Pythagoras

Pythagoras of SamosTemplate:Efn (Template:Langx; Template:Circa BC)Template:Efn was an ancient Ionian Greek 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").Template:Efn 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 Hippasus and Philolaus.

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.

Biographical sources

No authentic writings of Pythagoras have survived,Template:SfnpTemplate:SfnpTemplate:Sfnp and almost nothing is known for certain about his life.Template:SfnpTemplate:SfnpTemplate:Sfnp The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical.Template:SfnpTemplate:SfnpTemplate:Sfnp The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by the Greek philosopher Xenophanes of Colophon (Template:Circa BC), who had been one of his contemporaries.Template:SfnpTemplate:Sfnp In the poem, Xenophanes describes Pythagoras interceding on behalf of a dog that is being beaten, professing to recognize in its cries the voice of a departed friend.Template:EfnTemplate:SfnpTemplate:SfnpTemplate:Sfnp Alcmaeon of Croton (Template:Fl. BC), a doctor who lived in Croton at around the same time Pythagoras lived there,Template:Sfnp incorporates many Pythagorean teachings into his writingsTemplate:Sfnp and alludes to having possibly known Pythagoras personally.Template:Sfnp The poet Heraclitus of Ephesus (Template:Fl. BC), who was born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime,Template:Sfnp mocked Pythagoras as a clever charlatan,Template:SfnpTemplate:Sfnp 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."Template:SfnpTemplate:Sfnp

Fictionalized portrait of Pythagoras from a 17th-century engraving

The Greek poets Ion of Chios (Template:Circa BC) and Empedocles of Acragas (Template:Circa BC) both express admiration for Pythagoras in their poems.Template:Sfnp The first concise description of Pythagoras comes from the historian Herodotus of Halicarnassus (Template:Circa BC),Template:Sfnp who describes him as one of the greatest Greek teachersTemplate:Efn and states that Pythagoras taught his followers how to attain immortality.Template:Sfnp The accuracy of the works of Herodotus is controversial.Template:SfnpTemplate:SfnpTemplate:SfnpTemplate:SfnpTemplate:Sfnp The writings attributed to the Pythagorean philosopher Philolaus of Croton (Template:Circa BC) are the earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras.Template:Sfnp The Athenian rhetorician Isocrates (Template:Circa BC) was the first to describe Pythagoras as having visited Egypt.Template:Sfnp Aristotle (Template:Circa BC) wrote a treatise On the Pythagoreans, which no longer exists. Some of it may be preserved in the Protrepticus. Aristotle's disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus (who all lived in the 3rd century BC) also wrote on the same subject.Template:Sfnp

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

Life

Early life

Herodotus,Template:Sfnp Isocrates, and other early writers agree that Pythagoras was the son of Mnesarchus,Template:SfnpTemplate:Sfnp and that he was born on the Greek island of Samos in the eastern Aegean.Template:SfnpTemplate:SfnpTemplate:SfnpTemplate:Sfnp According to these biographers, Pythagoras's father was not born on the island, although he got naturalized there,Template:Sfnp but according to Iamblichus he was a native of the island.Template:Sfnp He is said to have been a gem-engraver or a wealthy merchantTemplate:SfnpTemplate:Sfnp but his ancestry is disputed and unclear.Template:Efn His mother was a native of Samos, descending from a geomoroi family.Template:Sfnp Apollonius of Tyana, gives her name as Pythaïs.Template:Sfnp Iamblichus tells the story that the Pythia prophesied to her while she was pregnant with him that she would give birth to a man supremely beautiful, wise, and beneficial to humankind.Template:Sfnp 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.Template:Sfnp Pythagoras's name led him to be associated with Pythian Apollo (Template:Transliteration); Aristippus of Cyrene in the 4th century BC explained his name by saying, "He spoke [[[:Template:Lang]], Template:Transliteration] the truth no less than did the Pythian [[[:Template:Lang]] Template:Transliteration]".Template:Sfnp

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.Template:Sfnp It was a major center of trade in the Aegean where traders brought goods from the Near East.Template:Sfnp According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions.Template:Sfnp Pythagoras's early life also coincided with the flowering of early Ionian natural philosophy.Template:SfnpTemplate:Sfnp He was a contemporary of the philosophers Anaximander, Anaximenes, and the historian Hecataeus, all of whom lived in Miletus, across the sea from Samos.Template:Sfnp

Reputed travels

Template:Anchor Pythagoras is traditionally thought to have received most of his education in the Near East.Template:Sfnp Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures.Template:Sfnp Like many other important Greek thinkers, Pythagoras was said to have studied in Egypt.Template:SfnpTemplate:SfnpTemplate:Sfnp By the time of Isocrates in the fourth century BC, Pythagoras's reputed studies in Egypt were already taken as fact.Template:SfnpTemplate:Sfnp The writer Antiphon, who may have lived during the Hellenistic Era, claimed in his lost work On Men of Outstanding Merit, used as a source by Porphyry, that Pythagoras learned to speak Egyptian from the Pharaoh Amasis II himself, that he studied with the Egyptian priests at Diospolis (Thebes), and that he was the only foreigner ever to be granted the privilege of taking part in their worship.Template:SfnpTemplate:Sfnp The Middle Platonist biographer Plutarch (Template:Circa AD) writes in his treatise On Isis and Osiris that, during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of Heliopolis (meanwhile Solon received lectures from a Sonchis of Sais).Template:Sfnp According to the Christian theologian Clement of Alexandria (Template:Circa AD), "Pythagoras was a disciple of Sonchis, an Egyptian archprophet, as well as a Plato of Sechnuphis."Template:Sfnp Some ancient writers claimed that Pythagoras learned geometry and the doctrine of metempsychosis from the Egyptians.Template:Sfnp

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

Alleged Greek teachers

Bust of Pythagoras in the Vatican Museums, Vatican City, showing him as a "tired-looking older man"Template:Sfnp

Bronze bust of a philosopher wearing a tainia from Villa of the Papyri, Herculaneum, possibly a fictional bust of PythagorasTemplate:SfnpTemplate:Sfnp

Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers.Template:Sfnp Some identify Hermodamas of Samos as a possible tutor.Template:Sfnp Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer.Template:Sfnp Others credit Bias of Priene, Thales,Template:Sfnp or Anaximander (a pupil of Thales).Template:SfnpTemplate:SfnpTemplate:Sfnp Other traditions claim the mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphic Mysteries.Template:Sfnp 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.Template:Sfnp Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship.Template:Sfnp 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.Template:Sfnp Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent.Template:Sfnp

Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros is mentioned most often.Template:Sfnp 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.Template:Sfnp Apollonius Paradoxographus, a paradoxographer who may have lived in the second century BC, identified Pythagoras's thaumaturgic ideas as a result of Pherecydes's influence.Template:Sfnp 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.Template:Sfnp Duris, the historian and tyrant of Samos, is reported to have patriotically boasted of an epitaph supposedly penned by Pherecydes which declared that Pythagoras's wisdom exceeded his own.Template:Sfnp 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.Template:Sfnp Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis.Template:Sfnp

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,Template:Sfnp also known for a special case of the inscribed angle theorem. Pythagoras's birthplace, the island of Samos, is situated in the Northeast Aegean Sea not far from Miletus.Template:Sfnp Diogenes Laërtius cites a statement from Aristoxenus (fourth century BC) stating that Pythagoras learned most of his moral doctrines from the Delphic priestess Themistoclea.Template:SfnpTemplate:SfnpTemplate:Sfnp Porphyry agrees with this assertionTemplate:Sfnp but calls the priestess Aristoclea (Aristokleia).Template:Sfnp Ancient authorities furthermore note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphic or Cretan mysteries, or the Delphic oracle.

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".Template:SfnpTemplate:Sfnp Here, Samians debated matters of public concern.Template:SfnpTemplate:Sfnp Supposedly, the school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach.Template:Sfnp Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends.Template:SfnpTemplate:Sfnp Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos,Template:Sfnp 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.Template:Sfnp

Around 530 BC, when Pythagoras was about forty years old, he left Samos.Template:SfnpTemplate:SfnpTemplate:SfnpTemplate:SfnpTemplate:Sfnp His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos;Template:Sfnp 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.Template:Sfnp 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. He arrived in the Greek colony of Croton (today's Crotone, in Calabria) in what was then Magna Graecia.Template:SfnpTemplate:SfnpTemplate:SfnpTemplate:Sfnp All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment.Template:SfnpTemplate:SfnpTemplate:Sfnp He served as an advisor to the elites in Croton and gave them frequent advice.Template:Sfnp 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.Template:Sfnp

Family and friends

Illustration from 1913 showing Pythagoras teaching a class of women. Many prominent members of his school were womenTemplate:SfnpTemplate:Sfnp and some modern scholars think that he may have believed that women should be taught philosophy as well as men.Template:Sfnp

Diogenes Laërtius states that Pythagoras "did not indulge in the pleasures of love"Template:Sfnp and that he cautioned others to only have sex "whenever you are willing to be weaker than yourself".Template:Sfnp According to Porphyry, Pythagoras married Theano, a lady of Crete and the daughter of PythenaxTemplate:Sfnp and had several children with her.Template:Sfnp Porphyry writes that Pythagoras had two sons named Telauges and Arignote,Template:Sfnp and a daughter named Myia,Template:Sfnp who "took precedence among the maidens in Croton and, when a wife, among married women."Template:Sfnp Iamblichus mentions none of these childrenTemplate:Sfnp and instead only mentions a son named Mnesarchus after his grandfather.Template:Sfnp This son was raised by Pythagoras's appointed successor Aristaeus and eventually took over the school when Aristaeus was too old to continue running it.Template:Sfnp Suda writes that Pythagoras had 4 children (Telauges, Mnesarchus, Myia and Arignote).

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

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.Template:Sfnp After the victory, some prominent citizens of Croton proposed a democratic constitution, which the Pythagoreans rejected.Template:Sfnp 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.Template:Sfnp 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.Template:SfnpTemplate:Sfnp 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.Template:SfnpTemplate:Sfnp The building was apparently set on fire,Template:Sfnp and many of the assembled members perished;Template:Sfnp only the younger and more active members managed to escape.

Sources disagree regarding whether Pythagoras was present when the attack occurred and, if he was, whether or not he managed to escape.Template:SfnpTemplate:Sfnp In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes.Template:Sfnp According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape,Template:Sfnp leading a small group of followers to the nearby city of Locris, where they pleaded for sanctuary, but were denied.Template:Sfnp 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.Template:SfnpTemplate:SfnpTemplate:SfnpTemplate:Sfnp 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.Template:Sfnp Pythagoras managed to escape, but was so despondent at the deaths of his beloved students that he committed suicide.Template:Sfnp 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.Template:SfnpTemplate:Sfnp This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself.Template:Sfnp

Teachings

Metempsychosis

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

Although the exact details of Pythagoras's teachings are uncertain,Template:SfnpTemplate:Sfnp it is possible to reconstruct a general outline of his main ideas.Template:SfnpTemplate:Sfnp Aristotle writes at length about the teachings of the Pythagoreans,Template:SfnpTemplate:Sfnp but without mentioning Pythagoras directly.Template:SfnpTemplate:Sfnp One of Pythagoras's main doctrines appears to have been metempsychosis,Template:SfnpTemplate:SfnpTemplate:SfnpTemplate:SfnpTemplate:SfnpTemplate:Sfnp the belief that all souls are immortal and that, after death, a soul is transferred into a new body.Template:SfnpTemplate:Sfnp This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus.Template:Sfnp Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur.Template:Sfnp

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

Mysticism

Another belief attributed to Pythagoras was that of the "harmony of the spheres",Template:SfnpTemplate:Sfnp which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony.Template:SfnpTemplate:Sfnp According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together.Template:Sfnp In his philosophical dialogue Protrepticus, Aristotle has his literary double say:

Pythagoras was said to have practiced divination and prophecy. The earliest mentions of divination by isopsephy in Greek literature associate it with Pythagoras; he was viewed as the founder of this practice. According to his biographer, Iamblichus, he taught his method of divination to a Scythian priest of Apollo by the name of Abaris the Hyperborean:Template:Sfnp

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 Template:Lang Template:Gloss or Template:Gloss, 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; these 'roots' or 'base numbers' could then be interpreted with other techniques, such as traditional Pythagorean attributions. This latter form of numerology flourished during the Byzantine era, and was first attested among the Gnostics of the second century AD. By that time, isopsephy had developed into several different techniques that were used for a variety of purposes; including divination, doctrinal allegory, and medical prognosis and treatment.

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.

Numerology

Pythagoras is credited with having devised the tetractys,Template:SfnpTemplate:Sfnp an important sacred symbol in later Pythagoreanism.Template:SfnpTemplate:Sfnp

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

Ten was regarded as the "perfect number"Template:Sfnp and the Pythagoreans honored it by never gathering in groups larger than ten.Template:Sfnp Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the perfect number, ten.Template:SfnpTemplate:Sfnp The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance.Template:SfnpTemplate:SfnpTemplate:Sfnp 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.Template:SfnpTemplate:SfnpTemplate:SfnpTemplate:Sfnp Andrew Gregory concludes that the tradition linking Pythagoras to the tetractys is probably genuine.Template:Sfnp

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

Pythagoreanism

Communal lifestyle

Pythagoreans Celebrate the Sunrise (1869) by Fyodor Bronnikov

Template:Main Both Plato and Isocrates state that, above all else, Pythagoras was known as the founder of a new way of life.Template:SfnpTemplate:Sfnp The organization Pythagoras founded at Croton was called a "school",Template:Sfnp but, in many ways, resembled a monastery.Template:Sfnp 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 commonTemplate:Sfnp and were devoted to each other to the exclusion of outsiders.Template:Sfnp Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans.Template:Sfnp One Pythagorean maxim was "koinà tà phílōn" ("All things in common among friends").Template:Sfnp 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. Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time.Template:Sfnp 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.Template:Sfnp Two groups existed within early Pythagoreanism: the mathematikoi ("learners") and the akousmatikoi ("listeners").Template:SfnpTemplate:Sfnp The akousmatikoi are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings;Template:Sfnp whereas the mathematikoi are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific.Template:Sfnp Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed the two approaches were compatible.Template:Sfnp The study of mathematics and music may have been connected to the worship of Apollo. The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body.Template:Sfnp 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.Template:Sfnp The Pythagoreans also placed particular emphasis on the importance of physical exercise;Template:Sfnp therapeutic dancing, daily morning walks along scenic routes, and athletics were major components of the Pythagorean lifestyle.Template:Sfnp Moments of contemplation at the beginning and end of each day were also advised.Template:Sfnp

Prohibitions and regulations

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

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

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

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

Pythagoreanism also entailed a number of dietary prohibitions.Template:SfnpTemplate:Sfnp It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beansTemplate:SfnpTemplate:Sfnp and the meat of non-sacrificial animals such as fish and poultry.Template:SfnpTemplate:Sfnp Both of these assumptions, however, have been contradicted.Template:Sfnp Pythagorean dietary restrictions may have been motivated by belief in the doctrine of metempsychosis.Template:SfnpTemplate:SfnpTemplate:SfnpTemplate:Sfnp Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet.Template:EfnTemplate:SfnpTemplate:Sfnp 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."Template:Sfnp 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.Template:Sfnp According to Heraclides Ponticus, Pythagoras ate the meat from sacrificesTemplate:Sfnp and established a diet for athletes dependent on meat.Template:Sfnp

Legends

Pythagoras Emerging from the Underworld (1662) by Salvator Rosa

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

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

Riedweg suggests that Pythagoras may have personally encouraged these legends,Template:Sfnp but Gregory states that there is no direct evidence of this.Template:Sfnp Anti-Pythagorean legends were also circulated.Template:Sfnp Diogenes Laërtes retells a story told by Hermippus of Samos, which states that Pythagoras had once gone into an underground room, telling everyone that he was descending to the underworld.Template:Sfnp He stayed in this room for months, while his mother secretly recorded everything that happened during his absence.Template:Sfnp After he returned from this room, Pythagoras recounted everything that had happened while he was gone,Template:Sfnp convincing everyone that he had really been in the underworldTemplate:Sfnp and leading them to trust him with their wives.Template:Sfnp

Attributed discoveries

In mathematics

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

Although Pythagoras is most famous today for his alleged mathematical discoveries,Template:SfnpTemplate:Sfnp classical historians dispute whether he himself ever actually made any significant contributions to the field.Template:SfnpTemplate:Sfnp 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,Template:SfnpTemplate:Sfnp 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"Template:Sfnp—that is, $a^2+b^2=c^2$. According to a popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole hecatomb, to the gods.Template:SfnpTemplate:Sfnp Cicero rejected this story as spuriousTemplate:Sfnp because of the much more widely held belief that Pythagoras forbade blood sacrifices.Template:Sfnp Porphyry attempted to explain the story by asserting that the ox was actually made of dough.Template:Sfnp

The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras,Template:SfnpTemplate:SfnpTemplate:SfnpTemplate:Sfnp but he may have been the first to introduce it to the Greeks.Template:SfnpTemplate:Sfnp Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof.Template:Sfnp Burkert rejects this suggestion as implausible,Template:Sfnp noting that Pythagoras was never credited with having proved any theorem in antiquity.Template:Sfnp 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.Template:Efn Pythagoras's biographers state that he also was the first to identify the five regular solidsTemplate:Sfnp and that he was the first to discover the Theory of Proportions.Template:Sfnp

In music

Late medieval woodcut from Franchino Gafurio's Theoria musice (1492), showing Pythagoras with bells and other instruments in Pythagorean tuningTemplate:Sfnp

Template:See also 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.Template:SfnpTemplate:Sfnp Thinking that the sounds of the hammers were beautiful and harmonious, except for one,Template:Sfnp he rushed into the blacksmith shop and began testing the hammers.Template:Sfnp 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.Template:SfnpTemplate:Sfnp

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

Later influence in antiquity

On Greek philosophy

Medieval manuscript of Calcidius's Latin translation of Plato's Timaeus, which is one of the Platonic dialogues with the most overt Pythagorean influencesTemplate:Sfnp

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

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.Template:Sfnp Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy, science, and morality.Template:Sfnp Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world"Template:Sfnp and both were probably influenced by Orphism.Template:Sfnp The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans.Template:Sfnp Bertrand Russell, in his A History of Western Philosophy, contends that the influence of Pythagoras on Plato and others was so great that he should be considered the most influential philosopher of all time.Template:Sfnp He concludes that "I do not know of any other man who has been as influential as he was in the school of thought."Template:Sfnp

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

On art and architecture

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

Greek sculpture sought to represent the permanent reality behind superficial appearances.Template:Sfnp Early Archaic sculpture represents life in simple forms, and may have been influenced by the earliest Greek natural philosophies.Template:Efn The Greeks generally believed that nature expressed itself in ideal forms and was represented by a type (Template:Lang), which was mathematically calculated.Template:SfnpTemplate:Sfnp When dimensions changed, architects sought to relay permanence through mathematics.Template:SfnpTemplate:Sfnp Maurice Bowra believes that these ideas influenced the theory of Pythagoras and his students, who believed that "all things are numbers".Template:Sfnp

During the sixth century BC, the number philosophy of the Pythagoreans triggered a revolution in Greek sculpture.Template:Sfnp Greek sculptors and architects attempted to find the mathematical relation (canon) behind aesthetic perfection.Template:Sfnp Possibly drawing on the ideas of Pythagoras,Template:Sfnp the sculptor Polykleitos wrote in his Canon that beauty consists in the proportion, not of the elements (materials), but of the interrelation of parts with one another and with the whole.Template:SfnpTemplate:Efn 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."Template:Sfnp

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

The emperor Hadrian's Pantheon in Rome was also built based on Pythagorean numerology.Template:Sfnp 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.Template:Sfnp The single oculus at the top of the dome symbolizes the monad and the sun-god Apollo.Template:Sfnp 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.Template:Sfnp The five coffered rings beneath the ribs represent the marriage of the sun and moon.Template:Sfnp

In early Christianity

Many early Christians had a deep respect for Pythagoras.Template:Sfnp Eusebius (Template:Circa AD), bishop of Caesarea, praises Pythagoras in his Against Hierokles for his rule of silence, his frugality, his "extraordinary" morality, and his wise teachings.Template:Sfnp In another work, Eusebius compares Pythagoras to Moses.Template:Sfnp In one of his letters, the Church Father Jerome (Template:Circa AD) praises Pythagoras for his wisdomTemplate:Sfnp and, in another letter, he credits Pythagoras for his belief in the immortality of the soul, which he suggests Christians inherited from him.Template:Sfnp Augustine of Hippo (354–430 AD) rejected Pythagoras's teaching of metempsychosis without explicitly naming him, but otherwise expressed admiration for him.Template:Sfnp 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".Template:Sfnp In another passage, Augustine defends Pythagoras's reputation, arguing that Pythagoras certainly never taught the doctrine of metempsychosis.Template:Sfnp

Influence after antiquity

In the Middle Ages

Pythagoras appears in a relief sculpture on one of the archivolts over the right door of the west portal at Chartres Cathedral.Template:Sfnp

During the Middle Ages, Pythagoras was revered as the founder of mathematics and music, two of the Seven Liberal Arts.Template:Sfnp He appears in numerous medieval depictions, in illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres.Template:Sfnp The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe,Template:Sfnp which led William of Conches (c. 1080–1160) to declare that Plato was Pythagorean.Template:Sfnp A large-scale translation movement emerged during the Abbasid Caliphate, translating many Greek texts into Arabic. Works ascribed to Pythagoras included the "Golden Verses" and snippets of his scientific and mathematical theories.Template:SfnpTemplate:Page needed By translating and disseminating Pythagorean texts, Islamic scholars ensured their survival and wider accessibility. This preserved knowledge that might have otherwise been lost through the decline of the Roman Empire and the neglect of classical learning in Europe.Template:SfnpTemplate:Page needed In the 1430s, the Camaldolese friar Ambrose Traversari translated Diogenes Laërtius's Lives and Opinions of Eminent Philosophers from Greek into LatinTemplate:Sfnp and, in the 1460s, the philosopher Marsilio Ficino translated Porphyry and Iamblichus's Lives of Pythagoras into Latin as well,Template:Sfnp thereby allowing them to be read and studied by western scholars.Template:Sfnp In 1494, the Greek Neopythagorean scholar Constantine Lascaris published The Golden Verses of Pythagoras, translated into Latin, with a printed edition of his Grammatica,Template:Sfnp thereby bringing them to a widespread audience.Template:Sfnp In 1499, he published the first Renaissance biography of Pythagoras in his work Vitae illustrium philosophorum siculorum et calabrorum, issued in Messina.Template:Sfnp

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,Template:SfnpTemplate:Sfnp 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.Template:Sfnp Johannes Kepler considered himself to be a Pythagorean.Template:SfnpTemplate:SfnpTemplate:Sfnp He believed in the Pythagorean doctrine of musica universalisTemplate:Sfnp and it was his search for the mathematical equations behind this doctrine that led to his discovery of the laws of planetary motion.Template:Sfnp Kepler titled his book on the subject Harmonices Mundi (Harmonics of the World), after the Pythagorean teaching that had inspired him.Template:SfnpTemplate:Sfnp Near the conclusion of the book, Kepler describes himself falling asleep to the sound of the heavenly music, "warmed by having drunk a generous draughtTemplate:Nbsp... from the cup of Pythagoras."Template:Sfnp He also called Pythagoras the "grandfather" of all Copernicans.Template:Sfnp

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

On vegetarianism

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

A fictionalized portrayal of Pythagoras appears in Book XV of Ovid's Metamorphoses,Template:Sfnp in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet.Template:Sfnp 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.Template:Sfnp John Donne's Progress of the Soul discusses the implications of the doctrines expounded in the speech,Template:Sfnp 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.Template:Sfnp William Shakespeare references the speech in his play The Merchant of Venice.Template:Sfnp John Dryden included a translation of the scene with Pythagoras in his 1700 work Fables, Ancient and Modern,Template:Sfnp and John Gay's 1726 fable "Pythagoras and the Countryman" reiterates its major themes, linking carnivorism with tyranny.Template:Sfnp Lord Chesterfield records that his conversion to vegetarianism had been motivated by reading Pythagoras's speech in Ovid's Metamorphoses.Template:Sfnp Until the word vegetarianism was coined in the 1840s, vegetarians were referred to in English as "Pythagoreans".Template:Sfnp Percy Bysshe Shelley wrote an ode entitled "To the Pythagorean Diet",Template:Sfnp and Leo Tolstoy adopted the Pythagorean diet himself.Template:Sfnp

On Western esotericism

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

Heinrich Cornelius Agrippa's popular and influential three-volume treatise De Occulta Philosophia cites Pythagoras as a "religious magi"Template:Sfnp and advances the idea that Pythagoras's mystical numerology operates on a supercelestial level,Template:Sfnp 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.Template:Sfnp Rosicrucianism used Pythagorean symbolism,Template:Sfnp as did Robert Fludd (1574–1637),Template:Sfnp who believed his own musical writings to have been inspired by Pythagoras.Template:Sfnp John Dee was heavily influenced by Pythagorean ideology,Template:SfnpTemplate:Sfnp particularly the teaching that all things are made of numbers.Template:SfnpTemplate:Sfnp Adam Weishaupt, the founder of the Illuminati, was a strong admirer of PythagorasTemplate:Sfnp and, in his book Pythagoras (1787), he advocated that society should be reformed to be more like Pythagoras's commune at Croton.Template:Sfnp Wolfgang Amadeus Mozart incorporated Masonic and Pythagorean symbolism into his opera The Magic Flute.Template:Sfnp Sylvain Maréchal, in his six-volume 1799 biography The Voyages of Pythagoras, declared that all revolutionaries in all time periods are the "heirs of Pythagoras".Template:Sfnp

On literature

Dante Alighieri's description of Heaven in his Paradiso incorporates Pythagorean numerology.Template:Sfnp

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

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

See also

• List of things named after Pythagoras
• Ex pede Herculem, "from his foot, [we can measure] Hercules" – a maxim based on the apocryphal story that Pythagoras estimated Hercules's stature based on the length of a racecourse at Pisae
• Pythagorean cup – a prank cup with a hidden siphon built in, attributed to Pythagoras
• Pythagorean means – the arithmetic mean, the geometric mean, and the harmonic mean, claimed to have been studied by Pythagoras

References

Classical sources

• Template:Citation. [The original Greek fragments of Xenophanes are provided, which are primarily preserved through the work of Diogenes (Template:Harvnb). For English translation see Template:Harvp.]
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Modern secondary sources

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Further reading

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External links

• Template:In Our Time
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• "Pythagoras of Samos", The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland
• "Pythagoras and the Pythagoreans, Fragments and Commentary", Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History
• "Pythagoras and the Pythagoreans" Template:Webarchive, Department of Mathematics, Texas A&M University
• "Pythagoras and Pythagoreanism", The Catholic Encyclopedia
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