Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the
Samian, or simply ; in
Ionian Greek
Ionic Greek ( grc, Ἑλληνικὴ Ἰωνική, Hellēnikē Iōnikē) was a subdialect of the Attic–Ionic or Eastern dialect group of Ancient Greek.
History
The Ionic dialect appears to have originally spread from the Greek mainland acr ...
; ) was an ancient
Ionian Greek philosopher
Ancient Greek philosophy arose in the 6th century BC, marking the end of the Greek Dark Ages. Greek philosophy continued throughout the Hellenistic period and the period in which Greece and most Greek-inhabited lands were part of the Roman Empire ...
and the eponymous founder of
Pythagoreanism. His political and religious teachings were well known in
Magna Graecia and influenced the philosophies of
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
,
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ph ...
, and, through them, the
West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of
Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to
Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal,
ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included
vegetarianism, although modern scholars doubt that he ever advocated complete vegetarianism.
The teaching most securely identified with Pythagoras is ''
metempsychosis
Metempsychosis ( grc-gre, μετεμψύχωσις), in philosophy, is the Reincarnation#Conceptual definitions, transmigration of the soul, especially its reincarnation after death. The term is derived from ancient Greek philosophy, and has be ...
'', or the "transmigration of souls", which holds that every
soul
In many religious and philosophical traditions, there is a belief that a soul is "the immaterial aspect or essence of a human being".
Etymology
The Modern English noun '' soul'' is derived from Old English ''sāwol, sāwel''. The earliest atte ...
is
immortal
Immortality is the ability to live forever, or eternal life.
Immortal or Immortality may also refer to:
Film
* ''The Immortals'' (1995 film), an American crime film
* ''Immortality'', an alternate title for the 1998 British film ''The Wisdom of ...
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 a philosophical concept that regards proportions in the movements of celestial bodies – the Sun, Moon, and planets – as a ...
'', which holds that the
planets move according to
mathematical
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
equations and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras developed the
numerological and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly
Philolaus of Croton. Following Croton's decisive victory over
Sybaris
Sybaris ( grc, Σύβαρις; it, Sibari) was an important city of Magna Graecia. It was situated in modern Calabria, in southern Italy, between two rivers, the Crathis (Crati) and the Sybaris (Coscile).
The city was founded in 720 BC ...
in around 510 BC, Pythagoras's followers came into conflict with supporters of
democracy
Democracy (From grc, δημοκρατία, dēmokratía, ''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 choo ...
, and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or he may have escaped to
Metapontum and died there.
In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the
Pythagorean theorem,
Pythagorean tuning, the
five regular solids, the
Theory of Proportions, the
sphericity of the Earth, and the identity of the
morning
Morning is the period from sunrise to noon. There are no exact times for when morning begins (also true of evening and night) because it can vary according to one's lifestyle and the hours of daylight at each time of year. However, morning s ...
and
evening stars as the planet
Venus
Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
. 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'') is the philosophical study of physics, that is, nature and the physical universe. It was dominant before the development of modern science.
From the ancient wo ...
.
Pythagoras influenced Plato, whose
dialogues
Dialogue (sometimes spelled dialog in American English) is a written or spoken conversational exchange between two or more people, and a literary and theatrical form that depicts such an exchange. As a philosophical or didactic device, it is chi ...
, especially his ''
Timaeus Timaeus (or Timaios) is a Greek name. It may refer to:
* ''Timaeus'' (dialogue), a Socratic dialogue by Plato
*Timaeus of Locri, 5th-century BC Pythagorean philosopher, appearing in Plato's dialogue
*Timaeus (historian) (c. 345 BC-c. 250 BC), Greek ...
'', exhibit Pythagorean teachings. Pythagorean ideas on mathematical perfection also impacted
ancient Greek art. His teachings underwent a major revival in the first century BC among
Middle Platonists
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 neoplatonis ...
, coinciding with the rise of
Neopythagoreanism. Pythagoras continued to be regarded as a great philosopher throughout the
Middle Ages
In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire ...
and his philosophy had a major impact on scientists such as
Nicolaus Copernicus,
Johannes Kepler, and
Isaac Newton. Pythagorean symbolism was used throughout early modern
European esotericism, and his teachings as portrayed in
Ovid
Pūblius Ovidius Nāsō (; 20 March 43 BC – 17/18 AD), known in English as Ovid ( ), was a Roman poet who lived during the reign of Augustus. He was a contemporary of the older Virgil and Horace, with whom he is often ranked as one of the th ...
's ''
Metamorphoses'' 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. The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by
Xenophanes of Colophon
Xenophanes of Colophon (; grc, Ξενοφάνης ὁ Κολοφώνιος ; c. 570 – c. 478 BC) was a Greek philosopher, theologian, poet, and critic of Homer from Ionia who travelled throughout the Greek-speaking world in early Classical An ...
, who had been one of his contemporaries. In the poem, Xenophanes describes Pythagoras interceding on behalf of a
dog
The dog (''Canis familiaris'' or ''Canis lupus familiaris'') is a domesticated descendant of the wolf. Also called the domestic dog, it is derived from the extinct Pleistocene wolf, and the modern wolf is the dog's nearest living relative. Do ...
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) was an early Greek medical writer and philosopher-scientist. He has been described as one of the most ...
, 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 fr ...
() 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 (), who describes him as "not the most insignificant" of Greek sages and states that Pythagoras taught his followers how to attain
immortality. 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
Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates ...
rhetorician
Isocrates (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 and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ph ...
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 Dikaiarchos (), was a Greek philosopher, geographer and author. Dicaearchus was a student of Aristotle in the Lyceum. Very little of his work remains exta ...
,
Aristoxenus
Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...
, and
Heraclides Ponticus also wrote on the same subject.
Most of the major sources on Pythagoras's life are from the
Roman period, by which point, according to the German classicist
Walter Burkert, "the history of Pythagoreanism was already... the laborious reconstruction of something lost and gone." Three
ancient biographies 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's ''
Lives and Opinions of Eminent Philosophers''. The two later biographies were written by the
Neoplatonist
Neoplatonism is a strand of Platonic philosophy that emerged in the 3rd century AD against the background of Hellenistic philosophy and religion. The term does not encapsulate a set of ideas as much as a chain of thinkers. But there are some id ...
philosophers
Porphyry and
Iamblichus and were partially intended as polemics against the
rise of Christianity. The later sources are much lengthier than the earlier ones, and even more fantastic in their descriptions of Pythagoras's achievements. Porphyry and Iamblichus 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, , }; BC) was an ancient Greek historian and geographer
A geographer is a physical scientist, social scientist or humanist whose area of study is geography, the study of Earth's natural environment and human society ...
,
Isocrates, and other early writers agree that Pythagoras was the son of Mnesarchus, and that he was born on the Greek island of
Samos in the eastern
Aegean. According to these biographers, Pythagoras' father wasn't born on the island, although he got naturalized there, but according to
Iamblichus he was a native of the island. He is said to have been a gem-engraver or a wealthy merchant, but his ancestry is disputed and unclear. His mother was a native of
Samos, descending from a ''
geomoroi'' family.
Apollonius of Tyana, gives her name as Pythaïs.
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 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...
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. Pythagoras's name led him to be associated with
Pythian
Apollo
Apollo, grc, Ἀπόλλωνος, Apóllōnos, label=genitive , ; , grc-dor, Ἀπέλλων, Apéllōn, ; grc, Ἀπείλων, Apeílōn, label= Arcadocypriot Greek, ; grc-aeo, Ἄπλουν, Áploun, la, Apollō, la, Apollinis, label ...
();
Aristippus of Cyrene
Aristippus of Cyrene (; grc, Ἀρίστιππος ὁ Κυρηναῖος; c. 435 – c. 356 BCE) was a hedonistic Greek philosopher and the founder of the Cyrenaic school of philosophy. He was a pupil of Socrates, but adopted a very differen ...
in the 4th century BC explained his name by saying, "He spoke
the truth no less than did the Pythian
.
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
The Tunnel of Eupalinos or Eupalinian aqueduct ( el, Ευπαλίνιον όρυγμα, translit=Efpalinion orygma) is a tunnel of length running through Mount Kastro in Samos, Greece, built in the 6th century BC to serve as an aqueduct. The tunn ...
, and for its riotous festival culture. It was a major center of trade in the Aegean where traders brought goods from the
Near East. 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'') is the philosophical study of physics, that is, nature and the physical universe. It was dominant before the development of modern science.
From the ancient wo ...
. He was a contemporary of the philosophers
Anaximander,
Anaximenes, and the historian
Hecataeus, all of whom lived in
Miletus, 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 was heavily influenced by those of
Levant
The Levant () is an approximate historical geographical term referring to a large area in the Eastern Mediterranean region of Western Asia. In its narrowest sense, which is in use today in archaeology and other cultural contexts, it is ...
ine and
Mesopotamia
Mesopotamia ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن or ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in the northern part of the ...
n cultures. Like many other important Greek thinkers, Pythagoras was said to have studied in
Egypt
Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and southwest corner of Asia via a land bridge formed by the Sinai Peninsula. It is bordered by the Medit ...
. 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 ἀντίφωνον, ἀντί "opposite" and φωνή "voice") is a short chant in Christian ritual, sung as a refrain. The texts of antiphons are the Psalms. Their form was favored by St Ambrose and they feature prominentl ...
, 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
Pharaoh (, ; Egyptian: '' pr ꜥꜣ''; cop, , Pǝrro; Biblical Hebrew: ''Parʿō'') is the vernacular term often used by modern authors for the kings of ancient Egypt who ruled as monarchs from the First Dynasty (c. 3150 BC) until the ...
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.
[Porphyry, ''Vit. Pyth.'' 6.] The
Middle Platonist biographer
Plutarch
Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for hi ...
() 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 Plu ...
'' 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). According to the
Christian theologian
Christian theology is the theology of Christian belief and practice. Such study concentrates primarily upon the texts of the Old Testament and of the New Testament, as well as on Christian tradition. Christian theologians use biblical exegesis ...
Clement of Alexandria
Titus Flavius Clemens, also known as Clement of Alexandria ( grc , Κλήμης ὁ Ἀλεξανδρεύς; – ), was a Christian theologian and philosopher who taught at the Catechetical School of Alexandria. Among his pupils were Origen an ...
(), "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 a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
of Sechnuphis of
Heliopolis." Some ancient writers claimed that Pythagoras learned geometry and the doctrine of
metempsychosis
Metempsychosis ( grc-gre, μετεμψύχωσις), in philosophy, is the Reincarnation#Conceptual definitions, transmigration of the soul, especially its reincarnation after death. The term is derived from ancient Greek philosophy, and has be ...
from the Egyptians.
Other ancient writers, however, claimed that Pythagoras had learned these teachings from the
Magi in
Persia
Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkmeni ...
or even from
Zoroaster himself.
[Diogenes Laërtius, viii. 1, 3.] Diogenes Laërtius asserts that Pythagoras later visited
Crete
Crete ( el, Κρήτη, translit=, Modern: , Ancient: ) is the largest and most populous of the Greek islands, the 88th largest island in the world and the fifth largest island in the Mediterranean Sea, after Sicily, Sardinia, Cyprus, ...
, where he went to the
Cave of Ida with
Epimenides.
The
Phoenicia
Phoenicia () was an ancient thalassocratic civilization originating in the Levant region of the eastern Mediterranean, primarily located in modern Lebanon. The territory of the Phoenician city-states extended and shrank throughout their histor ...
ns are reputed to have taught Pythagoras
arithmetic and the
Chaldeans to have taught him astronomy. By the third century BC, Pythagoras was already reported to have studied under the
Jews
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
as well. 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. The third-century AD
Sophist
A sophist ( el, σοφιστής, sophistes) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics, and mathematics. They taught ' ...
Philostratus
Philostratus or Lucius Flavius Philostratus (; grc-gre, Φιλόστρατος ; c. 170 – 247/250 AD), called "the Athenian", was a Greek sophist of the Roman imperial period. His father was a minor sophist of the same name. He was born probab ...
claims that, in addition to the Egyptians, Pythagoras also studied under sages or
gymnosophist
Gymnosophists ( grc, γυμνοσοφισταί, ''gymnosophistaí'', i.e. "naked philosophers" or "naked wise men" (from Greek γυμνός ''gymnós'' "naked" and σοφία ''sophía'' "wisdom")) is the name given by the Greeks to certain anc ...
s in
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
. Iamblichus expands this list even further by claiming that Pythagoras also studied with the
Celts
The Celts (, see pronunciation for different usages) or Celtic peoples () are. "CELTS location: Greater Europe time period: Second millennium B.C.E. to present ancestry: Celtic a collection of Indo-European peoples. "The Celts, an ancien ...
and
Iberians
The Iberians ( la, Hibērī, from el, Ἴβηρες, ''Iberes'') were an ancient people settled in the eastern and southern coasts of the Iberian peninsula, at least from the 6th century BC. They are described in Greek and Roman sources (amo ...
.
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
rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet
Homer
Homer (; grc, Ὅμηρος , ''Hómēros'') (born ) was a Greek poet who is credited as the author of the ''Iliad'' and the ''Odyssey'', two epic poems that are foundational works of ancient Greek literature. Homer is considered one of the ...
. Others credit
Bias of Priene, Thales,
[Iamblichus, ''Vit. Pyth.'' 9.] or
Anaximander (a pupil of Thales).
Other traditions claim the mythic bard
Orpheus as Pythagoras's teacher, thus representing the
Orphic Mysteries
Orphism (more rarely Orphicism; grc, Ὀρφικά, Orphiká) is the name given to a set of religious beliefs and practices originating in the ancient Greek and Hellenistic world, associated with literature ascribed to the mythical poet Orpheu ...
. 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
Leibethra or Libethra, in the modern pronunciation Leivithra ( gr, Λείβηθρα or Λίβηθρα) was an ancient Macedonian city at the foot of Mount Olympus, near the present settlement of Skotina. Archaeologists have discovered tombs there ...
. 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
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, 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
Thales of Miletus ( ; grc-gre, Θαλῆς; ) was a Greek mathematician, astronomer, statesman, and pre-Socratic philosopher from Miletus in Ionia, Asia Minor. He was one of the Seven Sages of Greece. Many, most notably Aristotle, regarded ...
, who would have been around fifty-four years older than him. Thales was a philosopher, scientist, mathematician, and engineer,
also known for a
special case of the
inscribed angle theorem
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.
Equivalently, an i ...
. Pythagoras's birthplace, the island of
Samos, is situated in the Northeast
Aegean Sea
The Aegean Sea ; tr, Ege Denizi (Greek: Αιγαίο Πέλαγος: "Egéo Pélagos", Turkish: "Ege Denizi" or "Adalar Denizi") is an elongated embayment of the Mediterranean Sea between Europe and Asia. It is located between the Balkans ...
not far from
Miletus. Diogenes Laërtius cites a statement from
Aristoxenus
Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...
(fourth century BC) stating that Pythagoras learned most of his
moral doctrines from the
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
Orphic or
Cretan mysteries, or the
Delphic oracle.
In Croton
Porphyry repeats an account from
Antiphon
An antiphon ( Greek ἀντίφωνον, ἀντί "opposite" and φωνή "voice") is a short chant in Christian ritual, sung as a refrain. The texts of antiphons are the Psalms. Their form was favored by St Ambrose and they feature prominentl ...
, 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
tyranny
A tyrant (), in the modern English usage of the word, is an absolute ruler who is unrestrained by law, or one who has usurped a legitimate ruler's sovereignty. Often portrayed as cruel, tyrants may defend their positions by resorting to ...
of
Polycrates 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. 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, a lady of
Crete
Crete ( el, Κρήτη, translit=, Modern: , Ancient: ) is the largest and most populous of the Greek islands, the 88th largest island in the world and the fifth largest island in the Mediterranean Sea, after Sicily, Sardinia, Cyprus, ...
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
Milo or Milon of Croton (late 6th century BC) was a famous ancient Greek athlete.
He was most likely a historical person, as he is mentioned by many classical authors, among them Aristotle, Pausanias, Cicero, Herodotus, Vitruvius, Epictetus, an ...
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. It was situated in modern Calabria, in southern Italy, between two rivers, the Crathis (Crati) and the Sybaris (Coscile).
The city was founded in 720 BC ...
in 510 BC. After the victory, some prominent citizens of Croton proposed a
democratic constitution, which the Pythagoreans rejected. 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. 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, 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, is the Reincarnation#Conceptual definitions, transmigration of the soul, especially its reincarnation after death. The term is derived from ancient Greek philosophy, and has be ...
'', the belief that all
soul
In many religious and philosophical traditions, there is a belief that a soul is "the immaterial aspect or essence of a human being".
Etymology
The Modern English noun '' soul'' is derived from Old English ''sāwol, sāwel''. The earliest atte ...
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 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
Hermes (; grc-gre, wikt:Ἑρμῆς, Ἑρμῆς) is an Olympian deity in ancient Greek religion and Greek mythology, mythology. Hermes is considered the herald of the gods. He is also considered the protector of human heralds, travelle ...
, who granted him the ability to remember all his past incarnations. Next, he was incarnated as
Euphorbus
In Greek mythology, Euphorbus (Ancient Greek: Εὔφορβος ''Euphorbos'') was a Trojan hero during the Trojan War.
Description
Euphorbus was a handsome man described to have the loveliest locks among the curly-haired. He had a lot of go ...
, a minor hero from the
Trojan War briefly mentioned in the ''
Iliad
The ''Iliad'' (; grc, Ἰλιάς, Iliás, ; "a poem about Ilium") is one of two major ancient Greek epic poems attributed to Homer. It is one of the oldest extant works of literature still widely read by modern audiences. As with the '' Odys ...
''. He then became the philosopher
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 Dikaiarchos (), was a Greek philosopher, geographer and author. Dicaearchus was a student of Aristotle in the Lyceum. Very little of his work remains exta ...
, was as a beautiful courtesan.
Mysticism
Another belief attributed to Pythagoras was that of the "
harmony of the spheres", which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony. According to Porphyry, Pythagoras taught that the seven
Muse
In ancient Greek religion and mythology, the Muses ( grc, Μοῦσαι, Moûsai, el, Μούσες, Múses) are the inspirational goddesses of literature, science, and the arts. They were considered the source of the knowledge embodied in the ...
s were actually the
seven planets
7 is a number, numeral, and glyph.
7 or seven may also refer to:
* AD 7, the seventh year of the AD era
* 7 BC, the seventh year before the AD era
* The month of
July
Music Artists
* Seven (Swiss singer) (born 1978), a Swiss recording artist
* ...
singing together. In his philosophical dialogue
''Protrepticus'',
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ph ...
has his literary double say:
Pythagoras was said to have practiced
divination and
prophecy
In religion, a prophecy is a message that has been communicated to a person (typically called a '' prophet'') by a supernatural entity. Prophecies are a feature of many cultures and belief systems and usually contain divine will or law, or pr ...
. In the visits to various places in Greece—
Delos,
Sparta,
Phlius,
Crete
Crete ( el, Κρήτη, translit=, Modern: , Ancient: ) is the largest and most populous of the Greek islands, the 88th largest island in the world and the fifth largest island in the Mediterranean Sea, after Sicily, Sardinia, Cyprus, ...
, 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
Monad may refer to:
Philosophy
* Monad (philosophy), a term meaning "unit"
**Monism, the concept of "one essence" in the metaphysical and theological theory
** Monad (Gnosticism), the most primal aspect of God in Gnosticism
* ''Great Monad'', a ...
) represented the origin of all things and the number two (the
dyad
Dyad or dyade may refer to:
Arts and entertainment
* Dyad (music), a set of two notes or pitches
* ''Dyad'' (novel), by Michael Brodsky, 1989
* ''Dyad'' (video game), 2012
* ''Dyad 1909'' and ''Dyad 1929'', ballets by Wayne McGregor
Other uses ...
) 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, la, Apollinis, label ...
. The number four signified the
four seasons and the
four elements
Classical elements typically refer to earth, water, air, fire, and (later) aether which were proposed to explain the nature and complexity of all matter in terms of simpler substances. Ancient cultures in Greece, Tibet, and India had simi ...
. The number seven was also sacred because it was the number of planets and the number of strings on a lyre, and because Apollo's birthday was celebrated on the seventh day of each month. They believed that
odd numbers
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because
\begin
-2 \cdot 2 &= -4 \\
0 \cdot 2 &= 0 \\
41 ...
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 tetractys ( el, τετρακτύς), or tetrad, or the tetractys of the decad is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the ...
, 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
t" 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,
proofless arithmetic, 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 a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
and
Isocrates 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
A monastery is a building or complex of buildings comprising the domestic quarters and workplaces of monastics, monks or nuns, whether living in communities or alone ( hermits). A monastery generally includes a place reserved for prayer whi ...
. The adherents were bound by a
vow to Pythagoras and each other, for the purpose of pursuing the
religious
Religion is usually defined as a social- cultural system of designated behaviors and practices, morals, beliefs, worldviews, texts, sanctified places, prophecies, ethics, or organizations, that generally relates humanity to supernatur ...
and
ascetic observances, and of studying his religious and
philosophical
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
theories. The members of the sect
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
Maxim or Maksim may refer to:
Entertainment
* ''Maxim'' (magazine), an international men's magazine
** ''Maxim'' (Australia), the Australian edition
** ''Maxim'' (India), the Indian edition
*Maxim Radio, ''Maxim'' magazine's radio channel on Sir ...
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
gods
A deity or god is a supernatural being who is considered divine or sacred. The ''Oxford Dictionary of English'' defines deity as a god or goddess, or anything revered as divine. C. Scott Littleton defines a deity as "a being with powers greater ...
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
dancing
Dance is a performing art form consisting of sequences of movement, either improvised or purposefully selected. This movement has aesthetic and often symbolic value. Dance can be categorized and described by its choreography, by its reperto ...
, daily morning walks along
scenic routes, and
athletics were major components of the Pythagorean lifestyle. Moments of contemplation at the beginning and end of each day were also advised.
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.
Pythagoreanism also entailed a number of dietary prohibitions. It is more or less agreed that Pythagoras issued a prohibition against the consumption of
fava beans
''Vicia faba'', commonly known as the broad bean, fava bean, or faba bean, is a species of vetch, a flowering plant in the pea and bean family Fabaceae. It is widely cultivated as a crop for human consumption, and also as a cover crop. Varieti ...
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, is the Reincarnation#Conceptual definitions, transmigration of the soul, especially its reincarnation after death. The term is derived from ancient Greek philosophy, and has be ...
. Some ancient writers present Pythagoras as enforcing a strictly
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 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...
, Pythagoras allowed the use of all kinds of animal food except the flesh of
oxen used for
ploughing, and
rams. According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices and established a diet for athletes dependent on meat.
Legends
Within his own lifetime, Pythagoras was already the subject of elaborate
hagiographic
A hagiography (; ) is a biography of a saint or an ecclesiastical leader, as well as, by extension, an adulatory and idealized biography of a founder, saint, monk, nun or icon in any of the world's religions. Early Christian hagiographies might ...
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
Olympic Games
The modern Olympic Games or Olympics (french: link=no, Jeux olympiques) are the leading international sporting events featuring summer and winter sports competitions in which thousands of athletes from around the world participate in a vari ...
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
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
Muslim tradition, Pythagoras was said to have been initiated by
Hermes
Hermes (; grc-gre, wikt:Ἑρμῆς, Ἑρμῆς) is an Olympian deity in ancient Greek religion and Greek mythology, mythology. Hermes is considered the herald of the gods. He is also considered the protector of human heralds, travelle ...
(Egyptian
Thoth).
Pythagoras was said to have dressed all in white. He is also said to have borne a golden
wreath
A wreath () is an assortment of flowers, leaves, fruits, twigs, or various materials that is constructed to form a circle .
In English-speaking countries, wreaths are used typically as household ornaments, most commonly as an Advent and Chri ...
atop his head and to have worn
trousers
Trousers (British English), slacks, or pants are an item of clothing worn from the waist to anywhere between the knees and the ankles, covering both legs separately (rather than with cloth extending across both legs as in robes, skirts, and ...
after the fashion of the
Thracians. Diogenes Laërtius presents Pythagoras as having exercised remarkable
self-control
Self-control, an aspect of inhibitory control, is the ability to regulate one's emotions, thoughts, and behavior in the face of temptations and impulses. As an executive function, it is a cognitive process that is necessary for regulating one' ...
; 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
his famous theorem, as well as discoveries in the fields of
music
Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspe ...
,
astronomy, and
medicine
Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...
. 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
o the sum ofthe squares of the two other sides"—that is,
. According to a popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole ''
hecatomb'', to the gods. 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
Babylonians
Babylonia (; Akkadian: , ''māt Akkadī'') was an ancient Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Syria). It emerged as an Amorite-ruled state c. 1 ...
and
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
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
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
hammers
A hammer is a tool, most often a hand tool, consisting of a weighted "head" fixed to a long handle that is swung to deliver an impact to a small area of an object. This can be, for example, to drive nails into wood, to shape metal (as wi ...
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.
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, the first to divide the globe into
five climatic zones, and the first to identify the
morning star and the
evening star as the same celestial object (now known as
Venus
Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
). 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
pseudepigrapha
Pseudepigrapha (also anglicized as "pseudepigraph" or "pseudepigraphs") are falsely attributed works, texts whose claimed author is not the true author, or a work whose real author attributed it to a figure of the past.Bauckham, Richard; "Pse ...
l 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
Babylonians over a thousand years earlier.
Later influence in antiquity
On Greek philosophy
Sizeable Pythagorean communities existed in Magna Graecia,
Phlius, and
Thebes during the early fourth century BC. Around the same time, the Pythagorean philosopher
Archytas was highly influential on the politics of the city of
Tarentum in Magna Graecia. According to 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
''Meno'' (; grc-gre, Μένων, ''Ménōn'') is a Socratic dialogue by Plato. Meno begins the dialogue by asking Socrates whether virtue is taught, acquired by practice, or comes by nature. In order to determine whether virtue is teachabl ...
'', ''
Phaedo'', and ''
The Republic'', have a strong "Pythagorean coloring", and his last few dialogues (particularly ''
Philebus'' and ''
Timaeus Timaeus (or Timaios) is a Greek name. It may refer to:
* ''Timaeus'' (dialogue), a Socratic dialogue by Plato
*Timaeus of Locri, 5th-century BC Pythagorean philosopher, appearing in Plato's dialogue
*Timaeus (historian) (c. 345 BC-c. 250 BC), Greek ...
'') are extremely Pythagorean in character.
According to
R. M. Hare, Plato's ''
Republic'' may be partially based on the "tightly organised community of like-minded thinkers" established 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
In many religious and philosophical traditions, there is a belief that a soul is "the immaterial aspect or essence of a human being".
Etymology
The Modern English noun '' soul'' is derived from Old English ''sāwol, sāwel''. The earliest atte ...
and its place in the material world" and it is probable that both were influenced by
Orphism. The historian of philosophy
Frederick Copleston states that Plato probably borrowed
his tripartite theory of the soul from the Pythagoreans.
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...
, in his ''
A History of Western Philosophy
''A History of Western Philosophy'' is a 1946 book by the philosopher Bertrand Russell. A survey of Western philosophy from the pre-Socratic philosophers to the early 20th century, it was criticised for Russell's over-generalization and omissio ...
'', 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 Platonist philosophers such as
Eudorus and
Philo of Alexandria
Philo of Alexandria (; grc, Φίλων, Phílōn; he, יְדִידְיָה, Yəḏīḏyāh (Jedediah); ), also called Philo Judaeus, was a Hellenistic Jewish philosopher who lived in Alexandria, in the Roman province of Egypt.
Philo's de ...
hailed the rise of a "new" Pythagoreanism in
Alexandria
Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandri ...
. At around the same time,
Neopythagoreanism 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
Moderatus of Gades ( el, Μοδερᾶτος) was a Greek philosopher of the Neopythagorean school, who lived in the 1st century AD (contemporary with Apollonius of Tyana). He wrote a great work on the doctrines of the Pythagoreans, and tried to s ...
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 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
Canon or Canons may refer to:
Arts and entertainment
* Canon (fiction), the conceptual material accepted as official in a fictional universe by its fan base
* Literary canon, an accepted body of works considered as high culture
** Western ca ...
) behind aesthetic perfection. Possibly drawing on the ideas of Pythagoras, the sculptor
Polykleitos
Polykleitos ( grc, Πολύκλειτος) was an ancient Greek sculptor in bronze of the 5th century BCE. Alongside the Athenian sculptors Pheidias, Myron and Praxiteles, he is considered one of the most important sculptors of classical an ...
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. 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
Nero Claudius Caesar Augustus Germanicus ( ; born Lucius Domitius Ahenobarbus; 15 December AD 37 – 9 June AD 68), was the fifth Roman emperor and final emperor of the Julio-Claudian dynasty, reigning from AD 54 unti ...
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
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 in
Rome
, established_title = Founded
, established_date = 753 BC
, founder = King Romulus (legendary)
, image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg
, map_caption ...
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, 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 Father
The Church Fathers, Early Church Fathers, Christian Fathers, or Fathers of the Church were ancient and influential Christian theologians and writers who established the intellectual and doctrinal foundations of Christianity. The historical pe ...
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
''On the Trinity'' ( la, De Trinitate) is a Latin book written by Augustine of Hippo to discuss the Trinity in context of the logos. Although not as well known as some of his other works, some scholars have seen it as his masterpiece, of more doc ...
'', 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 Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire ...
, Pythagoras was revered as the founder of mathematics and music, two of the
Seven Liberal Arts
Liberal arts education (from Latin "free" and "art or principled practice") is the traditional academic course in Western higher education. ''Liberal arts'' takes the term '' art'' in the sense of a learned skill rather than specifically th ...
. 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
Constantine Lascaris ( el, Κωνσταντῖνος Λάσκαρις ''Kostantinos Láskaris''; 1434 – 15 August 1501) was a Greek scholar and grammarian, one of the promoters of the revival of Greek learning in Italy during the Renaissance, ...
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 cites various Pythagoreans as the most important influences on the development of his
heliocentric model
Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth a ...
of the universe, deliberately omitting mention of
Aristarchus of Samos, a non-Pythagorean astronomer who had developed a fully heliocentric model in the fourth century BC, in effort to portray his model as fundamentally Pythagorean.
Johannes Kepler considered himself to be a Pythagorean. He believed in the Pythagorean doctrine of ''musica universalis'' and it was his search for the mathematical equations behind this doctrine that led to his discovery of the
laws of planetary motion. Kepler titled his book on the subject ''
Harmonices Mundi
''Harmonice Mundi (Harmonices mundi libri V)''The full title is ''Ioannis Keppleri Harmonices mundi libri V'' (''The Five Books of Johannes Kepler's The Harmony of the World''). (Latin: ''The Harmony of the World'', 1619) is a book by Johannes ...
'' (''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 firmly believed in the Pythagorean teaching of the mathematical harmony and order of the universe. Though Newton was notorious for rarely giving others credit for their discoveries, he attributed the discovery of the
Law of Universal Gravitation to Pythagoras.
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
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 Roman poet who lived during the reign of Augustus. He was a contemporary of the older Virgil and Horace, with whom he is often ranked as one of the th ...
's ''
Metamorphoses'', in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet. It was through
Arthur Golding's 1567 English translation of Ovid's ''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
William Shakespeare ( 26 April 1564 – 23 April 1616) was an English playwright, poet and actor. He is widely regarded as the greatest writer in the English language and the world's pre-eminent dramatist. He is often called England's nation ...
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
humanist
Humanism is a philosophical stance that emphasizes the individual and social potential and agency of human beings. It considers human beings the starting point for serious moral and philosophical inquiry.
The meaning of the term "human ...
scholar
Johannes Reuchlin
Johann Reuchlin (; sometimes called Johannes; 29 January 1455 – 30 June 1522) was a German Catholic humanist and a scholar of Greek and Hebrew, whose work also took him to modern-day Austria, Switzerland, and Italy and France. Most of Reuchlin ...
(1455–1522) synthesized Pythagoreanism with
Christian theology and Jewish
Kabbalah, arguing that Kabbalah and Pythagoreanism were both inspired by
Mosaic tradition and that Pythagoras was therefore a kabbalist. In his dialogue ''De verbo mirifico'' (1494), Reuchlin compared the Pythagorean tetractys to the
ineffable
Ineffability is the quality of something that surpasses the capacity of language to express it, often being in the form of a taboo or incomprehensible term. This property is commonly associated with philosophy, aspects of existence, and similar ...
divine name
YHWH, ascribing each of the four letters of the tetragrammaton a symbolic meaning according to Pythagorean mystical teachings.
Heinrich Cornelius Agrippa
Heinrich Cornelius Agrippa von Nettesheim (; ; 14 September 1486 – 18 February 1535) was a German polymath, physician, legal scholar, soldier, theologian, and occult writer. Agrippa's '' Three Books of Occult Philosophy'' published in 1533 dre ...
's popular and influential three-volume treatise ''
De Occulta Philosophia'' cites Pythagoras as a "religious magi" and indicates that Pythagoras's mystical numerology operates on a
supercelestial level. The
freemasons deliberately modeled their society on the community founded by 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
Purgatory (, borrowed into English via Anglo-Norman and Old French) is, according to the belief of some Christian denominations (mostly Catholic), an intermediate state after physical death for expiatory purification. The process of purgatory ...
, and
Heaven on Pythagorean numbers. Dante wrote that Pythagoras saw Unity as Good and Plurality as Evil and, in ''
Paradiso'' XV, 56–57, he declares: "five and six, if understood, ray forth from unity." The number eleven and its multiples are found throughout the ''
Divine Comedy
The ''Divine Comedy'' ( it, Divina Commedia ) is an Italian narrative poem by Dante Alighieri, begun 1308 and completed in around 1321, shortly before the author's death. It is widely considered the pre-eminent work in Italian literature ...
'', each book of which has thirty-three
cantos, except for the ''
Inferno
Inferno may refer to:
* Hell, an afterlife place of suffering
* Conflagration, a large uncontrolled fire
Film
* ''L'Inferno'', a 1911 Italian film
* Inferno (1953 film), ''Inferno'' (1953 film), a film noir by Roy Ward Baker
* Inferno (1973 fi ...
'', 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.
The
Transcendentalists read the ancient ''Lives of Pythagoras'' as guides on how to live a model life.
Henry David Thoreau was impacted by
Thomas Taylor's translations of Iamblichus's ''Life of Pythagoras'' and
Stobaeus
Joannes Stobaeus (; grc-gre, Ἰωάννης ὁ Στοβαῖος; fl. 5th-century AD), from Stobi in Macedonia, was the compiler of a valuable series of extracts from Greek authors. The work was originally divided into two volumes containin ...
'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
A masterpiece, ''magnum opus'' (), or ''chef-d’œuvre'' (; ; ) in modern use is a creation that has been given much critical praise, especially one that is considered the greatest work of a person's career or a work of outstanding creativity, ...
'', ''
Walden''.
See also
*
Cosmos
The cosmos (, ) is another name for the Universe. Using the word ''cosmos'' implies viewing the universe as a complex and orderly system or entity.
The cosmos, and understandings of the reasons for its existence and significance, are studied in ...
* ''
Ex pede Herculem''
*
Isopsephy Isopsephy (; ''isos'' meaning "equal" and ''psephos'' meaning "pebble") or isopsephism is the practice of adding up the number values of the letters in a word to form a single number. The total number is then used as a metaphorical bridge to othe ...
(
gematria
Gematria (; he, גמטריא or gimatria , plural or , ''gimatriot'') is the practice of assigning a numerical value to a name, word or phrase according to an alphanumerical cipher. A single word can yield several values depending on the cipher ...
)
*
List of things named after Pythagoras
*
Lute of Pythagoras
*
Pythagoras tree (fractal)
*
Pythagorean comma
In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as ...
*
Pythagorean cup
A Pythagorean cup (also known as a Pythagoras cup, Greedy Cup, Cup of Justice or Tantalus cup) is a practical joke device in a form of a drinking cup, credited to Pythagoras of Samos. When it is filled beyond a certain point, a siphoning effect ...
*
Pythagorean triple
A Pythagorean triple consists of three positive integers , , and , such that . Such a triple is commonly written , and a well-known example is . If is a Pythagorean triple, then so is for any positive integer . A primitive Pythagorean triple is ...
*
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, ''
Vitae philosophorum VIII'' (''Lives of Eminent Philosophers''), c. 200 AD, which in turn references the lost
doxography by
Alexander Polyhistor
Lucius Cornelius Alexander Polyhistor ( grc, Ἀλέξανδρος ὁ Πολυΐστωρ; flourished in the first half of the 1st century BC; also called Alexander of Miletus) was a Greek scholar who was enslaved by the Romans during the Mithri ...
—
*
Porphyry, ''Vita Pythagorae'' (''Life of Pythagoras''), c. 270 AD �
''Porphyry, Life of Pythagoras'' translated by
Kenneth Sylvan Guthrie (1920)
*
Iamblichus, ''De Vita Pythagorica'' (''On the Pythagorean Life''), c. 300 AD �
''Iamblichus, Life of Pythagoras'' translated by
Kenneth Sylvan Guthrie (1920)
*
Apuleius
Apuleius (; also called Lucius Apuleius Madaurensis; c. 124 – after 170) was a Numidian Latin-language prose writer, Platonist philosopher and rhetorician. He lived in the Roman province of Numidia, in the Berber city of Madauros, modern- ...
, following
Aristoxenus
Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...
, writes about Pythagoras in ''Apologia'', c. 150 AD, including a story of his being taught by
Zoroaster—a story also found in
Clement of Alexandria
Titus Flavius Clemens, also known as Clement of Alexandria ( grc , Κλήμης ὁ Ἀλεξανδρεύς; – ), was a Christian theologian and philosopher who taught at the Catechetical School of Alexandria. Among his pupils were Origen an ...
.
*
Hierocles of Alexandria, ''Golden Verses of Pythagoras'', c. 430 AD
Modern secondary sources
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External links
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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
Hanover College is a private college in Hanover, Indiana, affiliated with the Presbyterian Church (USA). Founded in 1827 by Reverend John Finley Crowe, it is Indiana's oldest private college. The Hanover athletic teams participate in the H ...
Department of History
"Pythagoras and the Pythagoreans" Department of Mathematics,
Texas A&M University
Texas A&M University (Texas A&M, A&M, or TAMU) is a public, land-grant, research university in College Station, Texas. It was founded in 1876 and became the flagship institution of the Texas A&M University System in 1948. As of late 2021, T ...
"Pythagoras and Pythagoreanism" ''
The Catholic Encyclopedia
The ''Catholic Encyclopedia: An International Work of Reference on the Constitution, Doctrine, Discipline, and History of the Catholic Church'' (also referred to as the ''Old Catholic Encyclopedia'' and the ''Original Catholic Encyclopedia'') i ...
''
*
*
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