Library.
Porphyry, Vita Pythagorae (Life of Pythagoras), c. 270 AD —
Porphyry, Life of Pythagoras, translated by Kenneth Sylvan Guthrie
Iamblichus, De Vita Pythagorica (On the Pythagorean Life), c. 300 AD
— Iamblichus, Life of Pythagoras, translated by Kenneth Sylvan
Apuleius, following Aristoxenus, writes about
Pythagoras in Apologia,
c. 150 AD, including a story of his being taught by Zoroaster—a
story also found in Clement of Alexandria.[a]
Hierocles of Alexandria, Golden Verses of Pythagoras, c. 430 AD
^ Vasunia, Phiroze (2007). "The Philosopher's Zarathushtra". In
Tuplin, Christopher. Persian Responses: Political and Cultural
Interaction with(in) the Achaemenid Empire. Swansea: The Classical
Press of Wales. p. 246. ISBN 978-1-910589-46-5.
Modern secondary sources
Bowra, C. M. (1994) , The Greek Experience, London, England:
Weidenfeld & Nicolson History, ISBN 978-1-85799-122-2
Bregman, Jay (2002), "
Neoplatonism and American Aesthetics", in
Alexandrakis, Aphrodite; Moulafakis, Nicholas J.,
Western Aesthetics, Studies in Neoplatonism: Ancient and Modern, 12,
Albany, New York: State University of New York Press,
Bruhn, Siglind (2005), The Musical Order of the Universe: Kepler,
Hesse, and Hindemith, Interfaces Series, Hillsdale, New York:
Pendragon Press, ISBN 978-1-57647-117-3
Borlik, Todd A. (2011), Ecocriticism and Early Modern English
Literature: Green Pastures, New York City, New York and London,
England: Routledge, ISBN 978-0-203-81924-1
Burkert, Walter (1 June 1972), Lore and
Science in Ancient
Pythagoreanism, Cambridge, Massachusetts: Harvard University Press,
Burkert, Walter (1985), Greek Religion, Cambridge, Massachusetts:
Harvard University Press, ISBN 0-674-36281-0
Carpenter, Rhys (1921), The Esthetic Basis Of Greek Art: Of The Fifth
And Fourth Centuries B.C., Bryn Mawr, Pennsylvania: Bryn Mawr College,
Christensen, Thomas (2002), The Cambridge History of Western Music
Theory, Cambridge, England: Cambridge University Press,
Cornelli, Gabriele; McKirahan, Richard (2013), In Search of
Pythagoreanism as an Historiographical Category,
Berlin, Germany: Walter de Gruyter, ISBN 978-3-11-030650-7
Dicks, D.R. (1970), Early Greek Astronomy to Aristotle, Ithaca, New
York: Cornell University Press, ISBN 978-0-8014-0561-7
Dillon, Sheila (24 December 2005),
Ancient Greek Portrait Sculpture:
Context, Subjects, and Styles, Cambridge, England: Cambridge
University Press, ISBN 978-1-107-61078-1
Ferguson, Kitty (2008), The
Music of Pythagoras: How an Ancient
Brotherhood Cracked the Code of the Universe and Lit the Path from
Antiquity to Outer Space, New York City, New York: Walker &
Company, ISBN 978-0-8027-1631-6
French, Peter J. (2002) , John Dee: The World of the Elizabethan
Magus, New York City, New York and London, England: Routledge,
Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (2010), The
Classical Tradition, Cambridge, Massachusetts and London, England: The
Belknap Press of Harvard University Press,
Grant, Michael (1989), The Classical Greeks, History of Civilization,
New York City, New York: Charles Schribner's Sons,
Guthrie, W. K. (1979), A History of Greek Philosophy: Earlier
Presocratics and the Pythagoreans, Cambridge, England: Cambridge
University Press, ISBN 0-521-29420-7
Haag, Michael (2013), Inferno Decoded: The Essential Companion to the
Myths, Mysteries and Locations of Dan Brown's Inferno, London,
England: Profile Books, Ltd., ISBN 978-1-78125-180-5
Hare, R.M. (1999) , "Plato", in Taylor, C.C.W.; Hare, R.M.;
Barnes, Jonathan, Greek Philosophers: Socrates, Plato, and Aristotle,
Past Masters, Oxford, England: Oxford University Press,
pp. 103–189, ISBN 978-0-19-285422-3
Hermann, Arnold (2005), To Think Like God:
Parmenides—the Origins of Philosophy, Las Vegas, Nevada: Parmenides
Publishing, ISBN 978-1-930972-00-1
Homann-Wedeking, Ernst (1968), The Art of Archaic Greece, Art of the
World, New York City, New York: Crown Publishers
Horky, Philip Sydney (2013),
Plato and Pythagoreanism, Oxford,
England: Oxford University Press, ISBN 978-0-19-989822-0
Joost-Gaugier, Christiane L. (2006), Measuring Heaven:
his Influence on Thought and Art in Antiquity and the Middle Ages,
Ithaca, New York: Cornell University Press,
Kahn, Charles H. (2001),
Pythagoras and the Pythagoreans: A Brief
History, Indianapolis, Indiana and Cambridge, England: Hackett
Publishing Company, ISBN 978-0-87220-575-8
Kingsley, Peter (1995), Ancient Philosophy, Mystery, and Magic:
Empedocles and the Pythagorean Tradition, Oxford, England: Oxford
McKeown, J. C. (2013), A Cabinet of Greek Curiosities: Strange Tales
and Surprising Facts from the Cradle of Western Civilization, Oxford,
England: Oxford University Press, ISBN 978-0-19-998210-3
O'Meara, Dominic J. (1989),
Pythagoras Revived, Oxford, England:
Oxford University Press, ISBN 0-19-823913-0
Press, Gerald A. (2003) , Development of the Idea of History in
Antiquity, Montreal, Canada and Kingston, New York: McGill-Queen's
University Press, ISBN 0-7735-1002-8
Pomeroy, Sarah B. (2013), Pythagorean Women: The History and Writings,
Baltimore, Maryland: The Johns Hopkins University Press,
Riedweg, Christoph (2005) , Pythagoras: His Life, Teachings, and
Influence, Ithaca, New York: Cornell University Press,
Russell, Bertrand (2008) , A History of Western Philosophy, A
Touchstone Book, New York City, New York: Simon & Schuster,
Russo, Attilio (2004), "Costantino Lascaris tra fama e oblio nel
Cinquecento messinese", Archivio Storico Messinese, Messina,
LXXXIV-LXXXV: 5–87, especially 51–53, ISSN 0392-0240
Schofield, Malcolm (2013), Aristotle,
Pythagoreanism in the
First Century BC: New Directions for Philosophy, Cambridge, England:
Cambridge University Press, ISBN 978-1-107-02011-5
Sherman, William Howard (1995), John Dee: The
Politics of Reading and
Writing in the English Renaissance, Amherst, Massachusetts: The
University of Massachusetts Press, ISBN 1-55849-070-1
Simoons, Frederick J. (1998), Plants of Life, Plants of Death,
Madison, Wisconsin: University of Wisconsin Press,
Whitehead, Afred North (1953) ,
Science and the Modern World,
Cambridge, England: Cambridge University Press,
Zhmud, Leonid (2012),
Pythagoras and the Early Pythagoreans,
translated by Windle, Kevin; Ireland, Rosh, Oxford, England: Oxford
University Press, ISBN 978-0-19-928931-8
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Huffman, Carl. "Pythagoras". In Zalta, Edward N. Stanford Encyclopedia
Pythagoras of Samos, The MacTutor History of
Mathematics and Statistics, University of St Andrews,
Pythagoras and the Pythagoreans, Fragments and Commentary, Arthur
Fairbanks Hanover Historical Texts Project, Hanover College Department
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