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Pythagoras of Samos, or simply ; in
Ionian Greek Ionic Greek ( grc, Ἑλληνική Ἰωνική, Hellēnikē Iōnikē) was a subdialect of the Attic–Ionic or Eastern dialect group of Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and t ...
() was an ancient Ionian
Greek philosopher Ancient Greek philosophy arose in the 6th century BC, at a time when the inhabitants of ancient Greece were struggling to repel devastating invasions from the east. Greek philosophy continued throughout the Hellenistic period The Hellenistic pe ...
and the eponymous founder of
Pythagoreanism Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras Pythagoras of Samos, or simply ; in () was an ancient and the eponymous founder of . His political and religious teachings were wel ...
. His political and religious teachings were well known in
Magna Graecia Magna Graecia (, ; Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republic ...

Magna Graecia
and influenced the philosophies of
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was an Classical Athens, Athenian philosopher during the Classical Greece, Classical period in Ancient Greece, founder of the Platonist school of thought and the Platoni ...

Plato
,
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questio ...

Aristotle
, and, through them,
Western philosophy Western philosophy encompasses the philosophical Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical or mental reality ...
. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of
Samos Samos (, also ; el, Σάμος ) is a Greece, Greek island in the eastern Aegean Sea, south of Chios, north of Patmos and the Dodecanese, and off the coast of western Turkey, from which it is separated by the -wide Mycale Strait. It is also a sep ...

Samos
. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to
Croton
Croton
in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a
communal A commune is an intentional community of people sharing living spaces, interests, values, beliefs, and often property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether ...
,
ascetic Asceticism (; from the el, ἄσκησις ''áskesis'', "exercise, training") is a lifestyle characterized by abstinence from sensual pleasures, often for the purpose of pursuing spiritual goals. Ascetics may withdraw from the world for their ...
lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included
vegetarianism Vegetarianism is the practice of abstaining from the consumption of meat Meat is animal Animals (also called Metazoa) are multicellular eukaryotic organisms that form the Kingdom (biology), biological kingdom Animalia. With few ex ...
, although modern scholars doubt that he ever advocated complete vegetarianism. The teaching most securely identified with Pythagoras is ''
metempsychosis Metempsychosis ( grc-gre, μετεμψύχωσις), in philosophy, refers to transmigration of the soul In many religious, philosophical, and myth Myth is a folklore genre consisting of narratives that play a fundamental role in a soci ...
'', or the "transmigration of souls", which holds that every
soul In many religious, philosophical, and myth Myth is a folklore genre consisting of narratives that play a fundamental role in a society, such as foundational tales or origin myths. The main characters in myths are usually non-humans, such as ...

soul
is
immortal Immortality is the ability to live forever, or eternal life. Immortal or Immortality may also refer to: Film * The Immortals (1995 film), ''The Immortals'' (1995 film), an American crime film * ''Immortality'', an alternate title for the 1998 Bri ...
and, upon death, enters into a new body. He may have also devised the doctrine of ''
musica universalis The ''musica universalis'' (literally universal music), also called music of the spheres or harmony of the spheres, is an ancient philosophical Philosophy (from , ) is the study of general and fundamental questions, such as those about ...
'', which holds that the
planets A planet is an astronomical body orbit In physics, an orbit is the gravitationally curved trajectory of an physical body, object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit r ...
move according to
mathematical Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
equation In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ge ...

equation
s and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras developed the
numerological Numerology is any belief in the divine or mysticism, mystical relationship between a number and one or more Coincidence#Interpretation, coinciding events. It is also the study of the numerical value of the letters in words, names, and ideas. I ...
and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly Philolaus of Croton. Following Croton's decisive victory over
Sybaris Sybaris ( grc, Σύβαρις; it, Sibari) was an important city of Magna Graecia Magna Graecia (, ; Latin meaning "Greater Greece", grc, Μεγάλη Ἑλλάς, ', it, Magna Grecia) was the name given by the Roman people, Romans to the c ...
in around 510 BC, Pythagoras's followers came into conflict with supporters of
democracy Democracy ( gr, δημοκρατία, ''dēmokratiā'', from ''dēmos'' 'people' and ''kratos'' 'rule') is a form of government in which people, the people have the authority to deliberate and decide legislation ("direct democracy"), or to cho ...
and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or escaped to
Metapontum Metapontum or Metapontium ( grc, Μεταπόντιον, Metapontion) was an important city of Magna Graecia Magna Graecia (, ; Latin meaning "Greater Greece", grc, Μεγάλη Ἑλλάς, ', it, Magna Grecia) was the name given by the Roman ...
, where he eventually died. In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the
Pythagorean theorem In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ...

Pythagorean theorem
,
Pythagorean tuning Pythagorean tuning is a system of musical tuning In music, there are two common meanings for tuning: * #Tuning practice, Tuning practice, the act of tuning an instrument or voice. * #Tuning systems, Tuning systems, the various systems of Pi ...
, the
five regular solids
five regular solids
, the Theory of Proportions, the sphericity of the Earth, and the identity of the
morning Morning is the period from sunrise 250px, Skyline of Kaohsiung harbour, Taiwan at sunrise. Sunrise (or sunup) is the moment when the upper rim of the Sun appears on the horizon in the morning. The term can also refer to the entire process of ...
and
evening stars
evening stars
as the planet
Venus Venus is the second planet from the Sun. It is named after the Venus (mythology), Roman goddess of love and beauty. As List of brightest natural objects in the sky, the brightest natural object in Earth's night sky after the Moon, Venus can ...

Venus
. It was said that he was the first man to call himself a philosopher ("lover of wisdom") 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 Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') was the philosophy, philosophical study of nature and the physical universe that was dominant before the development of modern science. From the ancient world, a ...
. Pythagoras influenced Plato, whose
dialogues Dialogue (sometimes spelled dialog in American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of variety (linguistics), varieties of the English language native ...
, especially his '' Timaeus'', exhibit Pythagorean teachings. Pythagorean ideas on mathematical perfection also impacted
ancient Greek art Ancient Greek art stands out among that of other ancient cultures for its development of naturalistic but idealized depictions of the human body, in which largely nude male figures were generally the focus of innovation. The rate of stylistic de ...
. His teachings underwent a major revival in the first century BC among
Middle Platonists Middle Platonism is the modern name given to a stage in the development of Platonic philosophy, lasting from about 90 BC – when Antiochus of Ascalon rejected the scepticism of the New Academy – until the development of Neoplatoni ...
, coinciding with the rise of
Neopythagoreanism Neopythagoreanism (or neo-Pythagoreanism) was a school of Hellenistic philosophy Hellenistic philosophy is the period of Western philosophy Western philosophy encompasses the philosophical Philosophy (from , ) is the study of gene ...
. Pythagoras continued to be regarded as a great philosopher throughout the
Middle Ages In the history of Europe The history of Europe concerns itself with the discovery and collection, the study, organization and presentation and the interpretation of past events and affairs of the people of Europe since the beginning of ...
and his philosophy had a major impact on scientists such as
Nicolaus Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, link=no, Niclas Koppernigk, modern: ''Nikolaus Kopernikus''; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic Church, C ...

Nicolaus Copernicus
,
Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer An astronomer is a in the field of who focuses their studies on a specific question or field outside the scope of . They observe s such as s, s, , s and ...

Johannes Kepler
, and
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

Isaac Newton
. Pythagorean symbolism was used throughout early modern European esotericism, and his teachings as portrayed in
Ovid Pūblius Ovidius Nāsō (; 20 March 43 BC – 17/18 AD), known in English as Ovid ( ), was a Augustan literature (ancient Rome), Roman poet who lived during the reign of Augustus. He was a contemporary of the older Virgil and Horace, with whom ...

Ovid
's ''
Metamorphoses The ''Metamorphoses'' ( la, Metamorphōsēs, from grc, μεταμορφώσεις: "Transformations") is an 8 AD Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured syste ...
'' influenced the modern vegetarian movement.


Biographical sources

No authentic writings of Pythagoras have survived, and almost nothing is known for certain about his life. The earliest sources on Pythagoras's life are brief, ambiguous, and often
satirical Satire is a genre Genre () is any form or type of communication in any mode (written, spoken, digital, artistic, etc.) with socially-agreed-upon conventions developed over time. In popular usage, it normally describes a Category of bein ...
. The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by Xenophanes of Colophon, who had been one of his contemporaries. In the poem, Xenophanes describes Pythagoras interceding on behalf of a
dog The dog or domestic dog (''Canis familiaris'' or ''Canis lupus familiaris'') is a domesticated Domestication is a sustained multi-generational relationship in which one group of organisms assumes a significant degree of influence over the ...

dog
that is being beaten, professing to recognize in its cries the voice of a departed friend.
Alcmaeon of Croton Alcmaeon of Croton (; el, Ἀλκμαίων ὁ Κροτωνιάτης, ''Alkmaiōn'', ''gen''.: Ἀλκμαίωνος; fl. 5th century BC) has been described as one of the most eminent natural philosophers and medical theorists of antiquity. H ...
, a doctor who lived in Croton at around the same time Pythagoras lived there, incorporates many Pythagorean teachings into his writings and alludes to having possibly known Pythagoras personally. The poet Heraclitus of Ephesus, who was born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime, mocked Pythagoras as a clever charlatan, remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, and selecting from these writings he manufactured a wisdom for himself—much learning, artful knavery." The Greek poets
Ion of Chios Ion of Chios (; grc-gre, Ἴων ὁ Χῖος; c. 490/480 – c. 420 BC) was a Greek writer, dramatist, lyric poet and philosopher. He was a contemporary of Aeschylus, Euripides and Sophocles. Of his many plays and poems only a few titles and ...
() and Empedocles of Acragas () both express admiration for Pythagoras in their poems. The first concise description of Pythagoras comes from the historian
Herodotus of Halicarnassus Herodotus (; grc, Ἡρόδοτος, ''Hēródotos'', ; BC) was an ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. ...
(), who describes him as "not the most insignificant" of Greek sages and states that Pythagoras taught his followers how to attain
immortality Immortality is eternal life, being exempt from death; unending existence. #Biological immortality, Some modern species may possess biological immortality. Some scientists, futurists, and philosophers have theorized about the immortality of the ...
. The accuracy of the works of Herodotus is controversial. The writings attributed to the Pythagorean philosopher Philolaus of Croton, who lived in the late fifth century BC, are the earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras. The
Athenian , image_skyline = File:Athens Montage L.png, center, 275px, alt=Athens montage. Clicking on an image in the picture causes the browser to load the appropriate article. rect 15 15 985 460 Acropolis of Athens The Acropo ...
rhetoric Rhetoric () is the Art (skill), art of persuasion, which along with grammar and logic (or dialectic – see Martianus Capella), is one of the Trivium, three ancient arts of discourse. Rhetoric aims to study the techniques writers or sp ...
ian
Isocrates Isocrates (; grc, Ἰσοκράτης ; 436–338 BC) was an ancient Greek rhetoric Rhetoric () is the Art (skill), art of persuasion, which along with grammar and logic (or dialectic – see Martianus Capella), is one of the Tri ...
(436–338 BC) was the first to describe Pythagoras as having visited Egypt.
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questio ...

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 Dicaearchus of Messana (; grc-gre, Δικαίαρχος ''Dikaiarkhos''; ), also written Dicearchus or Dicearch (), was a Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially t ...
,
Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born c. 375, fl. ''Floruit'' (), abbreviated fl. (or occasionally flor.), Latin Latin (, or , ) is a classical language A classical language is a langu ...
, and
Heraclides Ponticus Heraclides Ponticus ( grc-gre, Ἡρακλείδης ὁ Ποντικός ''Herakleides''; c. 390 BC – c. 310 BC) was a Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the ...
also wrote on the same subject. Most of the major sources on Pythagoras's life are from the
Roman period The Roman Empire ( la, Imperium Rōmānum ; grc-gre, Βασιλεία τῶν Ῥωμαίων, Basileía tôn Rhōmaíōn) was the post-Republican Republican can refer to: Political ideology * An advocate of a republic, a type of governme ...
, by which point, according to the German classicist
Walter Burkert Walter Burkert (; 2 February 1931 – 11 March 2015) was a German scholar of Greek mythology Greek mythology is the body of myth Myth is a folklore genre Folklore is the expressive body of culture shared by a particular group of ...
, "the history of Pythagoreanism was already... the laborious reconstruction of something lost and gone." Three
lives Lives may refer to: * The plural form of ''life Life is a characteristic that distinguishes physical entities A bubble of exhaled gas in water In common usage and classical mechanics, a physical object or physical body (or simply an o ...
of Pythagoras have survived from late antiquity, all of which are filled primarily with myths and legends. The earliest and most respectable of these is the one from
Diogenes Laërtius Diogenes Laërtius ( ; grc-gre, Διογένης Λαέρτιος, Dīogénēs Lāértios; ) was a biographer of the Ancient Greece, Greek philosophers. Nothing is definitively known about his life, but his surviving ''Lives and Opinions of Em ...
's ''
Lives and Opinions of Eminent Philosophers , codex 90, a 13th-century manuscript containing selections from Herodotus, Plutarch and (shown here) Diogenes Laertius ''Lives and Opinions of Eminent Philosophers'' ( grc-gre, Βίοι καὶ γνῶμαι τῶν ἐν φιλοσοφίᾳ εὐ ...
''. The two later lives were written by the
Neoplatonist Neoplatonism is a strand of Platonic Plato's influence on Western culture was so profound that several different concepts are linked by being called Platonic or Platonist, for accepting some assumptions of Platonism, but which do not imply accept ...
philosophers Porphyry and
Iamblichus Iamblichus (; grc-gre, Ἰάμβλιχος ; Safaitic Safaitic ( ''Ṣafāʾiyyah'') is a variety of the South Semitic script used by the nomads of the basalt desert of southern Syria and northern Jordan, the so-called Ḥarrah, to carve ro ...

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 used material from the lost writings of Aristotle's disciples and material taken from these sources is generally considered to be the most reliable.


Life


Early life

Herodotus Herodotus ( ; grc, Ἡρόδοτος, Hēródotos, ; BC) was an Classical Greece, ancient Greek writer, geographer, and historian born in the Greek city of Halicarnassus, part of the Achaemenid Empire, Persian Empire (now Bodrum, Turkey). He ...
,
Isocrates Isocrates (; grc, Ἰσοκράτης ; 436–338 BC) was an ancient Greek rhetoric Rhetoric () is the Art (skill), art of persuasion, which along with grammar and logic (or dialectic – see Martianus Capella), is one of the Tri ...
, and other early writers agree that Pythagoras was the son of Mnesarchus and that he was born on the Greek island of
Samos Samos (, also ; el, Σάμος ) is a Greece, Greek island in the eastern Aegean Sea, south of Chios, north of Patmos and the Dodecanese, and off the coast of western Turkey, from which it is separated by the -wide Mycale Strait. It is also a sep ...

Samos
in the eastern
Aegean Aegean may refer to: *Aegean Sea *Aegean Islands *Aegean Region (geographical), Turkey *Aegean Region (statistical), Turkey *Aegean civilizations *Aegean languages, a group of ancient languages and proposed language family *Aegean Sea (theme), a n ...

Aegean
. His father is said to have been a gem-engraver or a wealthy merchant, but his ancestry is disputed and unclear. Pythagoras's name led him to be associated with
Pythia The Pythia (; grc, Πυθία ) was the name of the high priestess of the Temple of Apollo at Delphi Delphi (; ), in legend previously called Pytho (Πυθώ), in ancient times was a sacred precinct that served as the seat of Pythia, the ...

Pythia
n
Apollo Apollo, grc, Ἀπόλλωνος, ''Apóllōnos'', label=genitive , ; , grc-dor, Ἀπέλλων, ''Apéllōn'', ; grc, Ἀπείλων, ''Apeílōn'', label=Arcadocypriot Greek, ; grc-aeo, Ἄπλουν, ''Áploun'', la, Apollō, ...

Apollo
(); Aristippus of Cyrene in the 4th century BC explained his name by saying, "He spoke the truth no less than did the Pythian . A late source gives Pythagoras's mother's name as Pythaïs.
Iamblichus Iamblichus (; grc-gre, Ἰάμβλιχος ; Safaitic Safaitic ( ''Ṣafāʾiyyah'') is a variety of the South Semitic script used by the nomads of the basalt desert of southern Syria and northern Jordan, the so-called Ḥarrah, to carve ro ...

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. As to the date of his birth,
Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born c. 375, fl. ''Floruit'' (), abbreviated fl. (or occasionally flor.), Latin Latin (, or , ) is a classical language A classical language is a langu ...
stated that Pythagoras left Samos in the reign of
Polycrates Polycrates (; grc, Πολυκράτης, in English usually Polycrates but sometimes Polykrates), son of Aeaces (father of Polycrates), Aeaces, was the tyrant of Samos from the 540s BC to 522 BC. He had a reputation as both a fierce warrior and an ...
, at the age of 40, which would give a date of birth around 570 BC. 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
Tunnel of Eupalinos
, and for its riotous festival culture. It was a major center of trade in the Aegean where traders brought goods from the
Near East The Near East ( ar, الشرق الأدنى, al-Sharq al-'Adnā, he, המזרח הקרוב, arc, ܕܢܚܐ ܩܪܒ, fa, خاور نزدیک, Xāvar-e nazdik, tr, Yakın Doğu) is a geographical term which roughly encompasses a transcontinental ...
. According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions. Pythagoras's early life also coincided with the flowering of early Ionian
natural philosophy Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') was the philosophy, philosophical study of nature and the physical universe that was dominant before the development of modern science. From the ancient world, a ...
. He was a contemporary of the philosophers
Anaximander Anaximander (; grc-gre, Ἀναξίμανδρος ''Anaximandros''; ) was a who lived in ,"Anaximander" in '. London: , 1961, Vol. 1, p. 403. a city of (in modern-day Turkey). He belonged to the and learned the teachings of his master . He s ...

Anaximander
, Anaximenes, and the historian Hecataeus, all of whom lived in
Miletus Miletus (; gr, Μῑ́λητος, Mīlētos; Hittite language, Hittite transcription ''Millawanda'' or ''Milawata'' (Exonym and endonym, exonyms); la, Miletus; tr, Milet) was an Ancient Greece, ancient Greek city on the western coast of Ana ...
, across the sea from Samos.


Reputed travels

Pythagoras is traditionally thought to have received most of his education in the Near East. Modern scholarship has shown that the culture of
Archaic Greece Archaic Greece was the period in Greek history The history of Greece encompasses the history of the territory of the modern nation-state of Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in ...
was heavily influenced by those of
Levant The Levant () is an term referring to a large area in the region of . In its narrowest sense, it is equivalent to the , which included present-day , , , , and most of southwest of the middle . In its widest historical sense, the Levant ...

Levant
ine and
Mesopotamia Mesopotamia ( grc, Μεσοποταμία ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in th ...

Mesopotamia
n cultures. Like many other important Greek thinkers, Pythagoras was said to have studied in
Egypt Egypt ( ar, مِصر, Miṣr), officially the Arab Republic of Egypt, is a transcontinental country This is a list of countries located on more than one continent A continent is one of several large landmasses. Generally identi ...

Egypt
. By the time of Isocrates in the fourth century BC, Pythagoras's reputed studies in Egypt were already taken as fact. The writer
Antiphon An antiphon (Greek language, Greek ἀντίφωνον, ἀντί "opposite" and φωνή "voice") is a short chant in Christianity, Christian ritual, sung as a refrain. The texts of antiphons are the Psalms. Their form was favored by St Ambrose a ...
, 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 Egyptian describes something of, from, or related to Egypt. Egyptian or Egyptians may refer to: Nations and ethnic groups * Egyptians, a national group in North Africa ** Egyptian culture, a complex and stable culture with thousands of years of r ...
from the
Pharaoh Pharaoh ( , ; cop, , Pǝrro) is the common title now used for the monarch A monarch is a head of state A head of state (or chief of state) is the public persona A persona (plural personae or personas), depending on the conte ...

Pharaoh
Amasis II Amasis II ( grc, Ἄμασις) or Ahmose II was a pharaoh (reigned 570526 BCE) of the Twenty-sixth Dynasty of Egypt, the successor of Apries at Sais, Egypt, Sais. He was the last great ruler of Ancient Egypt, Egypt before the Achaemenid Empire, P ...
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.Porphyry, ''Vit. Pyth.'' 6. The
Middle Platonist Middle Platonism is the modern name given to a stage in the development of Platonic philosophy, lasting from about 90 BC – when Antiochus of Ascalon rejected the Academic skepticism , scepticism of the New Academy – until the develop ...
biographer
Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; AD 46 – after AD 119) was a Greek Middle Platonist Middle Platonism is the modern name given to a stage in the development of Platonic philosophy, lasting from about 90 BC&nbs ...

Plutarch
() writes in his treatise ''
On Isis and Osiris The ''Moralia'' ( grc, Ἠθικά ''Ethika''; loosely translated as "Morals" or "Matters relating to customs and mores") is a group of manuscripts dating from the 10th-13th centuries, traditionally ascribed to the 1st-century Greek scholar Plutarc ...
'' that, during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of Heliopolis (meanwhile
Solon Solon ( grc-gre, Σόλων Solon ( grc-gre, wikt:Σόλων, Σόλων ''Sólōn'' ;  BC) was an Archaic Greece#Athens, Athenian statesman, lawmaker and poet. He is remembered particularly for his efforts to legislate against political, ...

Solon
received lectures from a
Sonchis of SaisSonchis of Saïs or the Saïte ( grc-gre, Σῶγχις ὁ Σαΐτης, ''Sō̂nkhis o Saḯtēs''; BC) was an Ancient Egypt, Egyptian priest, who is mentioned in Greek writings as relating the account of Atlantis. His status as a historical figur ...
). According to the
Christian theologian #REDIRECT Christian theology #REDIRECT Christian theology Christian theology is the theology of Christianity, Christian belief and practice. * help them better understand Christian tenets * make comparative religion, comparisons between Christia ...
Clement of Alexandria Titus Flavius Clemens, also known as Clement of Alexandria ( grc, Κλήμης ὁ Ἀλεξανδρεύς; – ), was a Christian theologian #REDIRECT Christian theology #REDIRECT Christian theology Christian theology is the theology of Chr ...
(), "Pythagoras was a disciple of Soches, an Egyptian archprophet, as well as
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was an Classical Athens, Athenian philosopher during the Classical Greece, Classical period in Ancient Greece, founder of the Platonist school of thought and the Platoni ...

Plato
of Sechnuphis of Heliopolis." Some ancient writers claimed that Pythagoras learned geometry and the doctrine of
metempsychosis Metempsychosis ( grc-gre, μετεμψύχωσις), in philosophy, refers to transmigration of the soul In many religious, philosophical, and myth Myth is a folklore genre consisting of narratives that play a fundamental role in a soci ...
from the Egyptians. Other ancient writers, however, claimed that Pythagoras had learned these teachings from the
Magi Magi (; singular magus ; from Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" o ...
in
Persia Iran ( fa, ایران ), also called Persia, and officially the Islamic Republic of Iran, is a country in Western Asia. It is bordered to the northwest by Armenia and Azerbaijan, to the north by the Caspian Sea, to the northeast by Tu ...

Persia
or even from
Zoroaster Zoroaster (, ; el, Ζωροάστρης, ''Zōroastrēs''), also known as Zarathustra (, ; ae, , ''Zaraθuštra''), Zarathushtra Spitama or Ashu Zarathushtra (Modern fa, زرتشت, ''Zartosht''), was an ancient Iranian Iranian may refer t ...

Zoroaster
himself.Diogenes Laërtius, viii. 1, 3. Diogenes Laërtius asserts that Pythagoras later visited
Crete Crete ( el, Κρήτη, translit=, Modern Modern may refer to: History *Modern history Human history, also known as world history, is the description of humanity's past. It is informed by archaeology Archaeology or archeology ...

Crete
, where he went to the
Cave of Ida
Cave of Ida
with
Epimenides Epimenides of Cnossos Knossos (also Cnossos, both pronounced ; grc, Κνωσός, Knōsós, ; Linear B: ''Ko-no-so'') is the largest Bronze Age archaeological site on Crete and has been called Europe's oldest city. Settled as early as the N ...

Epimenides
. The
Phoenicia Phoenicia () was an ancient Ancient history is the aggregate of past eventsWordNet Search – 3 ...
ns are reputed to have taught Pythagoras
arithmetic Arithmetic (from the Ancient Greek, Greek wikt:en:ἀριθμός#Ancient Greek, ἀριθμός ''arithmos'', 'number' and wikt:en:τική#Ancient Greek, τική wikt:en:τέχνη#Ancient Greek, έχνη ''tiké échne', 'art' or 'cr ...
and the
Chaldea Chaldea () was a small country that existed between the late 10th or early 9th and mid-6th centuries BCE, after which the country and its people were absorbed and assimilated into the indigenous population Babylonia Babylonia () was an ...
ns to have taught him astronomy. By the third century BC, Pythagoras was already reported to have studied under the
Jews Jews ( he, יְהוּדִים ISO 259-2 ISO The International Organization for Standardization (ISO ) is an international standard An international standard is a technical standard A technical standard is an established norm (social), ...

Jews
as well. Contradicting all these reports, the novelist
Antonius DiogenesAntonius Diogenes ( grc, Ἀντώνιος Διογένης) was the author of an ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 3 ...
, writing in the second century BC, reports that Pythagoras discovered all his doctrines himself by interpreting dreams. The third-century AD
Sophist A sophist ( el, σοφιστής, ''sophistes'') was a teacher in ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a civilization belonging to a period of History of Greece, Greek history from the Greek Dark Ages of the 12th ...
Philostratus Philostratus or Lucius Flavius Philostratus (; grc-gre, Φλάβιος Φιλόστρατος; c. 170 – 247/250 AD), called "the Athenian", was a Greek sophist of the Roman Empire, Roman imperial period. His father was a minor sophist of the sa ...
claims that, in addition to the Egyptians, Pythagoras also studied under
Hindu Hindus (; ) are persons who regard themselves as culturally, ethnically, or religiously adhering to aspects of Hinduism Hinduism () is an Indian religion Indian religions, sometimes also termed Dharmic religions or Indic re ...

Hindu
sages or
gymnosophist Gymnosophists ( grc, γυμνοσοφισταί, ''gymnosophistaí'', i.e. "naked philosophers" or "naked wise men") is the name given by the Greeks The Greeks or Hellenes (; el, Έλληνες, ''Éllines'' ) are an ethnic group An e ...
s in India. Iamblichus expands this list even further by claiming that Pythagoras also studied with the Celts and Iberians.


Alleged Greek teachers

Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers. Some identify Hermodamas of Samos as a possible tutor. Hermodamas represented the indigenous Samian Rhapsode, rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer. Others credit Bias of Priene, Thales,Iamblichus, ''Vit. Pyth.'' 9. or
Anaximander Anaximander (; grc-gre, Ἀναξίμανδρος ''Anaximandros''; ) was a who lived in ,"Anaximander" in '. London: , 1961, Vol. 1, p. 403. a city of (in modern-day Turkey). He belonged to the and learned the teachings of his master . He s ...

Anaximander
(a pupil of Thales). Other traditions claim the mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphism (religion), Orphic Mysteries. 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. Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship. 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. Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent. Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros is mentioned most often. 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. Apollonius Paradoxographus, a paradoxographer who may have lived in the second century BC, identified Pythagoras's Thaumaturgy, thaumaturgic ideas as a result of Pherecydes's influence. 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. Duris of Samos, 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. 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. Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis. 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 Thales' Theorem, special case of the inscribed angle theorem. Pythagoras's birthplace, the island of
Samos Samos (, also ; el, Σάμος ) is a Greece, Greek island in the eastern Aegean Sea, south of Chios, north of Patmos and the Dodecanese, and off the coast of western Turkey, from which it is separated by the -wide Mycale Strait. It is also a sep ...

Samos
, is situated in the Northeast Aegean Sea not far from
Miletus Miletus (; gr, Μῑ́λητος, Mīlētos; Hittite language, Hittite transcription ''Millawanda'' or ''Milawata'' (Exonym and endonym, exonyms); la, Miletus; tr, Milet) was an Ancient Greece, ancient Greek city on the western coast of Ana ...
. Diogenes Laërtius cites a statement from
Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born c. 375, fl. ''Floruit'' (), abbreviated fl. (or occasionally flor.), Latin Latin (, or , ) is a classical language A classical language is a langu ...
(fourth century BC) stating that Pythagoras learned most of his moral doctrines from the Pythia, Delphic priestess Themistoclea.Diogenes Laërtius
''Lives of Eminent Philosophers''
viii. 1, 8.
Porphyry agrees with this assertion, but calls the priestess Aristoclea (''Aristokleia''). Ancient authorities furthermore note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphism (religion), Orphic or Greco-Roman mysteries, Cretan mysteries, or the Pythia, Delphic oracle.


In Croton

Porphyry repeats an account from
Antiphon An antiphon (Greek language, Greek ἀντίφωνον, ἀντί "opposite" and φωνή "voice") is a short chant in Christianity, Christian ritual, sung as a refrain. The texts of antiphons are the Psalms. Their form was favored by St Ambrose a ...
, who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle". Here, Samians debated matters of public concern. Supposedly, the school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach. Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends. Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos, 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. Around 530 BC, when Pythagoras was about forty years old, he left Samos. His later admirers claimed that he left because he disagreed with the Tyrant#Historical forms, tyranny of
Polycrates Polycrates (; grc, Πολυκράτης, in English usually Polycrates but sometimes Polykrates), son of Aeaces (father of Polycrates), Aeaces, was the tyrant of Samos from the 540s BC to 522 BC. He had a reputation as both a fierce warrior and an ...
in Samos, 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. 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 Magna Graecia (, ; Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republic ...

Magna Graecia
. All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment. He served as an advisor to the elites in Croton and gave them frequent advice. 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.


Family and friends

Diogenes Laërtius states that Pythagoras "did not indulge in the pleasures of love" and that he cautioned others to only have sex "whenever you are willing to be weaker than yourself". According to Porphyry, Pythagoras married Theano (philosopher), Theano, a lady of
Crete Crete ( el, Κρήτη, translit=, Modern Modern may refer to: History *Modern history Human history, also known as world history, is the description of humanity's past. It is informed by archaeology Archaeology or archeology ...

Crete
and the daughter of Pythenax and had several children with her. Porphyry writes that Pythagoras had two sons named Telauges and Arignote, and a daughter named Myia, who "took precedence among the maidens in Croton and, when a wife, among married women." Iamblichus mentions none of these children and instead only mentions a son named Mnesarchus after his grandfather. This son was raised by Pythagoras's appointed successor Aristaeus and eventually took over the school when Aristaeus was too old to continue running it. 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 Pythagoras and was credited with having saved the philosopher's life when a roof was about to collapse. This association may been the result of confusion with a different man named Pythagoras, who was an athletics trainer. Diogenes Laërtius records Milo's wife's name as Myia. Iamblichus mentions Theano as the wife of Brontinus of Croton. Diogenes Laërtius states that the same Theano was Pythagoras's pupil and that Pythagoras's wife Theano was her daughter. Diogenes Laërtius also records that works supposedly written by Theano were still extant during his own lifetime and quotes several opinions attributed to her. These writings are now known to be pseudepigraphical.


Death

Pythagoras's emphasis on dedication and asceticism are credited with aiding in Croton's decisive victory over the neighboring colony of
Sybaris Sybaris ( grc, Σύβαρις; it, Sibari) was an important city of Magna Graecia Magna Graecia (, ; Latin meaning "Greater Greece", grc, Μεγάλη Ἑλλάς, ', it, Magna Grecia) was the name given by the Roman people, Romans to the c ...
in 510 BC. After the victory, some prominent citizens of Croton proposed a Greek democracy, democratic constitution, which the Pythagoreans rejected. The supporters of democracy, headed by Cylon of Croton, Cylon and Ninon of Croton, Ninon, the former of whom is said to have been irritated by his exclusion from Pythagoras's brotherhood, roused the populace against them. 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. Accounts of the attack are often contradictory and many probably confused it with later anti-Pythagorean rebellions. The building was apparently 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 present when the attack occurred and, if he was, whether or not he managed to escape. In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes. According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape, leading a small group of followers to the nearby city of Locris, where they pleaded for sanctuary, but were denied. They reached the city of
Metapontum Metapontum or Metapontium ( grc, Μεταπόντιον, Metapontion) was an important city of Magna Graecia Magna Graecia (, ; Latin meaning "Greater Greece", grc, Μεγάλη Ἑλλάς, ', it, Magna Grecia) was the name given by the Roman ...
, where they took shelter in the temple of the Muses and died there of starvation after forty days without food. 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. Pythagoras managed to escape, but was so despondent at the deaths of his beloved students that he committed suicide. 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. This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself.


Teachings


Metempsychosis

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 Metempsychosis ( grc-gre, μετεμψύχωσις), in philosophy, refers to transmigration of the soul In many religious, philosophical, and myth Myth is a folklore genre consisting of narratives that play a fundamental role in a soci ...
'', the belief that all
soul In many religious, philosophical, and myth Myth is a folklore genre consisting of narratives that play a fundamental role in a society, such as foundational tales or origin myths. The main characters in myths are usually non-humans, such as ...

soul
s are immortal and that, after death, a soul is transferred into a new body. This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus. Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur. 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 Heraclides Ponticus ( grc-gre, Ἡρακλείδης ὁ Ποντικός ''Herakleides''; c. 390 BC – c. 310 BC) was a Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the ...
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 of Clazomenae, Hermotimus, who recognized the shield of Euphorbus in the temple of Apollo. His final incarnation was as Pyrrhus, a fisherman from Delos. One of his past lives, as reported by
Dicaearchus Dicaearchus of Messana (; grc-gre, Δικαίαρχος ''Dikaiarkhos''; ), also written Dicearchus or Dicearch (), was a Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially t ...
, was as a beautiful courtesan.


Mysticism

Another belief attributed to Pythagoras was that of the "Musica universalis, 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 Classical planet, seven planets singing together. In his philosophical dialogue Protrepticus (Aristotle), ''Protrepticus'',
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questio ...

Aristotle
has his literary double say: Pythagoras was said to have practiced divination and prophecy. In the visits to various places in Greece—Delos, Sparta, Phlius,
Crete Crete ( el, Κρήτη, translit=, Modern Modern may refer to: History *Modern history Human history, also known as world history, is the description of humanity's past. It is informed by archaeology Archaeology or archeology ...

Crete
, etc.—which are ascribed to him, he usually appears either in his religious or priestly guise, or else as a lawgiver.


Numerology

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 (philosophy), monad) represented the origin of all things and the number two (the Dyad (Greek philosophy), 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 Apollo, grc, Ἀπόλλωνος, ''Apóllōnos'', label=genitive , ; , grc-dor, Ἀπέλλων, ''Apéllōn'', ; grc, Ἀπείλων, ''Apeílōn'', label=Arcadocypriot Greek, ; grc-aeo, Ἄπλουν, ''Áploun'', la, Apollō, ...

Apollo
. The number four signified the Seasons, four seasons and the Classical element, 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 Parity (mathematics), odd numbers were masculine, that even numbers were feminine, and that the number five represented marriage, because it was the sum of two and three. Ten was regarded as the "perfect number" and the Pythagoreans honored it by never gathering in groups larger than ten. Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the perfect number, ten. The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance. Iamblichus, in his ''Life of Pythagoras'', states that the tetractys was "so admirable, and so divinised by those who understood [it]," that Pythagoras's students would swear oaths by it. Andrew Gregory concludes that the tradition linking Pythagoras to the tetractys is probably genuine. Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton. In his landmark study ''Lore and Science in Ancient Pythagoreanism'', Walter Burkert argues that Pythagoras was a charismatic political and religious teacher, but that the number philosophy attributed to him was really an innovation by Philolaus. According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics. Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, Mathematical proof, proofless
arithmetic Arithmetic (from the Ancient Greek, Greek wikt:en:ἀριθμός#Ancient Greek, ἀριθμός ''arithmos'', 'number' and wikt:en:τική#Ancient Greek, τική wikt:en:τέχνη#Ancient Greek, έχνη ''tiké échne', 'art' or 'cr ...
, but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics.


Pythagoreanism


Communal lifestyle

Both
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was an Classical Athens, Athenian philosopher during the Classical Greece, Classical period in Ancient Greece, founder of the Platonist school of thought and the Platoni ...

Plato
and
Isocrates Isocrates (; grc, Ἰσοκράτης ; 436–338 BC) was an ancient Greek rhetoric Rhetoric () is the Art (skill), art of persuasion, which along with grammar and logic (or dialectic – see Martianus Capella), is one of the Tri ...
state that, above all else, Pythagoras was known as the founder of a new way of life. The organization Pythagoras founded at Croton was called a "school", but, in many ways, resembled a monastery. The adherents were bound by a vow to Pythagoras and each other, for the purpose of pursuing the religious and ascetic observances, and of studying his religious and philosophical theories. The members of the sect communalism, shared all their possessions in common and were devoted to each other to the exclusion of outsiders. Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans. One Pythagorean maxim (literature), maxim was "''koinà tà phílōn''" ("All things in common among friends"). Both Iamblichus and Porphyry provide detailed accounts of the organization of the school, although the primary interest of both writers is not historical accuracy, but rather to present Pythagoras as a divine figure, sent by the Greek gods, 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. Two groups existed within early Pythagoreanism: the ''mathematikoi'' ("learners") and the ''akousmatikoi'' ("listeners"). The ''akousmatikoi'' are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings; whereas the ''mathematikoi'' are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific. Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed the two approaches were compatible. 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. 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 dance, dancing, daily morning walks along scenic routes, and Sport of athletics, athletics were major components of the Pythagorean lifestyle. Moments of contemplation at the beginning and end of each day were also advised.


Prohibitions and regulations

Pythagorean teachings were known as "symbols" (''symbola'') 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. For instance, a saying which Leonid Zhmud concludes can probably be genuinely traced back to Pythagoras himself forbids his followers from wearing woolen garments. Other extant oral sayings forbid Pythagoreans from breaking bread, poking fires with swords, or picking up crumbs and teach that a person should always put the right sandal on before the left. The exact meanings of these sayings, however, 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: New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five-year initiation period, during which they were required to remain silent. Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women and female members of Pythagoras's school appear to have played an active role in its operations. Iamblichus provides a list of 235 famous Pythagoreans, seventeen of whom are women. In later times, many prominent female philosophers contributed to the development of
Neopythagoreanism Neopythagoreanism (or neo-Pythagoreanism) was a school of Hellenistic philosophy Hellenistic philosophy is the period of Western philosophy Western philosophy encompasses the philosophical Philosophy (from , ) is the study of gene ...
. Pythagoreanism also entailed a number of dietary prohibitions. It is more or less agreed that Pythagoras issued a prohibition against the consumption of Vicia faba, fava beans and the meat of non-sacrificial animals such as fish and poultry. Both of these assumptions, however, have been contradicted. Pythagorean dietary restrictions may have been motivated by belief in the doctrine of
metempsychosis Metempsychosis ( grc-gre, μετεμψύχωσις), in philosophy, refers to transmigration of the soul In many religious, philosophical, and myth Myth is a folklore genre consisting of narratives that play a fundamental role in a soci ...
. Some ancient writers present Pythagoras as enforcing a strictly Vegetarianism, vegetarian diet. 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 Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born c. 375, fl. ''Floruit'' (), abbreviated fl. (or occasionally flor.), Latin Latin (, or , ) is a classical language A classical language is a langu ...
, Pythagoras allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and sheep, rams. According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices and established a diet for athletes dependent on meat.


Legends

Within his own lifetime, Pythagoras was already the subject of elaborate hagiography, hagiographic legends. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure. In a fragment, Aristotle writes that Pythagoras had a golden thigh, which he publicly exhibited at the Ancient Olympic Games, Olympic Games and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo". Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications. He was supposedly once seen at both Metapontum and Croton bilocation, at the same time. When Pythagoras crossed the river Kosas (the modern-day Basento), "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 Hermes Trismegistus#In Islamic tradition, Muslim tradition, Pythagoras was said to have been initiated by Hermes Trismegistus, Hermes (Egyptian Thoth). Pythagoras was said to have dressed all in white. He is also said to have borne a golden wreath atop his head and to have worn trousers after the fashion of the Thrace, 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 fava 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. Riedweg suggests that Pythagoras may have personally encouraged these legends, but Gregory states that there is no direct evidence of this. Anti-Pythagorean legends were also circulated. Diogenes Laërtes retells a story told by Hermippus of Samos, which states that Pythagoras had once gone into an underground room, telling everyone that he was descending to the underworld. He stayed in this room for months, while his mother secretly recorded everything that happened during his absence. After he returned from this room, Pythagoras recounted everything that had happened while he was gone, convincing everyone that he had really been in the underworld and leading them to trust him with their wives.


Attributed discoveries


In mathematics

Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field. Many mathematical and scientific discoveries were attributed to Pythagoras, including Pythagorean theorem, his famous theorem, as well as discoveries in the fields of Music of ancient Greece, music, Greek astronomy, astronomy, and Ancient Greek medicine, 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, 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. Cicero rejected this story as spurious because of the much more widely held belief that Pythagoras forbade blood sacrifices. Porphyry attempted to explain the story by asserting that the ox was actually made of dough. The Pythagorean theorem was known and used by the Babylonian mathematics, Babylonians and Indian mathematics, Indians centuries before Pythagoras, but he may have been the first to introduce it to the Greeks. Some historians of mathematics have even suggested that he—or his students—may have constructed the first Mathematical proof, 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. Pythagoras's biographers state that he also was the first to identify the Platonic solid, five regular solids and that he was the first to discover the Theory of Proportions.


In music

According to legend, Pythagoras discovered that musical notes could be translated into mathematical equations when he passed blacksmiths at work one day and heard the sound of their Pythagorean hammers, 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 astronomy

In ancient times, Pythagoras and his contemporary Parmenides, Parmenides of Elea were both credited with having been the first to teach that the Spherical Earth, Earth was spherical, the first to divide the globe into five climatic zones, and the first to identify the Phosphorus (morning star), morning star and the Hesperus, evening star as the same celestial object (now known as
Venus Venus is the second planet from the Sun. It is named after the Venus (mythology), Roman goddess of love and beauty. As List of brightest natural objects in the sky, the brightest natural object in Earth's night sky after the Moon, Venus can ...

Venus
). Of the two philosophers, Parmenides has a much stronger claim to having been the first and the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem. Empedocles, who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical. By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals. The identity of the morning star and evening star was known to the Babylonia, Babylonians over a thousand years earlier.


Later influence in antiquity


On Greek philosophy

Sizeable Pythagorean communities existed in Magna Graecia, Phlius, and Thebes, Greece, 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 Taranto, Tarentum in Magna Graecia. According to later tradition, Archytas was elected as ''strategos'' ("general") seven times, even though others were prohibited from serving more than a year. Archytas was also a renowned mathematician and musician. He was a close friend of Plato and he is quoted in Plato's ''Republic''. Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans. Cicero repeats this statement, remarking that ''Platonem ferunt didicisse Pythagorea omnia'' ("They say Plato learned all things Pythagorean"). According to Charles H. Kahn, Plato's middle dialogues, including ''Meno'', ''Phaedo'', and ''Republic (Plato), 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 (Plato), Republic'' may be partially based on the "tightly organised community of like-minded thinkers" established by Pythagoras at Croton. Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy, science, and morality. Plato and Pythagoras shared a "mystical approach to the Soul (spirit), soul and its place in the material world" and it is probable that both were influenced by Orphicism, Orphism. The historian of philosophy Frederick Copleston states that Plato probably borrowed Plato's tripartite theory of soul, his tripartite theory of the soul from the Pythagoreans. Bertrand Russell, in his ''A History of Western Philosophy'', contends that the influence of Pythagoras on Plato and others was so great that he should be considered the most influential philosopher of all time. He concludes that "I do not know of any other man who has been as influential as he was in the school of thought." A revival of Pythagorean teachings occurred in the first century BC when Middle Platonism, Middle Platonist philosophers such as Eudorus of Alexandria, Eudorus and Philo of Alexandria hailed the rise of a "new" Pythagoreanism in Alexandria. At around the same time,
Neopythagoreanism Neopythagoreanism (or neo-Pythagoreanism) was a school of Hellenistic philosophy Hellenistic philosophy is the period of Western philosophy Western philosophy encompasses the philosophical Philosophy (from , ) is the study of gene ...
became prominent. The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings. The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy and probably understood the soul as a "kind of mathematical harmony." The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory. Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines.


On art and architecture

Greek sculpture sought to represent the permanent reality behind superficial appearances. Early Archaic Greece, Archaic sculpture represents life in simple forms, and may have been influenced by the earliest Greek natural philosophies. The Greeks generally believed that nature expressed itself in ideal forms and was represented by a type (), which was mathematically calculated. When dimensions changed, architects sought to relay permanence through mathematics. Maurice Bowra believes that these ideas influenced the theory of Pythagoras and his students, who believed that "all things are numbers". During the sixth century BC, the number philosophy of the Pythagoreans triggered a revolution in Greek sculpture. Greek sculptors and architects attempted to find the mathematical relation (Canon (basic principle), canon) behind aesthetic perfection. Possibly drawing on the ideas of Pythagoras, the sculptor Polykleitos wrote in Polykleitos#Canon of Polykleitos, his ''Canon'' that beauty consists in the proportion, not of the elements (materials), but of the interrelation of parts with one another and with the whole. In the Greek architectural orders, every element was calculated and constructed by mathematical relations. Rhys Carpenter states that the ratio 2:1 was "the generative ratio of the Doric order, and in Hellenistic times an ordinary Doric colonnade, beats out a rhythm of notes." The oldest known building designed according to Pythagorean teachings is the Porta Maggiore Basilica, a subterranean basilica which was built during the reign of the Roman emperor Nero as a secret place of worship for Pythagoreans. The basilica was built underground because of the Pythagorean emphasis on secrecy and also because of the legend that Pythagoras had sequestered himself in a cave on Samos. The basilica's apse is in the east and its atrium in the west out of respect for the rising sun. It has a narrow entrance leading to a small pool where the initiates could purify themselves. The building is also designed according to Pythagorean numerology, with each table in the sanctuary providing seats for seven people. Three aisles lead to a single altar, symbolizing the three parts of the soul approaching the unity of Apollo. The apse depicts a scene of the poet Sappho leaping off the Lefkada, Leucadian cliffs, clutching her lyre to her breast, while Apollo stands beneath her, extending his right hand in a gesture of protection, symbolizing Pythagorean teachings about the immortality of the soul. The interior of the sanctuary is almost entirely white because the color white was regarded by Pythagoreans as sacred. The emperor Hadrian's Pantheon, Rome, Pantheon in Rome was also built based on Pythagorean numerology. The temple's circular plan, central axis, hemispherical dome, and alignment with the four cardinal directions symbolize Pythagorean views on the order of the universe. The single oculus at the top of the dome symbolizes the monad and the sun-god Apollo. The twenty-eight ribs extending from the oculus symbolize the moon, because twenty-eight was the same number of months on the Pythagorean lunar calendar. The five coffered rings beneath the ribs represent the marriage of the sun and moon.


In early Christianity

Many early Christians had a deep respect for Pythagoras. Eusebius ( 260 – 340 AD), bishop of Caesarea Maritima, Caesarea, praises Pythagoras in his ''Against Hierokles'' for his rule of silence, his frugality, his "extraordinary" morality, and his wise teachings. In another work, Eusebius compares Pythagoras to Moses. In one of his letter, the Church Fathers, Church Father Jerome ( 347 – 420 AD) praises Pythagoras for his wisdom and, in another letter, he credits Pythagoras for his belief in the immortality of the soul, which he suggests Christians inherited from him. Augustine of Hippo (354 – 430 AD) rejected Pythagoras's teaching of metempsychosis without explicitly naming him, but otherwise expressed admiration for him. 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". In another passage, Augustine defends Pythagoras's reputation, arguing that Pythagoras certainly never taught the doctrine of metempsychosis.


Influence after antiquity


In the Middle Ages

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


On modern science

In his preface to his book ''On the Revolution of the Heavenly Spheres'' (1543),
Nicolaus Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, link=no, Niclas Koppernigk, modern: ''Nikolaus Kopernikus''; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic Church, C ...

Nicolaus Copernicus
cites various Pythagoreans as the most important influences on the development of his Heliocentrism, 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 Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer An astronomer is a in the field of who focuses their studies on a specific question or field outside the scope of . They observe s such as s, s, , s and ...

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 Kepler's laws of planetary motion, 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." He also called Pythagoras the "grandfather" of all Copernicans.Jamie James, The Music of the Spheres: Music, Science, and the Natural Order of the Universe, p 142.
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

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 Newton's law of universal gravitation, Law of Universal Gravitation to Pythagoras. Albert Einstein believed that a scientist may also be "a Platonist or a Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research." The English philosopher Alfred North Whitehead argued that "In a sense, Plato and Pythagoras stand nearer to modern physical science than does Aristotle. The two former were mathematicians, whereas Aristotle was the son of a doctor". By this measure, Whitehead declared that Einstein and other modern scientists like him are "following the pure Pythagorean tradition."


On vegetarianism

A fictionalized portrayal of Pythagoras appears in Book XV of
Ovid Pūblius Ovidius Nāsō (; 20 March 43 BC – 17/18 AD), known in English as Ovid ( ), was a Augustan literature (ancient Rome), Roman poet who lived during the reign of Augustus. He was a contemporary of the older Virgil and Horace, with whom ...

Ovid
's ''
Metamorphoses The ''Metamorphoses'' ( la, Metamorphōsēs, from grc, μεταμορφώσεις: "Transformations") is an 8 AD Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured syste ...
'', in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet. It was through Arthur Golding's 1567 English translation of Ovid's ''Metamorphoses'' that Pythagoras was best known to English-speakers throughout the early modern period. John Donne's ''Progress of the Soul'' discusses the implications of the doctrines expounded in the speech, and Michel de Montaigne quoted the speech no less than three times in his treatise "Of Cruelty" to voice his moral objections against the mistreatment of animals. William Shakespeare references the speech in his play ''The Merchant of Venice''. John Dryden included a translation of the scene with Pythagoras in his 1700 work ''Fables, Ancient and Modern'', and John Gay's 1726 fable "Pythagoras and the Countryman" reiterates its major themes, linking carnivorism with tyranny. Lord Chesterfield records that his conversion to vegetarianism had been motivated by reading Pythagoras's speech in Ovid's ''Metamorphoses''. Until the word ''vegetarianism'' was coined in the 1840s, vegetarians were referred to in English as "Pythagoreans". Percy Bysshe Shelley wrote an ode entitled "To the Pythagorean Diet", and Leo Tolstoy adopted the Pythagorean diet himself.


On Western esotericism

Early modern European esotericism drew heavily on the teachings of Pythagoras. The German Renaissance humanism, humanist scholar Johannes Reuchlin (1455–1522) synthesized Pythagoreanism with Christian theology and Jewish Kabbalah, arguing that Kabbalah and Pythagoreanism were both inspired by Moses, Mosaic tradition and that Pythagoras was therefore a kabbalist. In his dialogue ''De verbo mirifico'' (1494), Reuchlin compared the Pythagorean tetractys to the Ineffability, ineffable divine name Tetragrammaton, YHWH, ascribing each of the four letters of the tetragrammaton a symbolic meaning according to Pythagorean mystical teachings. Heinrich Cornelius Agrippa's popular and influential three-volume treatise ''Three Books of Occult Philosophy, De Occulta Philosophia'' cites Pythagoras as a "religious magi" and indicates that Pythagoras's mystical numerology operates on a Allegory in Renaissance literature#Three world theory, supercelestial level. The Freemasonry, freemasons deliberately modeled their society on the community founded by Pythagoras at Croton. Rosicrucianism used Pythagorean symbolism, as did Robert Fludd (1574–1637), who believed his own musical writings to have been inspired by Pythagoras. John Dee was heavily influenced by Pythagorean ideology, particularly the teaching that all things are made of numbers. Adam Weishaupt, the founder of the Illuminati, was a strong admirer of Pythagoras and, in his book ''Pythagoras'' (1787), he advocated that society should be reformed to be more like Pythagoras's commune at Croton. Wolfgang Amadeus Mozart incorporated Masonic and Pythagorean symbolism into his opera ''The Magic Flute''. Sylvain Maréchal, in his six-volume 1799 biography ''The Voyages of Pythagoras'', declared that all revolutionaries in all time periods are the "heirs of Pythagoras".


On literature

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 (Dante), 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 (Dante), 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 , which was the Pythagorean approximation of pi. Hell, Purgatory, and Heaven are all described as circular and Dante compares the wonder of God in Christianity, 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 Portinari, Beatrice is associated with the number nine, which is equal to three times three. The Transcendentalism, Transcendentalists read the ancient ''Lives of Pythagoras'' as guides on how to live a model life. Henry David Thoreau was impacted by Thomas Taylor (neoplatonist), Thomas Taylor's translations of Iamblichus's ''Life of Pythagoras'' and Stobaeus's ''Pythagoric Sayings'' and his views on nature may have been influenced by the Pythagorean idea of images corresponding to archetypes. The Pythagorean teaching of ''musica universalis'' is a recurring theme throughout Thoreau's ''magnum opus'', ''Walden''.


See also

* Cosmos * ''Ex pede Herculem'' * Isopsephy (gematria) * List of things named after Pythagoras * Lute of Pythagoras * Pythagoras tree (fractal) * Pythagorean comma * Pythagorean cup * Pythagorean triple * Pythagoras (sculptor) * Sacred geometry


References


Footnotes


Citations


Works cited

Only a few relevant source texts deal with Pythagoras and the Pythagoreans; most are available in different translations. Later texts usually build solely upon information in these works. Classical sources *
Diogenes Laërtius Diogenes Laërtius ( ; grc-gre, Διογένης Λαέρτιος, Dīogénēs Lāértios; ) was a biographer of the Ancient Greece, Greek philosophers. Nothing is definitively known about his life, but his surviving ''Lives and Opinions of Em ...
, ''Lives and Opinions of Eminent Philosophers, Vitae philosophorum VIII'' (''Lives of Eminent Philosophers''), c. 200 AD, which in turn references the lost work ''Successions of Philosophers'' by Alexander Polyhistor — * Porphyry, ''Vita Pythagorae'' (''Life of Pythagoras''), c. 270 AD
''Porphyry, Life of Pythagoras''
translated by Kenneth Sylvan Guthrie (1920) *Iamblichus (philosopher), Iamblichus, ''De Vita Pythagorica'' (''On the Pythagorean Life''), c. 300 AD
''Iamblichus, Life of Pythagoras''
translated by Kenneth Sylvan Guthrie (1920) *Apuleius, following
Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born c. 375, fl. ''Floruit'' (), abbreviated fl. (or occasionally flor.), Latin Latin (, or , ) is a classical language A classical language is a langu ...
, writes about Pythagoras in ''Apologia'', c. 150 AD, including a story of his being taught by
Zoroaster Zoroaster (, ; el, Ζωροάστρης, ''Zōroastrēs''), also known as Zarathustra (, ; ae, , ''Zaraθuštra''), Zarathushtra Spitama or Ashu Zarathushtra (Modern fa, زرتشت, ''Zartosht''), was an ancient Iranian Iranian may refer t ...

Zoroaster
—a story also found in
Clement of Alexandria Titus Flavius Clemens, also known as Clement of Alexandria ( grc, Κλήμης ὁ Ἀλεξανδρεύς; – ), was a Christian theologian #REDIRECT Christian theology #REDIRECT Christian theology Christian theology is the theology of Chr ...
. *Hierocles of Alexandria, ''Golden Verses of Pythagoras'', c. 430 AD Modern secondary sources * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


External links

* *
"Pythagoras of Samos"
The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland
"Pythagoras and the Pythagoreans, Fragments and Commentary"
Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History
"Pythagoras and the Pythagoreans"
Department of Mathematics, Texas A&M University
"Pythagoras and Pythagoreanism"
''The Catholic Encyclopedia'' * * {{Authority control Pythagoras, 570s BC births 490s BC deaths 6th-century BC Greek people 6th-century BC mathematicians 6th-century BC philosophers 5th-century BC Greek people 5th-century BC mathematicians 5th-century BC philosophers Ancient Greek ethicists Ancient Greek mathematicians Ancient Greek metaphilosophers Ancient Greek metaphysicians Ancient Greek music theorists Ancient Greek philosophers of mind Ancient Greek political philosophers Ancient Greek political refugees Ancient Greek shamans Ancient Samians Ascetics Cultural critics Epistemologists Esotericists Founders of philosophical traditions Founders of religions Geometers History of philosophy History of mathematics History of science History of vegetarianism Intellectual history Metaphilosophers Metaphysicians Moral philosophers Music theorists Mystics Nonviolence advocates Numerologists Ontologists Philosophers of culture Philosophers of education Philosophers of ethics and morality Philosophers of mathematics Philosophers of mind Philosophers of science Philosophy of mathematics Philosophy of music Political philosophers Presocratic philosophers Pythagoreans Social critics Social philosophers Theorists on Western civilization Vegetarianism and religion Wonderworkers Writers about activism and social change Writers about religion and science 6th-century BC religious leaders 5th-century BC religious leaders