Pythagoras
Overview
 
Pythagoras of Samos was an Ionian
Ionians
The Ionians were one of the four major tribes into which the Classical Greeks considered the population of Hellenes to have been divided...

 Greek philosopher
Greek philosophy
Ancient Greek philosophy arose in the 6th century BCE and continued through the Hellenistic period, at which point Ancient Greece was incorporated in the Roman Empire...

, mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, and founder of the religious movement called Pythagoreanism
Pythagoreanism
Pythagoreanism was the system of esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics. Pythagoreanism originated in the 5th century BCE and greatly influenced Platonism...

. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos
Samoš
Samoš is a village in Serbia. It is situated in the Kovačica municipality, in the South Banat District, Vojvodina province. The village has a Serb ethnic majority and its population numbering 1,247 people .-See also:...

, and might have travelled widely in his youth, visiting Egypt
Egypt
Egypt , officially the Arab Republic of Egypt, Arabic: , is a country mainly in North Africa, with the Sinai Peninsula forming a land bridge in Southwest Asia. Egypt is thus a transcontinental country, and a major power in Africa, the Mediterranean Basin, the Middle East and the Muslim world...

 and other places seeking knowledge. He had a teacher named Themistoclea
Themistoclea
Themistoclea was a priestess, philosopher and mathematician at Delphi.. According to surviving sources she was Pythagoras’ teacher, although she may also have been his sister...

, who introduced him to the principles of ethics
Ethics
Ethics, also known as moral philosophy, is a branch of philosophy that addresses questions about morality—that is, concepts such as good and evil, right and wrong, virtue and vice, justice and crime, etc.Major branches of ethics include:...

.
Quotations

I was Euphorbus|Euphorbus at the siege of Troy.

As reported by Heraclides Ponticus|Heraclides Ponticus (c. 360 B.C), and Diogenes Laërtius, and quoted in Cosmic Optimism : A Study of the Interpretation of Evolution (1949) by Frederick William Conner

By the air which I breathe, and by the water which I drink, I will not endure to be blamed on account of this discourse.

As reported by Heraclides Ponticus|Heraclides Ponticus (c. 360 B.C), and Diogenes Laërtius, in Lives and Opinions of Eminent Philosophers|Lives and Opinions of Eminent Philosophers, "Pythagoras", Sect.5, in the translation of C. D. Yonge (1853)

Dear youths, I warn you cherish peace divine, And in your hearts lay deep these words of mine.

As reported by Heraclides, son of Sarapion, and Diogenes Laërtius, in Lives and Opinions of Eminent Philosophers|Lives and Opinions of Eminent Philosophers, "Pythagoras", Sect. 6, in the translation of C. D. Yonge (1853)

The soul of man is divided into three parts, intelligence, reason, and passion. Intelligence and passion are possessed by other animals, but reason by man alone.

As reported by Alexander Polyhistor|Alexander Polyhistor, and Diogenes Laërtius in Lives and Opinions of Eminent Philosophers|Lives and Opinions of Eminent Philosophers, "Pythagoras", Sect. 8, in the translation of C. D. Yonge (1853)

We ought so to behave to one another as to avoid making enemies of our friends, and at the same time to make friends of our enemies.

As quoted in Lives and Opinions of Eminent Philosophers|Lives and Opinions of Eminent Philosophers, by Diogenes Laërtius, "Pythagoras", Sect. 8, as translated in Dictionary of Quotations (1906) by Thomas Benfield Harbottle, p. 320

In anger we should refrain both from speech and action.

As quoted in Lives and Opinions of Eminent Philosophers, by Diogenes Laërtius, "Pythagoras", Sect. 8, as translated in Dictionary of Quotations (1906) by Thomas Benfield Harbottle, p. 370

Reason is immortal, all else mortal.

As quoted in Lives and Opinions of Eminent Philosophers by Diogenes Laërtius, as translated by Robert Drew Hicks (1925); also in The Demon and the Quantum : From the Pythagorean Mystics to Maxwell's Demon (2007) by Robert J. Scully, Marlan O. Scully, p. 11

The most momentous thing in human life is the art of winning the soul to good or to evil.

As quoted in Lives and Opinions of Eminent Philosophers by Diogenes Laërtius, as translated by Robert Drew Hicks (1925)

Friends share all things.

As quoted in Lives and Opinions of Eminent Philosophers|Lives and Opinions of Eminent Philosophers, by Diogenes Laërtius, "Pythagoras", Sect. 10

Power is the near neighbour of necessity.

As quoted in Aurea Carmina by Hierocles of Alexandria|Hierocles of Alexandria, as translated in Dictionary of Quotations (1906) by Thomas Benfield Harbottle, p. 356

Encyclopedia
Pythagoras of Samos was an Ionian
Ionians
The Ionians were one of the four major tribes into which the Classical Greeks considered the population of Hellenes to have been divided...

 Greek philosopher
Greek philosophy
Ancient Greek philosophy arose in the 6th century BCE and continued through the Hellenistic period, at which point Ancient Greece was incorporated in the Roman Empire...

, mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, and founder of the religious movement called Pythagoreanism
Pythagoreanism
Pythagoreanism was the system of esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics. Pythagoreanism originated in the 5th century BCE and greatly influenced Platonism...

. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos
Samoš
Samoš is a village in Serbia. It is situated in the Kovačica municipality, in the South Banat District, Vojvodina province. The village has a Serb ethnic majority and its population numbering 1,247 people .-See also:...

, and might have travelled widely in his youth, visiting Egypt
Egypt
Egypt , officially the Arab Republic of Egypt, Arabic: , is a country mainly in North Africa, with the Sinai Peninsula forming a land bridge in Southwest Asia. Egypt is thus a transcontinental country, and a major power in Africa, the Mediterranean Basin, the Middle East and the Muslim world...

 and other places seeking knowledge. He had a teacher named Themistoclea
Themistoclea
Themistoclea was a priestess, philosopher and mathematician at Delphi.. According to surviving sources she was Pythagoras’ teacher, although she may also have been his sister...

, who introduced him to the principles of ethics
Ethics
Ethics, also known as moral philosophy, is a branch of philosophy that addresses questions about morality—that is, concepts such as good and evil, right and wrong, virtue and vice, justice and crime, etc.Major branches of ethics include:...

. Around 530 BC, he moved to Croton
Crotone
Crotone is a city and comune in Calabria, southern Italy, on the Ionian Sea. Founded circa 710 BC as the Achaean colony of Croton , it was known as Cotrone from the Middle Ages until 1928, when its name was changed to the current one. In 1994 it became the capital of the newly established...

, a Greek colony in southern Italy
Magna Graecia
Magna Græcia is the name of the coastal areas of Southern Italy on the Tarentine Gulf that were extensively colonized by Greek settlers; particularly the Achaean colonies of Tarentum, Crotone, and Sybaris, but also, more loosely, the cities of Cumae and Neapolis to the north...

, and there set up a religious sect. His followers pursued the religious rites and practices developed by Pythagoras, and studied his philosophical theories. The society took an active role in the politics of Croton, but this eventually led to their downfall. The Pythagorean meeting-places were burned, and Pythagoras was forced to flee the city. He is said to have ended his days in Metapontum
Metapontum
Metapontum, Metapontium or Metapontion , was an important city of Magna Graecia, situated on the gulf of Tarentum, between the river Bradanus and the Casuentus . It was distant about 20 km from Heraclea and 40 from Tarentum...

.

Pythagoras made influential contributions to philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

 and religious teaching in the late 6th century BC. He is often revered as a great mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, mystic
Mysticism
Mysticism is the knowledge of, and especially the personal experience of, states of consciousness, i.e. levels of being, beyond normal human perception, including experience and even communion with a supreme being.-Classical origins:...

 and scientist
Scientist
A scientist in a broad sense is one engaging in a systematic activity to acquire knowledge. In a more restricted sense, a scientist is an individual who uses the scientific method. The person may be an expert in one or more areas of science. This article focuses on the more restricted use of the word...

, but he is best known for the Pythagorean theorem
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...

 which bears his name. However, because legend and obfuscation cloud his work even more than with the other pre-Socratic philosophers
Pre-Socratic philosophy
Pre-Socratic philosophy is Greek philosophy before Socrates . In Classical antiquity, the Presocratic philosophers were called physiologoi...

, one can give account of his teachings to a little extent, and some have questioned whether he contributed much to mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 and natural philosophy
Natural philosophy
Natural philosophy or the philosophy of nature , is a term applied to the study of nature and the physical universe that was dominant before the development of modern science...

. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Whether or not his disciples believed that everything was related to mathematics and that numbers were the ultimate reality is unknown. It was said that he was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

, and through him, all of Western philosophy
Western philosophy
Western philosophy is the philosophical thought and work of the Western or Occidental world, as distinct from Eastern or Oriental philosophies and the varieties of indigenous philosophies....

.

Biographical sources

Accurate facts about the life of Pythagoras are so few, and most information concerning him is of so late a date, and so untrustworthy, that it is impossible to provide more than a vague outline of his life. The lack of information by contemporary writers, together with the secrecy which surrounded the Pythagorean brotherhood, meant that invention took the place of facts. The stories which were created were eagerly sought by the Neoplatonist writers who provide most of the details about Pythagoras, but who were uncritical concerning anything which related to the gods or which was considered divine. Thus many myths were created – such as that Apollo
Apollo
Apollo is one of the most important and complex of the Olympian deities in Greek and Roman mythology...

 was his father; that Pythagoras gleamed with a supernatural
Supernatural
The supernatural or is that which is not subject to the laws of nature, or more figuratively, that which is said to exist above and beyond nature...

 brightness; that he had a golden thigh
Thigh
In humans the thigh is the area between the pelvis and the knee. Anatomically, it is part of the lower limb.The single bone in the thigh is called the femur...

; that Abaris
Abaris the Hyperborean
Italic text:Abaris redirects here. For the Baroque opera see Les BoréadesAbaris the Hyperborean , son of Seuthes, was a legendary sage, healer, and priest of Apollo known to the Ancient Greeks. He was supposed to have learned his skills in his homeland of Hyperborea, near the Caucasus, which he...

 came flying to him on a golden arrow
Arrow
An arrow is a shafted projectile that is shot with a bow. It predates recorded history and is common to most cultures.An arrow usually consists of a shaft with an arrowhead attached to the front end, with fletchings and a nock at the other.- History:...

; that he was seen in different places at one and the same time. With the exception of a few remarks by Xenophanes
Xenophanes
of Colophon was a Greek philosopher, theologian, poet, and social and religious critic. Xenophanes life was one of travel, having left Ionia at the age of 25 he continued to travel throughout the Greek world for another 67 years. Some scholars say he lived in exile in Siciliy...

, Heraclitus
Heraclitus
Heraclitus of Ephesus was a pre-Socratic Greek philosopher, a native of the Greek city Ephesus, Ionia, on the coast of Asia Minor. He was of distinguished parentage. Little is known about his early life and education, but he regarded himself as self-taught and a pioneer of wisdom...

, Herodotus
Herodotus
Herodotus was an ancient Greek historian who was born in Halicarnassus, Caria and lived in the 5th century BC . He has been called the "Father of History", and was the first historian known to collect his materials systematically, test their accuracy to a certain extent and arrange them in a...

, Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

, Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

, and Isocrates
Isocrates
Isocrates , an ancient Greek rhetorician, was one of the ten Attic orators. In his time, he was probably the most influential rhetorician in Greece and made many contributions to rhetoric and education through his teaching and written works....

, we are mainly dependent on Diogenes Laërtius
Diogenes Laertius
Diogenes Laertius was a biographer of the Greek philosophers. Nothing is known about his life, but his surviving Lives and Opinions of Eminent Philosophers is one of the principal surviving sources for the history of Greek philosophy.-Life:Nothing is definitively known about his life...

, Porphyry
Porphyry (philosopher)
Porphyry of Tyre , Porphyrios, AD 234–c. 305) was a Neoplatonic philosopher who was born in Tyre. He edited and published the Enneads, the only collection of the work of his teacher Plotinus. He also wrote many works himself on a wide variety of topics...

, and Iamblichus for the biographical details. Aristotle had written a separate work on the Pythagoreans, which unfortunately has not survived. His disciples Dicaearchus
Dicaearchus
Dicaearchus of Messana was a Greek philosopher, cartographer, geographer, mathematician and author. Dicaearchus was Aristotle's student in the Lyceum. Very little of his work remains extant. He wrote on the history and geography of Greece, of which his most important work was his Life of Greece...

, Aristoxenus
Aristoxenus
Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony, survives incomplete, as well as some fragments concerning rhythm and...

, and Heraclides Ponticus
Heraclides Ponticus
Heraclides Ponticus , also known as Herakleides and Heraklides of Pontus, was a Greek philosopher and astronomer who lived and died at Heraclea Pontica, now Karadeniz Ereğli, Turkey. He is best remembered for proposing that the earth rotates on its axis, from west to east, once every 24 hours...

 had written on the same subject. These writers, late as they are, were among the best sources from whom Porphyry and Iamblichus drew, besides the legendary accounts and their own inventions. Hence historians are often reduced to considering the statements based on their inherent probability, but even then, if all the credible stories concerning Pythagoras were supposed true, his range of activity would be impossibly vast.

Life

Herodotus
Herodotus
Herodotus was an ancient Greek historian who was born in Halicarnassus, Caria and lived in the 5th century BC . He has been called the "Father of History", and was the first historian known to collect his materials systematically, test their accuracy to a certain extent and arrange them in a...

, Isocrates
Isocrates
Isocrates , an ancient Greek rhetorician, was one of the ten Attic orators. In his time, he was probably the most influential rhetorician in Greece and made many contributions to rhetoric and education through his teaching and written works....

, and other early writers all agree that Pythagoras was born on Samos
Samoš
Samoš is a village in Serbia. It is situated in the Kovačica municipality, in the South Banat District, Vojvodina province. The village has a Serb ethnic majority and its population numbering 1,247 people .-See also:...

, the Greek island in the eastern Aegean
Aegean Sea
The Aegean Sea[p] is an elongated embayment of the Mediterranean Sea located between the southern Balkan and Anatolian peninsulas, i.e., between the mainlands of Greece and Turkey. In the north, it is connected to the Marmara Sea and Black Sea by the Dardanelles and Bosporus...

, and we also learn that Pythagoras was the son of Mnesarchus. His father was a gem-engraver or a merchant. His name led him to be associated with Pythia
Pythia
The Pythia , commonly known as the Oracle of Delphi, was the priestess at the Temple of Apollo at Delphi, located on the slopes of Mount Parnassus. The Pythia was widely credited for her prophecies inspired by Apollo. The Delphic oracle was established in the 8th century BC...

n Apollo
Apollo
Apollo is one of the most important and complex of the Olympian deities in Greek and Roman mythology...

; Aristippus
Aristippus
Aristippus of Cyrene, , was the founder of the Cyrenaic school of Philosophy. He was a pupil of Socrates, but adopted a very different philosophical outlook, teaching that the goal of life was to seek pleasure by adapting circumstances to oneself and by maintaining proper control over both...

 explained his name by saying, "He spoke (agor-) the truth no less than did the Pythian (Pyth-)," and Iamblichus tells the story that the Pythia prophesied that his pregnant mother would give birth to a man supremely beautiful, wise, and beneficial to humankind. A late source gives his mother's name as Pythais. As to the date of his birth, Aristoxenus
Aristoxenus
Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony, survives incomplete, as well as some fragments concerning rhythm and...

 stated that Pythagoras left Samos in the reign of Polycrates
Polycrates
Polycrates , son of Aeaces, was the tyrant of Samos from c. 538 BC to 522 BC.He took power during a festival of Hera with his brothers Pantagnotus and Syloson, but soon had Pantagnotus killed and exiled Syloson to take full control for himself. He then allied with Amasis II, pharaoh of Egypt, as...

, at the age of 40, which would give a date of birth around 570 BC.

It was natural for the ancient biographers to inquire as to the origins of Pythagoras' remarkable system. In the absence of reliable information, however, a huge range of teachers were assigned to Pythagoras. Some made his training almost entirely Greek, others exclusively Egyptian
Late Period of Ancient Egypt
The Late Period of Ancient Egypt refers to the last flowering of native Egyptian rulers after the Third Intermediate Period from the 26th Saite Dynasty into Persian conquests and ended with the death of Alexander the Great...

 and Oriental. We find mentioned as his instructors Creophylus
Creophylus of Samos
Creophylus or Kreophylos is the name of a legendary early Greek singer, native to Samos or Chios. He was said to have been a contemporary of Homer and author of the lost epic Capture of Oechalia. According to some sources Homer gave the poem to Creophylus in return for hospitality; one source...

, Hermodamas, Bias
Bias of Priene
Bias , the son of Teutamus and a citizen of Priene was a Greek philosopher. Satyrus puts him as the wisest of all the Seven Sages of Greece. He was renowned for his goodness....

, Thales
Thales
Thales of Miletus was a pre-Socratic Greek philosopher from Miletus in Asia Minor, and one of the Seven Sages of Greece. Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition...

, Anaximander
Anaximander
Anaximander was a pre-Socratic Greek philosopher who lived in Miletus, a city of Ionia; Milet in modern Turkey. He belonged to the Milesian school and learned the teachings of his master Thales...

, and Pherecydes of Syros
Pherecydes of Syros
Pherecydes of Syros was a Greek thinker from the island of Syros, of the 6th century BC. Pherecydes authored the Pentemychos or Heptamychos, one of the first attested prose works in Greek literature, which formed an important bridge between mythic and pre-Socratic thought.- Life :Very little is...

. The Egyptians are said to have taught him geometry, the Phoenicia
Phoenicia
Phoenicia , was an ancient civilization in Canaan which covered most of the western, coastal part of the Fertile Crescent. Several major Phoenician cities were built on the coastline of the Mediterranean. It was an enterprising maritime trading culture that spread across the Mediterranean from 1550...

ns arithmetic, the Chaldea
Chaldea
Chaldea or Chaldaea , from Greek , Chaldaia; Akkadian ; Hebrew כשדים, Kaśdim; Aramaic: ܟܐܠܕܘ, Kaldo) was a marshy land located in modern-day southern Iraq which came to briefly rule Babylon...

ns astronomy, the Magi
Magi
Magi is a term, used since at least the 4th century BC, to denote a follower of Zoroaster, or rather, a follower of what the Hellenistic world associated Zoroaster with, which...

ans the principles of religion and practical maxims for the conduct of life. Of the various claims regarding his Greek teachers, Pherecydes is mentioned most often.

Diogenes Laertius reported that Pythagoras had undertaken extensive travels, and had visited not only Egypt
Egypt
Egypt , officially the Arab Republic of Egypt, Arabic: , is a country mainly in North Africa, with the Sinai Peninsula forming a land bridge in Southwest Asia. Egypt is thus a transcontinental country, and a major power in Africa, the Mediterranean Basin, the Middle East and the Muslim world...

, but Arabia, Phoenicia
Phoenicia
Phoenicia , was an ancient civilization in Canaan which covered most of the western, coastal part of the Fertile Crescent. Several major Phoenician cities were built on the coastline of the Mediterranean. It was an enterprising maritime trading culture that spread across the Mediterranean from 1550...

, Judaea
Judea
Judea or Judæa was the name of the mountainous southern part of the historic Land of Israel from the 8th century BCE to the 2nd century CE, when Roman Judea was renamed Syria Palaestina following the Jewish Bar Kokhba revolt.-Etymology:The...

, Babylon
Babylon
Babylon was an Akkadian city-state of ancient Mesopotamia, the remains of which are found in present-day Al Hillah, Babil Province, Iraq, about 85 kilometers south of Baghdad...

, and even India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...

, for the purpose of collecting all available knowledge, and especially to learn information concerning the secret or mystic cults of the gods. Plutarch
Plutarch
Plutarch then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus , c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia...

 asserted in his book On Isis and Osiris
Moralia
The Moralia of the 1st-century Greek scholar Plutarch of Chaeronea is an eclectic collection of 78 essays and transcribed speeches. They give an insight into Roman and Greek life, but often are also fascinating timeless observations in their own right...

that during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of
Heliopolis
Heliopolis (ancient)
Heliopolis was one of the oldest cities of ancient Egypt, the capital of the 13th Lower Egyptian nome that was located five miles east of the Nile to the north of the apex of the Nile Delta...

. Other ancient writers asserted his visit to Egypt. Enough of Egypt was known to attract the curiosity of an inquiring Greek, and contact between Samos and other parts of Greece with Egypt is mentioned.

It is not easy to say how much Pythagoras learned from the Egyptian priests, or indeed, whether he learned anything at all from them. There was nothing in the symbolism which the Pythagoreans adopted which showed the distinct traces of Egypt. The secret religious rites of the Pythagoreans exhibited nothing but what might have been adopted in the spirit of Greek religion, by those who knew nothing of Egyptian mysteries. The philosophy and the institutions of Pythagoras might easily have been developed by a Greek mind exposed to the ordinary influences of the age. Even the ancient authorities note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphic
Orphism (religion)
Orphism is the name given to a set of religious beliefs and practices in the ancient Greek and the Hellenistic world, as well as by the Thracians, associated with literature ascribed to the mythical poet Orpheus, who descended into Hades and returned...

 or Cretan mysteries
Greco-Roman mysteries
Mystery religions, sacred Mysteries or simply mysteries, were religious cults of the Greco-Roman world, participation in which was reserved to initiates....

, or the Delphic oracle
Pythia
The Pythia , commonly known as the Oracle of Delphi, was the priestess at the Temple of Apollo at Delphi, located on the slopes of Mount Parnassus. The Pythia was widely credited for her prophecies inspired by Apollo. The Delphic oracle was established in the 8th century BC...

.

There is little direct evidence as to the kind and amount of knowledge which Pythagoras acquired, or as to his definite philosophical views. Everything of the kind mentioned by Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

 and Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 is attributed not to Pythagoras, but to the Pythagoreans. Heraclitus
Heraclitus
Heraclitus of Ephesus was a pre-Socratic Greek philosopher, a native of the Greek city Ephesus, Ionia, on the coast of Asia Minor. He was of distinguished parentage. Little is known about his early life and education, but he regarded himself as self-taught and a pioneer of wisdom...

 stated that he was a man of extensive learning; and Xenophanes
Xenophanes
of Colophon was a Greek philosopher, theologian, poet, and social and religious critic. Xenophanes life was one of travel, having left Ionia at the age of 25 he continued to travel throughout the Greek world for another 67 years. Some scholars say he lived in exile in Siciliy...

 claimed that he believed in the transmigration of souls
Metempsychosis
Metempsychosis is a philosophical term in the Greek language referring to transmigration of the soul, especially its reincarnation after death. It is a doctrine popular among a number of Eastern religions such as Hinduism, Buddhism, Jainism and Druzism wherein an individual incarnates from one...

. Xenophanes mentions the story of his interceding on behalf of a dog
Dog
The domestic dog is a domesticated form of the gray wolf, a member of the Canidae family of the order Carnivora. The term is used for both feral and pet varieties. The dog may have been the first animal to be domesticated, and has been the most widely kept working, hunting, and companion animal in...

 that was being beaten, professing to recognise in its cries the voice of a departed friend. Pythagoras is supposed to have claimed that he had been Euphorbus
Euphorbus
Euphorbus , the son of Panthous and Phrontis, was a Trojan hero during the Trojan War. He wounded Patroclus before Patroclus was killed by Hector. In the fight for Patroclus' body, Euphorbus was killed by Menelaus. He was apparently one of Troy's finest warriors. Menelaus later took Euphorbus'...

, the son of Panthus, in the Trojan war
Trojan War
In Greek mythology, the Trojan War was waged against the city of Troy by the Achaeans after Paris of Troy took Helen from her husband Menelaus, the king of Sparta. The war is among the most important events in Greek mythology and was narrated in many works of Greek literature, including the Iliad...

, as well as various other characters, a tradesman, a courtesan, etc. In his book The Life of Apollonius of Tyana, Philostratus
Philostratus
Philostratus or Lucius Flavius Philostratus , , 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 probably around 172, and is said by the Suda to have been living in the reign of emperor Philip the Arab . His death...

 wrote that Pythagoras knew not only who he was himself, but also who he had been.

Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...

, as well as discoveries in the field of music
Music of Ancient Greece
The music of ancient Greece was almost universally present in society, from marriages and funerals to religious ceremonies, theatre, folk music and the ballad-like reciting of epic poetry. It thus played an integral role in the lives of ancient Greeks...

, astronomy
Greek astronomy
Greek astronomy is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the...

, and medicine. But it was the religious element which made the profoundest impression upon his contemporaries. Thus the people of Croton were supposed to have identified him with the Hyperborean Apollo
Apollo
Apollo is one of the most important and complex of the Olympian deities in Greek and Roman mythology...

, and he was said to have practised divination
Divination
Divination is the attempt to gain insight into a question or situation by way of an occultic standardized process or ritual...

 and prophecy
Prophecy
Prophecy is a process in which one or more messages that have been communicated to a prophet are then communicated to others. Such messages typically involve divine inspiration, interpretation, or revelation of conditioned events to come as well as testimonies or repeated revelations that the...

. In the visits to various places in Greece – Delos
Delos
The island of Delos , isolated in the centre of the roughly circular ring of islands called the Cyclades, near Mykonos, is one of the most important mythological, historical and archaeological sites in Greece...

, Sparta
Sparta
Sparta or Lacedaemon, was a prominent city-state in ancient Greece, situated on the banks of the River Eurotas in Laconia, in south-eastern Peloponnese. It emerged as a political entity around the 10th century BC, when the invading Dorians subjugated the local, non-Dorian population. From c...

, Phlius
Phlius
Phlius was a Greek city in the northwestern Argolid, in the Peloponnese, said to be named after the Greek hero, Phlias. Although geographically close to Argos, the city became a Spartan ally and a member of the Peloponnesian League....

, Crete
Crete
Crete is the largest and most populous of the Greek islands, the fifth largest island in the Mediterranean Sea, and one of the thirteen administrative regions of Greece. It forms a significant part of the economy and cultural heritage of Greece while retaining its own local cultural traits...

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

After his travels, Pythagoras moved (around 530 BC) to Croton
Crotone
Crotone is a city and comune in Calabria, southern Italy, on the Ionian Sea. Founded circa 710 BC as the Achaean colony of Croton , it was known as Cotrone from the Middle Ages until 1928, when its name was changed to the current one. In 1994 it became the capital of the newly established...

, in Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

 (Magna Graecia
Magna Graecia
Magna Græcia is the name of the coastal areas of Southern Italy on the Tarentine Gulf that were extensively colonized by Greek settlers; particularly the Achaean colonies of Tarentum, Crotone, and Sybaris, but also, more loosely, the cities of Cumae and Neapolis to the north...

). Possibly the tyranny of Polycrates
Polycrates
Polycrates , son of Aeaces, was the tyrant of Samos from c. 538 BC to 522 BC.He took power during a festival of Hera with his brothers Pantagnotus and Syloson, but soon had Pantagnotus killed and exiled Syloson to take full control for himself. He then allied with Amasis II, pharaoh of Egypt, as...

 in Samos made it difficult for him to achieve his schemes there. His later admirers claimed that Pythagoras was so overburdened with public duties in Samos, because of the high estimation in which he was held by his fellow-citizens, that he moved to Croton. On his arrival in Croton, he quickly attained extensive influence, and many people began to follow him. Later biographers tell fantastical stories of the effects of his eloquent speech in leading the people of Croton to abandon their luxurious and corrupt way of life and devote themselves to the purer system which he came to introduce.

His followers established a select brotherhood or club for the purpose of pursuing the religious and ascetic practices developed by their master. The accounts agree that what was done and taught among the members was kept a profound secret. The esoteric teachings may have concerned the secret religious doctrines and usages, which were undoubtedly prominent in the Pythagorean system, and may have been connected with the worship of Apollo. Temperance of all kinds seems to have been strictly urged. There is disagreement among the biographers as to whether Pythagoras forbade all animal food, or only certain types. The club was in practice at once "a philosophical school, a religious brotherhood, and a political association."

Such an aristocratic and exclusive club could easily have made many people in Croton jealous and hostile, and this seems to have led to its destruction. The circumstances, however, are uncertain. Conflict seems to have broken out between the towns of Sybaris
Sybaris
Sybaris was an ancient city in Magna Graecia on the western shore of the Gulf of Taranto. The wealth of the city during the 6th century BC was so great that the Sybarites became synonymous with pleasure and luxury...

 and Croton. The forces of Croton were headed by the Pythagorean Milo
Milo of Croton
Milo of Croton was a 6th century BC wrestler from the Magna Graecian city of Croton in southern Italy who enjoyed a brilliant wrestling career and won many victories in the most important athletic festivals of ancient Greece...

, and it is likely that the members of the brotherhood took a prominent part. After the decisive victory by Croton, a proposal for establishing a more democratic constitution, was unsuccessfully resisted by the Pythagoreans. Their enemies, headed by Cylon and Ninon, the former of whom is said to have been irritated by his exclusion from the brotherhood, roused the populace against them. An attack was made upon them while assembled either in the house of Milo, or in some other meeting-place. The building was set on fire, and many of the assembled members perished; only the younger and more active escaping. Similar commotions ensued in the other cities of Magna Graecia in which Pythagorean clubs had been formed.

As an active and organised brotherhood the Pythagorean order was everywhere suppressed, and did not again revive. Still the Pythagoreans continued to exist as a sect, the members of which kept up among themselves their religious observances and scientific pursuits, while individuals, as in the case of Archytas
Archytas
Archytas was an Ancient Greek philosopher, mathematician, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato....

, acquired now and then great political influence. Concerning the fate of Pythagoras himself, the accounts varied. Some say that he perished in the temple with his disciples, others that he fled first to Tarentum
Taranto
Taranto is a coastal city in Apulia, Southern Italy. It is the capital of the Province of Taranto and is an important commercial port as well as the main Italian naval base....

, and that, being driven from there, he escaped to Metapontum
Metapontum
Metapontum, Metapontium or Metapontion , was an important city of Magna Graecia, situated on the gulf of Tarentum, between the river Bradanus and the Casuentus . It was distant about 20 km from Heraclea and 40 from Tarentum...

, and there starved himself to death. His tomb was shown at Metapontum in the time of Cicero
Cicero
Marcus Tullius Cicero , was a Roman philosopher, statesman, lawyer, political theorist, and Roman constitutionalist. He came from a wealthy municipal family of the equestrian order, and is widely considered one of Rome's greatest orators and prose stylists.He introduced the Romans to the chief...

.

According to some accounts Pythagoras married Theano, a lady of Croton. Their children are variously stated to have included a son, Telauges
Telauges
Telauges was a Pythagorean philosopher and, according to tradition, the son of Pythagoras and Theano.Little is known about the life of Telauges. According to tradition, he was the son of Pythagoras and Theano. Iamblichus claims that Pythagoras died when Telauges was very young, and that Telauges...

, and three daughters, Damo, Arignote
Arignote
Arignote was a Pythagorean philosopher, a student of Pythagoras and Theano, and, according to some traditions, their daughter as well.According to the Suda, she wrote a Bacchica concerning the mysteries of Demeter, which was also entitled the Sacred Narrative. The Suda mentions a separate work...

, and Myia
Myia
Myia was a Pythagorean philosopher and, according to later tradition, one of the daughters of Theano and Pythagoras. She was married to Milo of Croton, the famous athlete. She was a choir leader as a girl, and as a woman, she was noted for her exemplary religious behaviour...

.

Writings

No texts by Pythagoras are known to have survived, although forgeries under his name — a few of which remain extant — did circulate in antiquity
Classical antiquity
Classical antiquity is a broad term for a long period of cultural history centered on the Mediterranean Sea, comprising the interlocking civilizations of ancient Greece and ancient Rome, collectively known as the Greco-Roman world...

. Critical ancient sources like Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 and Aristoxenus
Aristoxenus
Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony, survives incomplete, as well as some fragments concerning rhythm and...

 cast doubt on these writings. Ancient Pythagoreans usually quoted their master's doctrines with the phrase autos ephe ("he himself said") — emphasizing the essentially oral nature of his teaching.

Mathematics


Pythagorean theorem

Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...

, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides—that is, .

While the theorem that now bears his name was known and previously utilized by the Babylonians
Babylonian mathematics
Babylonian mathematics refers to any mathematics of the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited...

 and Indians
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics , important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today was first...

, he, or his students, are often said to have constructed the first proof. It must, however, be stressed that the way in which the Babylonians handled 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
Cuneiform
Cuneiform can refer to:*Cuneiform script, an ancient writing system originating in Mesopotamia in the 4th millennium BC*Cuneiform , three bones in the human foot*Cuneiform Records, a music record label...

 sources. Because of the secretive nature of his school and the custom of its students to attribute everything to their teacher, there is no evidence that Pythagoras himself worked on or proved this theorem. For that matter, there is no evidence that he worked on any mathematical or meta-mathematical problems. Some attribute it as a carefully constructed myth by followers of Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

 over two centuries after the death of Pythagoras, mainly to bolster the case for Platonic meta-physics, which resonate well with the ideas they attributed to Pythagoras. This attribution has stuck down the centuries up to modern times. The earliest known mention of Pythagoras's name in connection with the theorem occurred five centuries after his death, in the writings of Cicero
Cicero
Marcus Tullius Cicero , was a Roman philosopher, statesman, lawyer, political theorist, and Roman constitutionalist. He came from a wealthy municipal family of the equestrian order, and is widely considered one of Rome's greatest orators and prose stylists.He introduced the Romans to the chief...

 and Plutarch
Plutarch
Plutarch then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus , c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia...

.

Musical theories and investigations

According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when one day he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how this had happened by looking at their tools, he discovered that it was because the hammers
Pythagorean hammers
According to legend, Pythagoras discovered the foundations of music by listening to the sounds of four blacksmith's hammers, which produced consonance and dissonance when they were struck simultaneously...

 were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on."

This legend has since proven to be false by virtue of the fact that these ratios are only relevant to string length (such as the string of a monochord
Monochord
A monochord is an ancient musical and scientific laboratory instrument. The word "monochord" comes from the Greek and means literally "one string." A misconception of the term lies within its name. Often a monochord has more than one string, most of the time two, one open string and a second string...

), and not to hammer weight. However, it may be that Pythagoras was indeed responsible for discovering these properties of string length.

Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Another belief attributed to Pythagoras was that of the "harmony of the spheres
Musica universalis
Musica universalis is an ancient philosophical concept that regards proportions in the movements of celestial bodies—the Sun, Moon, and planets—as a form of musica . This 'music' is not usually thought to be literally audible, but a harmonic and/or mathematical and/or religious concept...

". Thus the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony.

Tetractys

Pythagoras was also credited with devising the tetractys
Tetractys
The tetractys , or tetrad, is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row...

, the triangular figure of four rows, which add up to the perfect number, ten. As a mystical symbol, it was very important to the worship of the Pythagoreans, who would swear oaths by it:

Religion and science

Pythagoras’ religious and scientific views were, in his opinion, inseparably interconnected. Religiously, Pythagoras was a believer of metempsychosis
Metempsychosis
Metempsychosis is a philosophical term in the Greek language referring to transmigration of the soul, especially its reincarnation after death. It is a doctrine popular among a number of Eastern religions such as Hinduism, Buddhism, Jainism and Druzism wherein an individual incarnates from one...

. He believed in transmigration, or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables until it became immortal. His ideas of reincarnation were influenced by ancient Greek religion. Heraclides Ponticus
Heraclides Ponticus
Heraclides Ponticus , also known as Herakleides and Heraklides of Pontus, was a Greek philosopher and astronomer who lived and died at Heraclea Pontica, now Karadeniz Ereğli, Turkey. He is best remembered for proposing that the earth rotates on its axis, from west to east, once every 24 hours...

 reports the story that Pythagoras claimed that he had lived four lives that he could remember in detail, and, according to Xenophanes
Xenophanes
of Colophon was a Greek philosopher, theologian, poet, and social and religious critic. Xenophanes life was one of travel, having left Ionia at the age of 25 he continued to travel throughout the Greek world for another 67 years. Some scholars say he lived in exile in Siciliy...

, Pythagoras heard the cry of his dead friend in the bark of a dog.

Lore

Pythagoras became the subject of elaborate legends surrounding his historic persona. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure, attributing to him such aspects as a golden thigh, which was a sign of divinity. According to Muslim tradition, Pythagoras was said to have been initiated by Hermes
Hermes Trismegistus
Hermes Trismegistus is the eponymous author of the Hermetic Corpus, a sacred text belonging to the genre of divine revelation.-Origin and identity:...

 (Egyptian Thoth
Thoth
Thoth was considered one of the more important deities of the Egyptian pantheon. In art, he was often depicted as a man with the head of an ibis or a baboon, animals sacred to him. His feminine counterpart was Seshat...

). According to Aristotle and others' accounts, some ancients believed that he had the ability to travel through space and time, and to communicate with animals and plants. An extract from Brewer's Dictionary of Phrase and Fable
Brewer's Dictionary of Phrase and Fable
Brewer's Dictionary of Phrase and Fable, sometimes referred to simply as Brewer's, is a reference work containing definitions and explanations of many famous phrases, allusions and figures, whether historical or mythical.-History:...

's entry entitled "Golden Thigh":

Pythagoras is said to have had a golden thigh, which he showed to Abaris, the Hyperborean priest, and exhibited in the Olympic games.


Another legend describes his writing on the moon:
Pythagoras asserted he could write on the moon. His plan of operation was to write on a looking-glass in blood, and place it opposite the moon, when the inscription would appear photographed or reflected on the moon's disc.

Pythagoreans

Both Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

 and Isocrates
Isocrates
Isocrates , an ancient Greek rhetorician, was one of the ten Attic orators. In his time, he was probably the most influential rhetorician in Greece and made many contributions to rhetoric and education through his teaching and written works....

 affirm that, above all else, Pythagoras was famous for leaving behind him a way of life. Both Iamblichus and Porphyry
Porphyry (philosopher)
Porphyry of Tyre , Porphyrios, AD 234–c. 305) was a Neoplatonic philosopher who was born in Tyre. He edited and published the Enneads, the only collection of the work of his teacher Plotinus. He also wrote many works himself on a wide variety of topics...

 give detailed accounts of the organisation of the school, although the primary interest of both writers is not historical accuracy, but rather to present Pythagoras as a divine figure, sent by the gods to benefit humankind.

Pythagoras set up an organization which was in some ways a school, in some ways a brotherhood (and here it should be noted that sources indicate that as well as men there were many women among the adherents of Pythagoras), and in some ways a monastery. It was based upon the religious teachings of Pythagoras and was very secretive. The adherents were bound by a vow
Vow
A vow is a promise or oath.-Marriage vows:Marriage vows are binding promises each partner in a couple makes to the other during a wedding ceremony. Marriage customs have developed over history and keep changing as human society develops...

 to Pythagoras and each other, for the purpose of pursuing the religious and ascetic observances, and of studying his religious and philosophical theories. The claim that they put all their property into a common stock is perhaps only a later inference from certain Pythagorean maxims and practices.

As to the internal arrangements of the sect, we are informed that what was done and taught among the members was kept a profound secret towards all. Porphyry stated that this silence was "of no ordinary kind." Candidates had to pass through a period of probation, in which their powers of maintaining silence (echemythia) were especially tested, as well as their general temper, disposition, and mental capacity. There were also gradations among the members themselves. It was an old Pythagorean maxim, that every thing was not to be told to every body. Thus the Pythagoreans were divided into an inner circle called the mathematikoi ("learners") and an outer circle called the akousmatikoi ("listeners"). Iamblichus describes them in terms of esoterikoi and exoterikoi (or alternatively Pythagoreioi and Pythagoristai), according to the degree of intimacy which they enjoyed with Pythagoras. Porphyry wrote "the mathematikoi learned the more detailed and exactly elaborated version of this knowledge, the akousmatikoi (were) those who had heard only the summary headings of his (Pythagoras's) writings, without the more exact exposition."

There were ascetic practices (many of which had, perhaps, a symbolic meaning) in the way of life of the sect. Some represent Pythagoras as forbidding all animal food, advocating a plant-based diet, and prohibiting consumption of beans. This may have been due to the doctrine of metempsychosis
Metempsychosis
Metempsychosis is a philosophical term in the Greek language referring to transmigration of the soul, especially its reincarnation after death. It is a doctrine popular among a number of Eastern religions such as Hinduism, Buddhism, Jainism and Druzism wherein an individual incarnates from one...

. Other authorities contradict the statement. According to Aristoxenus
Aristoxenus
Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony, survives incomplete, as well as some fragments concerning rhythm and...

, he allowed the use of all kinds of animal food except the flesh of oxen used for plough
Plough
The plough or plow is a tool used in farming for initial cultivation of soil in preparation for sowing seed or planting. It has been a basic instrument for most of recorded history, and represents one of the major advances in agriculture...

ing, and rams. There is a similar discrepancy as to the prohibition of fish
Fish
Fish are a paraphyletic group of organisms that consist of all gill-bearing aquatic vertebrate animals that lack limbs with digits. Included in this definition are the living hagfish, lampreys, and cartilaginous and bony fish, as well as various extinct related groups...

 and beans. But temperance of all kinds seems to have been urged. It is also stated that they had common meals, resembling the Sparta
Sparta
Sparta or Lacedaemon, was a prominent city-state in ancient Greece, situated on the banks of the River Eurotas in Laconia, in south-eastern Peloponnese. It emerged as a political entity around the 10th century BC, when the invading Dorians subjugated the local, non-Dorian population. From c...

n system, at which they met in companies of ten.

Considerable importance seems to have been attached to music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

 and gymnastics
Gymnastics
Gymnastics is a sport involving performance of exercises requiring physical strength, flexibility, agility, coordination, and balance. Internationally, all of the gymnastic sports are governed by the Fédération Internationale de Gymnastique with each country having its own national governing body...

 in the daily exercises of the disciples. Their whole discipline is represented as encouraging a lofty serenity and self-possession, of which, there were various anecdotes in antiquity. Iamblichus (apparently on the authority of Aristoxenus
Aristoxenus
Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony, survives incomplete, as well as some fragments concerning rhythm and...

) gives a long description of the daily routine of the members, which suggests many similarities with Sparta. The members of the sect showed a devoted attachment to each other, to the exclusion of those who did not belong to their ranks. There were even stories of secret symbols, by which members of the sect could recognise each other, even if they had never met before.

Influence on Plato

Pythagoras, or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

. According to R. M. Hare
R. M. Hare
Richard Mervyn Hare was an English moral philosopher who held the post of White's Professor of Moral Philosophy at the University of Oxford from 1966 until 1983. He subsequently taught for a number of years at the University of Florida...

, this influence consists of three points: (1) The platonic Republic
Republic (Plato)
The Republic is a Socratic dialogue written by Plato around 380 BC concerning the definition of justice and the order and character of the just city-state and the just man...

 might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton. (2) There is evidence that Plato possibly took from Pythagoras the idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for substantial theses in science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

 and morals". (3) Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world". It is probable that both were influenced by Orphism.

Aristotle claimed that the philosophy of Plato closely followed the teachings of the Pythagoreans, and Cicero repeats this claim: Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean"). Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...

, in his A History of Western Philosophy, contended that the influence of Pythagoras on Plato and others was so great that he should be considered the most influential of all Western philosophers.

Influence on esoteric groups

Pythagoras started a secret society called the Pythagorean brotherhood devoted to the study of mathematics. This had a great effect on future esoteric traditions, such as Rosicrucianism and Freemasonry
Freemasonry
Freemasonry is a fraternal organisation that arose from obscure origins in the late 16th to early 17th century. Freemasonry now exists in various forms all over the world, with a membership estimated at around six million, including approximately 150,000 under the jurisdictions of the Grand Lodge...

, both of which were occult groups dedicated to the study of mathematics and both of which claimed to have evolved out of the Pythagorean brotherhood. The mystical and occult qualities of Pythagorean mathematics are discussed in a chapter of Manly P. Hall's The Secret Teachings of All Ages entitled "Pythagorean Mathematics".
Pythagorean theory was tremendously influential on later numerology
Numerology
Numerology is any study of the purported mystical relationship between a count or measurement and life. It has many systems and traditions and beliefs...

, which was extremely popular throughout the Middle East
Middle East
The Middle East is a region that encompasses Western Asia and Northern Africa. It is often used as a synonym for Near East, in opposition to Far East...

 in the ancient world. The 8th-century Muslim
Muslim
A Muslim, also spelled Moslem, is an adherent of Islam, a monotheistic, Abrahamic religion based on the Quran, which Muslims consider the verbatim word of God as revealed to prophet Muhammad. "Muslim" is the Arabic term for "submitter" .Muslims believe that God is one and incomparable...

 alchemist
Alchemy
Alchemy is an influential philosophical tradition whose early practitioners’ claims to profound powers were known from antiquity. The defining objectives of alchemy are varied; these include the creation of the fabled philosopher's stone possessing powers including the capability of turning base...

 Jabir ibn Hayyan grounded his work in an elaborate numerology greatly influenced by Pythagorean theory. Today, Pythagoras is revered as a prophet by the Ahl al-Tawhid or Druze
Druze
The Druze are an esoteric, monotheistic religious community, found primarily in Syria, Lebanon, Israel, and Jordan, which emerged during the 11th century from Ismailism. The Druze have an eclectic set of beliefs that incorporate several elements from Abrahamic religions, Gnosticism, Neoplatonism...

 faith along with his fellow Greek, Plato.

See also

  • Apollonius of Tyana
    Apollonius of Tyana
    Apollonius of Tyana was a Greek Neopythagorean philosopher from the town of Tyana in the Roman province of Cappadocia in Asia Minor. Little is certainly known about him...

  • Lute of Pythagoras
    Lute of Pythagoras
    The lute of Pythagoras is a geometric form made of pentagons with inscribed pentagrams where the sides of the pentagrams are the sides of the smaller pentagons. The form is a fractal, like the Koch snowflake where an infinite progression of forms fits into a finite space. The sides of the lute are...

  • Neopythagoreanism
    Neopythagoreanism
    Neopythagoreanism was a Graeco-Alexandrian school of philosophy, reviving Pythagorean doctrines, which became prominent in the 1st and 2nd centuries CE...

  • Pythagorean comma
    Pythagorean comma
    In musical tuning, the Pythagorean comma , named after the ancient mathematician and philosopher Pythagoras, is the small interval existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B , or D and C...

  • Pythagorean triple
    Pythagorean triple
    A Pythagorean triple consists of three positive integers a, b, and c, 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 k. A primitive Pythagorean triple is one in which a, b and c are pairwise coprime...


  • Pythagorean cup
    Pythagorean cup
    A Pythagorean cup is a form of drinking cup which forces its user to imbibe only in moderation. Credited to Pythagoras of Samos, it allows the user to fill the cup with wine up to a certain level. If the user fills the cup only up to that level he may enjoy his drink in peace...

  • Pythagoras tree (fractal)
  • Sacred geometry
    Sacred geometry
    Sacred geometry is the geometry used in the planning and construction of religious structures such as churches, temples, mosques, religious monuments, altars, tabernacles; as well as for sacred spaces such as temenoi, sacred groves, village greens and holy wells, and the creation of religious art...

  • The golden verses of Pythagoras
    The golden verses of Pythagoras
    The Golden Verses of Pythagoras are a collection of moral exhortations. They comprise 71 lines written in dactyl hexameter verse and are traditionally attributed to Pythagoras....

  • List of things named after Pythagoras


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