Pythagoras

Source

• Born: 570 B.C.
• Birthplace: Samos, Greece
• Died: c. 500 B.C.
• Best Known As: The guy they named the Pythagorean Theorem after

Pythagoras was the thinker who discovered the Pythagorean Theorem in geometry (although none of his actual writings are extant). The theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. Not much is known about Pythagoras, other than that he was a mathematician and philosopher who founded a community in southern Italy sometime in the 6th century B.C. His followers were extremely secretive and loyal, and held a mystical view of numbers and their relation to nature.

For more information on Pythagoras, visit Britannica.com.

Greek mathematician and philosopher (c. 580 bc–c. 500 bc)

All that is known of the life of Pythagoras with any certainty is that he left his birthplace, Samos, in about 520 bc to settle in Croton (now Crotone) in southern Italy and, as a result of political trouble, made a final move to Metapontum in about 500.

In Croton Pythagoras established his academy and became a cult leader. His community was governed by a large number of rules, some dietary, such as those commanding abstinence from meat and from beans, and others of obscure origin, such as the commands not to let a swallow nest under the roof or not to sit on a quart measure.

The movement was united by the belief that “all is number.” While the exact meaning of this may be none too clear, that it led to one of the great periods of mathematics is beyond doubt. Not only were the properties of numbers explored in a totally new way and important theorems discovered, of which the familiar theorem of Pythagoras is the best example, but there also emerged what is arguably the first really deep mathematical truth – the discovery of irrational numbers with the realization of the incommensurability of the square root of 2.

Greek philosopher and religious teacher. He emigrated from Samos to Croton in southern Italy c 531bc. Doctrines of his school include the harmony of the spheres and a belief in the importance of numbers as a guide to the interpretation of the world. The discovery of the numerical ratios corresponding to the principal intervals of the musical scale is attributed to him. He became an almost legendary figure, and from the 5th century onwards his followers constituted one of the principal schools of Greek musical theory.

The Greek philosopher, scientist, and religious teacher Pythagoras (ca. 575-ca. 495 B.C.) evolved a school of thought that accepted the transmigration of souls and established number as the principle in the universe.

Born on the island of Samos, Pythagoras was the son of Mnesarchus. He fled to southern Italy to escape the tyranny of Polycrates, who came to power about 538, and he is said to have traveled to Egypt and Babylon. He and his followers became politically powerful in Croton in southern Italy, where Pythagoras had established a school for his newly formed sect. It is probable that the Pythagoreans took positions in the local government in order to lead men to the pure life which their teachings set forth. Eventually, however, a rival faction launched an attack on the Pythagoreans at a gathering of the sect, and the group was almost completely annihilated. Pythagoras either had been banished from Croton or had left voluntarily shortly before this attack. He died in Metapontum early in the 5th century.

Religious Teachings

Pythagoras and his followers were important for their contributions to both religion and science. His religious teachings were based on the doctrine of metempsychosis, which held that the soul was immortal and was destined to a cycle of rebirths until it could liberate itself from the cycle through the purity of its life. A number of precepts were drawn up as inviolable rules by which initiates must live.

Pythagoreanism differed from the other philosophical systems of its time in being not merely an intellectual search for truth but a whole way of life which would lead to salvation. In this respect it had more in common with the mystery religions than with philosophy. Several taboos and mystical beliefs were taught which sprang from a variety of primitive sources such as folk taboo, ritual, and sympathetic magic and were examples of the traditional beliefs that the Greeks continued to hold while developing highly imaginative and rational scientific systems.

An important underlying tenet of Pythagoreanism was the kinship of all life. A universal life spirit was thought to be present in animal and vegetable life, although there is no evidence to show that Pythagoras believed that the soul could be born in the form of a plant. It could be born, however, in the body of an animal, and Pythagoras claimed to have heard the voice of a dead friend in the howl of a dog being beaten.

The number of lives which the soul had to live before being liberated from the cycle is uncertain. Its liberation came through an ascetic life of high moral and ethical standards and strict adherence to the teachings and practices of the sect. Pythagoras himself claimed to remember four different lives. Followers of the sect were enjoined to secrecy, although the discussions of Pythagoras's teachings in other writers proved that the injunction was not faithfully observed.

Mathematical Teachings

The Pythagoreans posited the dualism between Limited and Unlimited. It was probably Pythagoras himself who declared that number was the principle in the universe, limiting and giving shape to matter. His study of musical intervals, leading to the discovery that the chief intervals can be expressed in numerical ratios between the first four integers, also led to the theory that the number 10, the sum of the first four integers, embraced the whole nature of number.

So great was the Pythagoreans' veneration for the "Tetractys of the Decad" (the sum of 1 + 2 + 3 + 4) that they swore their oaths by it rather than by the gods, as was conventional. Pythagoras may have discovered the theorem which still bears his name (in right triangles, the square on the hypotenuse equals the sum of the squares on the other sides), although this proposition has been discovered on a tablet dating from the time of the Babylonian king Hammurabi. Regardless of their sources, the Pythagoreans did important work in systematizing and extending the body of mathematical knowledge.

As a more general scheme, the Pythagoreans posited the two contraries, Limited and Unlimited, as ultimate principles. Numerical oddness and evenness are equated with Limited and Unlimited, as are one and plurality, right and left, male and female, motionlessness and movement, straight and crooked, light and darkness, good and bad, and square and oblong. It is not clear whether an ultimate One, or Monad, was posited as the cause of the two categories.

Cosmological Views

As a result of their religious beliefs and their careful study of mathematics, the Pythagoreans developed a cosmology which differed in some important respects from the world views of their contemporaries, the most important of which was their view of the earth as a sphere which circled the center of the universe. The center of this system was fire, which was invisible to man because his side of the earth was turned from it. The sun reflected that fire; there was a counterearth closer to the center, and the other five planets were farther away and followed longer courses around the center. It is not known how much of this theory was attributable to Pythagoras himself. Later writers ascribe much of it to Philolaos (active 400 B.C.), although it circulated as a view of the school as a whole.

The systematization of mathematical knowledge carried out by Pythagoras and his followers would have sufficed to make him an important figure in the history of Western thought. However, his religious sect and the asceticism which he taught, embracing as it did a vast number of ancient beliefs, make him one of the great teachers of religion in the ancient Greek world.

Further Reading

Pythagoras left no written works. A first-rate technical book, J. A. Philip, Pythagoras and Early Pythagoreanism (1966), separates the valid from the spurious among the legends that surround Pythagoras and his views. An excellent and thorough treatment of the evidence for his life and teachings is in W. K. C. Guthrie, A History of Greek Philosophy (3 vols., 1962-1969). A good account of Pythagoras and his followers is in Kathleen Freeman, The Pre-Socratic Philosophers (1946; 3d ed. 1953), and G. S. Kirk and J. E. Raven, The Presocratic Philosophers (1962). Briefer treatments of the Pythagoreans and the intellectual currents of their time are in the standard histories of Greek literature, such as Albin Lesky, A History of Greek Literature (trans. 1966), or in accounts of Greek philosophy, such as John Burnet, Greek Philosophy (1914).

Pȳthagoras, Greek polymath, philosopher, and mystic of the sixth century BC. He wrote no books, but so impressive were his doctrines, his learning, and his way of life that by the end of the fifth century he had become a figure of mystery and legend with a reputation as a great sage and a possessor of miraculous powers (as well as of a golden thigh). The traditions concerning his life are contradictory and confused, but it is believed that he was born at Samos c.580 BC and emigrated (perhaps through hostility to the tyranny of Polycratēs) to Croton in Magna Graecia. There he attracted followers, both men and women, who formed a community and lived according to his rule of life. Even after his death, c.500 BC, Pythagorean societies continued to flourish in Croton and elsewhere in Magna Graecia. The members seem to have been active in the politics of the time and, presenting a united front, were no doubt a powerful force; they became unpopular and eventually (c.450 BC) the societies were broken up and the members killed or exiled.

Part of Pythagoras' teaching was religious and mystical, and it was presumably this aspect which led his contemporary Heracleitus to regard him as a fraud. Another contemporary, Xenophanēs, mocked the most celebrated aspect of his teaching, his doctrine of reincarnation or the transmigration of souls (metempsychōsis), with the story that Pythagoras once claimed to recognize a friend's voice in the howling of a puppy which was being beaten. Pythagoras also declared that he remembered his own previous incarnations, including that as the Trojan Euphorbus, killed in the siege. Pythagoras taught that the soul (a combination of life-principle, self, and mind) is immortal, a fallen divinity imprisoned in the body as in a tomb. Since the soul is rational and responsible for its actions, the choices it makes determine the kind of body into which it is reincarnated, human or animal (perhaps even plant; Empedoclēs, who was greatly influenced by Pythagorean ideas, declares that in one of his incarnations he was a bush). By keeping itself pure from the pollutions of the body the soul may eventually win release from it (see also ORPHEUS and compare Orphic beliefs, with which Pythagoras obviously had much in common). Pythagoras and his followers adhered to a rule of life by which release for the soul might be attained; this was an austere regimen the details of which are not clear but which perhaps entailed silence, self-examination, and abstention from eating flesh and beans (no reason is known for this latter prohibition). The idea of metempsychosis is foreign to Greek tradition and its source uncertain; it may have reached Greece from central Asia or even India. Many precepts of Pythagoras were collected at some time under the name of acusmata (Gk. akousmata, ‘ (oral) instructions’). Some sound like taboo-prohibitions, e.g. ‘Do not poke the fire with a sword’ (which Porphyry interpreted as meaning, ‘Do not vex with sharp words a man swollen with anger’). Others sound like traditional wisdom: ‘What is the wisest of the things in our power? Medicine. What is the fairest thing? Harmony. What is the most powerful? Knowledge. What is the best? Happiness.’

Pythagoras' name is also linked to the study of numbers and proportions as well as astronomy. It is impossible to ascertain what discoveries should be attributed to him personally, but he is credited with the discovery that the relation between the chief musical intervals produced on a vibrating string can be expressed as ratios between the first four whole numbers: octave, 2 : 1; fifth, 3 : 2; fourth, 4 : 3. From this evolved the idea that the explanation of the universe is to be sought in numbers and their relations, of which the objects of sense are representations. According to Aristotle, even abstracts like ‘opinion’ or ‘opportunity’ or ‘injustice’ were numbers in the Pythagorean system, and had their place in the cosmos. Since the first four whole numbers are important in expressing musical harmonies and since their sum can be represented as an equilateral triangular array of ten dots in rows of one, two, three, and four, it was thought that this pattern, the tetraktys, ‘foursome’, of the decad, was of mystical significance, embracing the whole nature of number: the number one could be identified with the point, two with the line, three with the surface, and four with the solid. Pythagoras is also credited with the theorem that still goes under his name, namely that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides; on discovering it he is said to have made the important sacrifice of a hecatomb. The Pythagoreans believed that the earth is a sphere; later Pythagoreans had an astronomical system in which the heavenly bodies (the sphere of the fixed stars, the five planets, the sun, moon, earth, and counter-earth, the last included to bring the number of bodies up to ten) revolve around a central fire, a system to which an earlier belief in a ‘harmony of the spheres’ was accommodated.

Pythagoreanism influenced not only Empedocles but also Plato, whose science and metaphysics are infused with Pythagorean ideas. Later the doctrines were revived at Rome under the early empire, and became confused with Orphic beliefs with which they had affinities.

(b. c. 570 BC) Pythagoras was the son of Mnesarchus of Samos, and emigrated c. 531 BC to Croton in southern Italy. Here he founded a religious society, but was forced into exile and died at Metapontum. Membership of the society entailed self-discipline, silence, and the observance of various taboos, especially against eating flesh and beans. Pythagoras taught the doctrine of metempsychosis, or the cycle of reincarnation, and was supposed able to remember former existences. The soul, which has its own divinity and may have existed as an animal or plant, can, however, gain release by a religious dedication to study, after which it may rejoin the universal world-soul. Pythagoras is usually, but doubtfully, credited with having discovered the basis of acoustics, the numerical ratios underlying the musical scale, thereby initiating the arithmetical interpretation of nature. This tremendous success inspired the view that the whole of the cosmos should be explicable in terms of harmonia or number. The view represents a magnificent break from the Milesian attempt to ground physics on a conception of a prime matter, or undifferentiated basis shared by all things, and to concentrate instead on form, meaning that physical natures receive an intelligible grounding in different geometric structures. The view is vulgarized in the doctrine usually attributed to Pythagoras that all things are numbers. However, the association of abstract qualities with numbers reached remarkable heights, with occult attachments, for instance between justice and the number four, and mystical significances, especially of the number ten. Cosmologically Pythagoras explained the origin of the universe in mathematical terms, as the imposition of limit on the limitless by a kind of injection of a unit. Followers of Pythagoras included Philolaus, the earliest cosmologist known to have understood that the earth is a moving planet. It is also likely that the Pythagoreans discovered the irrationality of the square root of two: see Hippasus of Metapontum. See also harmony of the spheres.

Pythagoras (c. 580–c. 580 B.C.E.) was a Greek mathematician, philosopher, and mystic. He wrote nothing himself, so his ideas survive through the writings of others, including Aristotle. Many people are familiar with him as the mathematician who formulated the Pythagorean theorem in geometry that relates the lengths of the sides in a right triangle. Others know him as a mystic and the first person known to be motivated by moral and philosophical concerns to adopt a vegetarian diet.

The schools and societies Pythagoras founded in the southern Italian area of Magna Graecia flourished for a while, and they developed and spread many of his concepts, which were later adopted and expanded by others. These concepts include bodily humors (evident in modern descriptions of melancholic and phlegmatic personalities), a tripartite soul, reincarnation, and the numerical ratios that determine the concordant intervals of the musical scales. Permeating all of his thoughts was the idea that all things are numbers. Numbers (individuals, groups, and series) were imbued with mystical properties that were carefully guarded and only shared among initiates to the Pythagorean schools founded by him or his disciples.

Pythagoras and his followers practiced one of the first recorded diets known as vegetarianism. He advocated a diet devoid of the flesh of slaughtered animals partially because he felt food influenced the distribution of the bodily humors and thereby the health of the individual and partially because it would prevent the killing of a reincarnated individual and its transmigrated soul. Up until the late nineteenth century non–meat eaters were generally known as "Pythagoreans."

Pythagoras is also alleged to have admonished his disciples to abstain from eating beans. Ancient and medieval writers ingeniously ascribed this pronouncement to the belief that beans contained or transmitted souls. The Greek phrase supporting this gastronomic recommendation, however, could also be construed to imply that his followers should avoid politics. Black and white beans were used as counters in voting in Magna Graecia. The school Pythagoras founded there became actively involved in the populist political views that gained ascendancy in the town of Kroton, where he lived for many years. Later an opposing aristocratic party gained control of the city and banished him and his followers for their political views and activism. Pythagoras died in exile. His supposed warning to "abstain from beans" is therefore thought to have meant "avoid politics." Alternatively he may have realized that eating undercooked broad (fave) beans (Vica faba vulgaris), a common food of the Mediterranean region, produced a severe hemolytic anemia (favism) in some people. Interestingly the same mutant gene that makes people sensitive to favism also increases their resistance to the malarial parasite, possibly accounting for the widespread presence of the mutant gene in regions with endemic malaria.

Bibliography

Bamford, Christopher, ed. Homage to Pythagoras. Hudson, N.Y.: Lindisfarne Press, 1994.

Gorman, Peter. Pythagoras. London: Routledge and Kegan Paul, 1979.

Spencer, Colin. The Heretic's Feast: A History of Vegetarianism. London: Fourth Estate, 1993.

Walters, Kerry S., and Lisa Portmess, eds. Ethical Vegetarianism: From Pythagoras to Peter Singer. Albany: State University of New York Press, 1999.

—Mikal E. Saltveit

Pythagoras was among the early Greek philosophers. He is said to have visited Thales and studied with Anaximander. He traveled to Egypt and Mesopotamia, learning the basics of philosophy, science, and mathematics. After returning to Samos and teaching there, he moved to Croton (Crotone, Italy). There he formed a secret society of men and women who shared their knowledge of science and mathematics. Today they are known as Pythagoreans. Credit for many discoveries attributed to Pythagoras probably belongs to other members of his secret society.

The society was both a mystical religion and one of the most productive schools of mathematics in history. A fundamental mystical belief of the Pythagorean society was that "all is number," which is to say that the entire universe can be explained in terms of numbers. The Pythagoreans had other mystical beliefs as well, such as an aversion to beans and a belief in the transmigration of souls (that is, that people's souls after death occupy the bodies of animals and vice versa).

But the principal ideas of the Pythagoreans that have been handed down concern numbers. The Pythagoreans assigned gender to numbers, saying that odd numbers are male and even numbers female. They also worked with figurate numbers, numbers that can be identified by a shape when dots are used. Square numbers of dots can be formed into squares, triangular numbers form dot triangles, and so forth.

Although the name Pythagoras is most closely associated with the Pythagorean theorem (the sum of the squares on the legs of a right triangle equals the square on the hypotenuse), this theorem was known to the Chinese and probably to the Babylonians before the time of Pythagoras.

When Pythagoreans talked about numbers, they meant the natural numbers, 1, 2, 3, and so forth. Fractions are simply ratios of natural numbers, so fractions posed no problem. But the Pythagoreans proved that objects in the real world cannot always be measured completely with natural numbers. For example, if the unit chosen to be one is the side of a square, the diagonal of the square cannot be measured exactly using that unit.

Quotes:

"Friends are as companions on a journey, who ought to aid each other to persevere in the road to a happier life."

"Rest satisfied with doing well, and leave others to talk of you as they will."

"In this theater of man's life, it is reserved only for God and angels to be lookers-on."

"Above the cloud with its shadow is the star with its light. Above all things reverence thyself."

"It is better wither to be silent, or to say things of more value than silence. Sooner throw a pearl at hazard than an idle or useless word; and do not say a little in many words, but a great deal in a few."

"Strength of mind rests in sobriety; for this keeps your reason unclouded by passion."

See more famous quotes by Pythagoras

"Pythagoras of Samos" redirects here. For the Samian statuary, see Pythagoras (sculptor).

For other uses, see Pythagoras (disambiguation).

Pythagoras

Pythagoras Pre-Socratic philosophy
Bust of Pythagoras of Samos in the Capitoline Museums, Rome
Full name	Pythagoras (Πυθαγόρας)
Born	c. 570 BC Samos Island
Died	c. 495 BC Metapontum
School/tradition	Pythagoreanism
Main interests	Metaphysics, Music, Mathematics, Ethics, Politics
Notable ideas	Musica universalis, Golden ratio, Pythagorean tuning, Pythagorean theorem
Influenced by Thales, Anaximander, Pherecydes
Influenced Philolaus, Alcmaeon, Parmenides, Plato, Euclid, Empedocles, Hippasus, Kepler

Pythagoras of Samos (Greek: Ὁ Πυθαγόρας ὁ Σάμιος, O Pūthagoras o Samios, "Pythagoras the Samian", or simply Ὁ Πυθαγόρας; c. 570-c. 495 BC^[1]) was an Ionian Greek philosopher and founder of the religious movement called Pythagoreanism. Most of our information about Pythagoras was written down centuries after he lived, thus very little reliable information is known about him. He was born on the island of Samos, and may have travelled widely in his youth, visiting Egypt and other places seeking knowledge. Around 530 BC, he moved to Croton, a Greek colony in southern Italy, 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 by some to have ended his days in Metapontum.

Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. He is often revered as a great mathematician, mystic and scientist, and he is best known for the Pythagorean theorem which bears his name. However, because legend and obfuscation cloud his work even more than with the other pre-Socratic philosophers, one can say little with confidence about his teachings, and some have questioned whether he contributed much to mathematics and natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. We do know that his disciples believed that everything was related to mathematics and that numbers were the ultimate reality. It was said that he was the first man to call himself a philosopher, or lover of wisdom,^[2] and Pythagorean ideas exercised a marked influence on Plato, and through him, all of western philosophy.

Contents 1 Biographical sources 2 Life 3 Writings 4 Mathematics 4.1 Pythagorean theorem 4.2 Musical theories and investigations 4.3 Tetractys 5 Religion and science 5.1 Lore 6 Pythagoreans 7 Influence 7.1 Influence on Plato 7.2 Influence on esoteric groups 8 See also 9 References 10 Sources 10.1 Classical secondary sources 10.2 Modern secondary sources 11 External links

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.^[3] Thus many myths were created – such as that Apollo was his father; that Pythagoras gleamed with a supernatural brightness; that he had a golden thigh; that Abaris came flying to him on a golden arrow; that he was seen in different places at one and the same time.^[4] With the exception of a few remarks by Xenophanes, Heraclitus, Herodotus, Plato, Aristotle, and Isocrates, we are mainly dependent on Diogenes Laërtius, Porphyry, and Iamblichus for the biographical details. Aristotle had written a separate work on the Pythagoreans, which unfortunately has not survived.^[5] His disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus had written on the same subject. These writers, late as they are, are 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.^[6]

Life

Bust of Pythagoras, Vatican

Herodotus, Isocrates, and other early writers all agree that Pythagoras was born on Samos, the Greek island in the eastern Aegean, and we also learn that Pythagoras was the son of Mnesarchus.^[7] His father was a gem-engraver or a merchant. His name led him to be associated with Pythian Apollo; Aristippus 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.^[8] A late source gives his mother's name as Pythias.^[9] As to the date of his birth, Aristoxenus stated that Pythagoras left Samos in the reign of Polycrates, at the age of 40, which would give a date of birth around 570 BC.^[10]

It was natural for the ancient biographers to inquire as to 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 and Oriental. We find mentioned as his instructors Creophylus,^[11] Hermodamas,^[12] Bias,^[11] Thales,^[11] Anaximander,^[13] and Pherecydes of Syros.^[14] The Egyptians are said to have taught him geometry, the Phoenicians arithmetic, the Chaldeans astronomy, the Magians the principles of religion and practical maxims for the conduct of life.^[15] Of the various claims regarding his Greek teachers, Pherecydes is mentioned most often.

It was the standard belief in antiquity that Pythagoras had undertaken extensive travels, and had visited not only Egypt, but Arabia, Phoenicia, Judaea, Babylon, and even India, for the purpose of collecting all available knowledge, and especially to learn information concerning the secret or mystic cults of the gods.^[16] The journey to Babylon is possible, and not very unlikely. That Pythagoras visited Egypt, may be more probable, and many ancient writers asserted this.^[17] 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.^[18]

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 or Cretan mysteries,^[19] or the Delphic oracle.^[20]

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 and Aristotle is attributed not to Pythagoras, but to the Pythagoreans. Heraclitus stated that he was a man of extensive learning;^[21] and Xenophanes claimed that he believed in the transmigration of souls.^[22] Xenophanes mentions the story of his interceding on behalf of a dog 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, the son of Panthus, in the Trojan war, as well as various other characters, a tradesman, a courtesan, etc.^[23]

Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem,^[24] as well as discoveries in the field of music,^[25] astronomy,^[26] and medicine.^[27] 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,^[28] and he was said to have practised divination and prophecy.^[29] In the visits to various places in Greece - Delos, Sparta, Phlius, Crete, etc. which are ascribed to him, he usually appears either in his religious or priestly guise, or else as a law­giver.^[30]

Croton on the southern coast of Italy

After his travels, Pythagoras moved (around 530 BC) to Croton, in Italy (Magna Graecia). Possibly the tyranny of Polycrates in Samos made it difficult for him to achieve his schemes there. His later admirers claimed that Pythaogras 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.^[31] 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.^[32]

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.^[33] Temperance of all kinds seems to have been strictly urged. There is disagreement among the biographers as to whether Pythagoras forbade all animal food,^[34] or only certain types.^[35] The club was in practice at once "a philosophical school, a religious brotherhood, and a political association."^[36]

Pythagoras, depicted on a 3rd-century coin

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 seem to have broken out between the towns of Sybaris and Croton. The forces of Croton were headed by the Pythagorean Milo, and it is likely that the members of the brotherhood took a prominent part. After the 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.^[37] 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, 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,^[38] others that he fled first to Tarentum, and that, being driven from there, he escaped to Metapontum, and there starved himself to death.^[39] His tomb was shown at Metapontum in the time of Cicero.^[40]

According to some accounts Pythagoras married Theano, a lady of Croton. Their children are variously stated to have included a son, Telauges, and three daughters, Damo, Arignote, and Myia.

Writings

No texts by Pythagoras survive, although forgeries under his name — a few of which remain extant — did circulate in antiquity. Critical ancient sources like Aristotle and Aristoxenus 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

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

—Aristotle, Metaphysics 1-5 , cc. 350 BC

Pythagorean theorem

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

Since the fourth century AD, 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 (the side opposite the right angle), c, is equal to the sum of the squares of the other two sides, b and a—that is, a² + b² = c².

While the theorem that now bears his name was known and previously utilized by the Babylonians and Indians, 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 sources.^[41] 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 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.^[42] The earliest known mention of Pythagoras's name in connection with the theorem occurred five centuries after his death, in the writings of Cicero and Plutarch.

Musical theories and investigations

Medieval woodcut showing Pythagoras with bells in Pythagorean tuning

See also: Pythagorean tuning

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

The 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." Thus the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony.^[43]

Tetractys

Pythagoras was also credited with devising the tetractys, 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:

And the inventions were so admirable, and so divinised by those who understood them, that the members used them as forms of oath: "By him who handed to our generation the tetractys, source of the roots of ever-flowing nature."

—Iamblichus, Vit. Pyth., 29

Religion and science

Pythagoras’ religious and scientific views were, in his opinion, inseparably interconnected. Religiously, Pythagoras was a believer of metempsychosis. He believed in transmigration, or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables until it became moral. His ideas of reincarnation were influenced by ancient Greek religion. He himself claimed to have lived four lives that he could remember in detail, and 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 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.^[44] An extract from Brewer's Dictionary of Phrase and Fable'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.^[45]

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.^[46]

Pythagoreans

See also: Pythagoreanism

Pythagoras, the man in the center with the book, teaching music, in The School of Athens by Raphael

Both Plato and Isocrates affirm that, above all else, Pythagoras was famous for leaving behind him a way of life.^[47] Both Iamblichus and Porphyry 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.^[48]

Pythagoras set up an organization which was in some ways a school, in some ways a brotherhood, 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 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.^[49] On the other hand, it seems certain that there were many women among the adherents of Pythagoras.^[50]

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.^[51] 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.^[52] Thus the Pythagoreans were divided into an inner circle called the mathematikoi ("learners") and an outer circle called the akousmatikoi ("listeners").^[53] Iamblichus describes them in terms of esoterikoi and exoterikoi (or alternatively Pythagoreioi and Pythagoristai),^[54] 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.^[55] Some represent Pythagoras as forbidding all animal food. This may have been due to the doctrine of metempsychosis.^[56] Other authorities contradict the statement. According to Aristoxenus,^[57] he allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and rams.^[58] There is a similar discrepancy as to the prohibition of fish and beans.^[59] But temperance of all kinds seems to have been urged. It is also stated that they had common meals, resembling the Spartan system, at which they met in companies of ten.^[60]

Considerable importance seems to have been attached to music and gymnastics 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.^[61] Iamblichus (apparently on the authority of Aristoxenus)^[62] 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.^[63] There were even stories of secret symbols, by which members of the sect could recognise each other, even if they had never met before.^[64]

Influence

Pythagoras, depicted as a medieval scholar in the Nuremberg Chronicle

Influence on Plato

Pythagoras or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of Plato. According to R. M. Hare, his influence consists of three points: a) the platonic Republic might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton. b) 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 and morals". c) Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world". It is probable that both have been influenced by Orphism.^[65]

Bertrand Russell, in his 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. But Pythagoras also had his critics, such as Heraclitus who said that "much learning does not teach wisdom; otherwise it would have taught Hesiod and Pythagoras, and again Xenophanes and Hecataeus".^[66]

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, 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, which was extremely popular throughout the Middle East in the ancient world. The 8th-century Muslim alchemist Jabir ibn Hayyan grounded his work in an elaborate numerology greatly influenced by Pythagorean theory.^{[citation needed]} Today, Pythagoras is revered as a prophet by the Ahl al-Tawhid or Druze faith along with his fellow Greek, Plato.

See also

Apollonius of Tyana Harmony of the spheres Lute of Pythagoras Neopythagoreanism Pythagoreanism Pythagorean comma

Pythagorean cup Pythagorean theorem Pythagoras tree Sacred geometry The golden verses of Pythagoras

References

1. ^ "The dates of his life cannot be fixed exactly, but assuming the approximate correctness of the statement of Aristoxenus (ap. Porph. V.P. 9) that he left Samos to escape the tyranny of Polycrates at the age of forty, we may put his birth round about 570 BC, or a few years earlier. The length of his life was variously estimated in antiquity, but it is agreed that he lived to a fairly ripe old age, and most probably he died at about seventy-five or eighty." William Keith Chambers Guthrie, (1978), A history of Greek philosophy, Volume 1: The earlier Presocratics and the Pythagoreans, page 173. Cambridge University Press
2. ^ Cicero, Tusculan Disputations, 5.3.8-9 = Heraclides Ponticus fr. 88 Wehrli, Diogenes Laërtius 1.12, 8.8, Iamblichus VP 58. Burkert attempted to discredit this ancient tradition, but it has been defended by C.J. De Vogel, Pythagoras and Early Pythagoreanism (1966), pp. 97-102, and C. Riedweg, Pythagoras: His Life, Teaching, And Influence (2005), p. 92.
3. ^ Iamblichus, Adhort. ad Philos. p. 324, ed. Kiessling.
4. ^ Comp. Herodian, iv. 94, etc.
5. ^ He alludes to it himself, Met. i. 5. p. 986. 12, ed. Bekker.
6. ^ This article incorporates text from the public domain Dictionary of Greek and Roman Biography and Mythology by William Smith (1870).
7. ^ Herodotus, iv. 95, Isocrates, Busiris, 28-9; Later writers called him a Tyrrhenian or Phliasian, and gave Marmacus, or Demaratus, as the name of his father, Diogenes Laërtius, viii. 1; Porphyry, Vit. Pyth. 1, 2; Justin, xx. 4; Pausanias, ii. 13.
8. ^ Riedweg, Christoph (2005). Pythagoras: His Life, Teaching and Influence. Cornell University. pp. 5–6, 59, 73. 
9. ^ Apollonius of Tyana ap. Porphyry, Vit. Pyth. 2
10. ^ Porphyry, Vit. Pyth. 9
11. ^ ^{a b c} Iamblichus, Vit. Pyth. 9
12. ^ Porphyry, Vit. Pyth. 2, Diogenes Laërtius, viii. 2
13. ^ Iamblichus, Vit. Pyth. 9; Porphyry, Vit. Pyth. 2
14. ^ Aristoxenus and others in Diogenes Laërtius, i. 118, 119; Cicero, de Div. i. 49
15. ^ Porphyry, Vit. Pyth. 6
16. ^ Diogenes Laërtius, viii. 2; Porphyry, Vit. Pyth. 11, 12; Iamblichus, Vit. Pyth. 14, etc.
17. ^ Antiphon. ap. Porphyry, Vit. Pyth. 7; Isocrates, Busiris, 28-9; Cicero, de Finibus, v. 27; Strabo, xiv.
18. ^ Herodotus, ii. 134, 135, iii. 39.
19. ^ Iamblichus, Vit. Pyth. 25; Porphyry, Vit. Pyth. 17; Diogenes Laërtius, viii. 3
20. ^ Ariston. ap. Diogenes Laërtius, viii. 8, 21; Porphyry, Vit. Pyth. 41
21. ^ Diogenes Laërtius, viii. 6, ix. 1, comp. Herodotus, i. 29, ii. 49, iv. 95
22. ^ Diogenes Laërtius, viii. 36, comp. Aristotle, de Anima, i. 3; Herodotus, ii. 123.
23. ^ Porphyry, Vit. Pyth. 26; Pausanias, ii. 17; Diogenes Laërtius, viii. 5; Horace, Od. i. 28,1. 10
24. ^ Diogenes Laërtius, viii. 12 ; Plutarch, Non posse suav. vivi sec. Ep. p. 1094
25. ^ Porphyry, in Ptol. Harm. p. 213; Diogenes Laërtius, viii. 12
26. ^ Diogenes Laërtius, viii. 14 ; Pliny, Hist. Nat. ii. 8
27. ^ Diogenes Laërtius, viii. 12, 14, 32
28. ^ Porphyry, Vit. Pyth. 20; Iamblichus, Vit. Pyth. 31, 140; Aelian, Varia Historia, ii. 26; Diogenes Laërtius, viii. 36.
29. ^ Cicero, de Divin. i. 3, 46; Porphyry, Vit. Pyth. 29.
30. ^ Iamblichus, Vit. Pyth. 25; Porphyry, Vit. Pyth. 17; Diogenes Laërtius, viii. 3, 13; Cicero, Tusc. Qu. v. 3
31. ^ Iamblichus, Vit. Pyth. 28; Porphyry, Vit. Pyth. 9
32. ^ Porphyry, Vit. Pyth. 18; Iamblichus, Vit. Pyth. 37, etc.
33. ^ Aelian, Varia Historia, ii. 26; Diogenes Laërtius, viii. 13; Iamblichus, Vit. Pyth. 8, 91, 141
34. ^ as Empedocles did afterwards, Aristotle, Rhet. i. 14. § 2; Sextus Empiricus, ix. 127. This was also one of the Orphic precepts, Aristoph. Ran. 1032
35. ^ Aristo ap. Diogenes Laërtius, viii. 20; comp. Porphyry, Vit. Pyth. 7; Iamblichus, Vit. Pyth. 85, 108
36. ^ Thirlwall, Hist. of Greece, vol. ii. p. 148
37. ^ Iamblichus, Vit. Pyth. 255-259; Porphyry, Vit. Pyth. 54-57; Diogenes Laërtius, viii. 39; comp. Plutarch, de Gen. Socr. p. 583
38. ^ Arnob. adv. Gentes, i. p. 23
39. ^ Diogenes Laërtius, viii. 39, 40; Porphyry, Vit. Pyth. 56; Iamblichus, Vit. Pyth. 249; Plutarch, de Stoic. Rep. 37
40. ^ Cicero, de Fin. v. 2
41. ^ There are about 100,000 unpublished cuneiform sources in the British Museum alone. Babylonian knowledge of proof of the Pythagorean Theorem is discussed by J. Høyrup, 'The Pythagorean "Rule" and "Theorem" - Mirror of the Relation between Babylonian and Greek Mathematics,' in: J. Renger (red.): Babylon. Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne (1999).
42. ^ From Christoph Riedweg , Pythagoras, His Life, Teaching and Influence, Cornell: Cornell University Press, 2005: "Had Pythagoras and his teachings not been since the early Academy overwritten with Plato’s philosophy, and had this ‘palimpsest’ not in the course of the Roman Empire achieved unchallenged authority among Platonists, it would be scarcely conceivable that scholars from the Middle Ages and modernity down to the present would have found the Presocratic charismatic from Samos so fascinating. In fact, as a rule it was the image of Pythagoras elaborated by Neopythagoreans and Neoplatonists that determined the idea of what was Pythagorean over the centuries."
43. ^ Christoph Riedweg, Pythagoras: His Life, Teaching and Influence, Cornell: Cornell University Press, 2005 .
44. ^ Huffman, Carl. Pythagoras (Stanford Encyclopedia of Philosophy)
45. ^ Brewer, E. Cobham, Brewer's Dictionary of Phrase and Fable
46. ^ Brewer, E. Cobham, Brewer's Dictionary of Phrase and Fable
47. ^ Plato, Republic, 600a, Isocrates, Busiris, 28
48. ^ John Dillon and Jackson Hershbell, (1991), Iamblichus, On the Pythagorean Way of Life, page 14. Scholars Press.; D. J. O'Meara, (1989), Pythagoras Revived. Mathematics and Philosophy in Late Antiquity, pages 35-40. Clarendon Press.
49. ^ comp. Cicero, de Leg. i. 12, de Off. i. 7; Diogenes Laërtius, viii. 10
50. ^ Porphyry, Vit. Pyth. 19
51. ^ Aristonexus ap. Iamblichus, Vit. Pyth. 94
52. ^ Diogenes Laërtius, viii. 15; Aristonexus ap. Iamblichus, Vit. Pyth. 31
53. ^ Iamblichus, Vit. Pyth. 80, cf. Aulus Gellius, i. 9
54. ^ Iamblichus, Vit. Pyth. 80
55. ^ comp. Porphyry, Vit. Pyth. 32; Iamblichus, Vit. Pyth. 96, etc.
56. ^ Plutarch, de Esu Carn. pp. 993, 996, 997
57. ^ Aristoxenus ap. Diogenes Laërtius, viii. 20
58. ^ comp. Porphyry, Vit. Pyth. 7; Iamblichus, Vit. Pyth. 85, 108
59. ^ Diogenes Laërtius, viii. 19, 34; Aulus Gellius, iv. 11; Porphyry, Vit. Pyth. 34, de Abst. i. 26; Iamblichus, Vit. Pyth. 98
60. ^ Iamblichus, Vit. Pyth. 98; Strabo, vi.
61. ^ Athenaeus, xiv. 623; Aelian, Varia Historia, xiv. 18; Iamblichus, Vit. Pyth. 197
62. ^ Iamblichus, Vit. Pyth. 96-101
63. ^ Aristonexus ap. Iamblichus, Vit. Pyth. 94, 101, etc., 229, etc.; comp. the story of Damon and Phintias; Porphyry, Vit. Pyth. 60; Iamblichus, Vit. Pyth. 233, etc.
64. ^ Scholion ad Aristophanes, Nub. 611; Iamblichus, Vit. Pyth. 237, 238
65. ^ R.M. Hare, Plato in C.C.W. Taylor, R.M. Hare and Jonathan Barnes, Greek Philosophers, Socrates, Plato, and Aristotle, Oxford: Oxford University Press, 1999 (1982), 103-189, here 117-9.
66. ^ Diog. L. ix. 1 (Fr. 40 in Vorsokratiker, i³, p. 86. 1-3)

Sources

Classical secondary sources

Only a few relevant source texts deal with Pythagoras and the Pythagoreans, most are available in different translations. Other texts usually build solely on information in these works.

• Diogenes Laërtius, Vitae philosophorum VIII (Lives of Eminent Philosophers), c. 200 AD, which in turn reference the lost work Successions of Philosophers by Alexander Polyhistor) — Pythagoras, Translation by C.D. Yonge
• Porphyry, Vita Pythagorae (Life of Pythagoras), c. 270 AD
• Iamblichus, De Vita Pythagorica (On the Pythagorean Life), c. 300 AD
• Apuleius also writes about Pythagoras in Apologia, including a story of him being taught by Babylonian disciples of Zoroaster, c. 150 AD
• Hierocles of Alexandria, Golden Verses of Pythagoras, Concord Grove Pr., 1983 c.430 AD

Modern secondary sources

• Burkert, Walter. Lore and Science in Ancient Pythagoreanism. Harvard University Press, June 1, 1972. ISBN 0-674-53918-4
• Burnyeat, M. F. "The Truth about Pythagoras". London Review of Books, 22 February 2007.
• Guthrie, W. K. A History of Greek Philosophy: Earlier Presocratics and the Pythagoreans, Cambridge University Press, 1979. ISBN 0-521-29420-7
• Kingsley, Peter. Ancient Philosophy, Mystery, and Magic: Empedocles and the Pythagorean Tradition. Oxford University Press, 1995.
• Hermann, Arnold. To Think Like God: Pythagoras and Parmenides—the Origins of Philosophy. Parmenides Publishing, 2005. ISBN 978-1-930972-00-1
• O'Meara, Dominic J. Pythagoras Revived. Oxford University Press, 1989. ISBN 0-19-823913-0 (paperback), ISBN 0-19-824485-1 (hardcover)

External links

Wikiquote has a collection of quotations related to: Pythagoras

Wikimedia Commons has media related to: Pythagoras

• "Pythagoras" article by Carl Huffman in the Stanford Encyclopedia of Philosophy
• Pythagoras of Samos, The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland
• Pythagoras and the Pythagoreans, Fragments and Commentary, Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History
• Pythagoras and the Pythagoreans, Department of Mathematics, Texas A&M University
• Pythagoras and Pythagoreanism, The Catholic Encyclopedia
• Tetraktys
• Golden Verses of Pythagoras
• Pythagoras on Vegetarianism Quotes from primary source historical literature on Pythagoras' view on Vegetarianism, Justice and Kindness
• Homage to Pythagoras
• Occult conception of Pythagoreanism
• Pythagoreanism Web Article
• Wandering Souls: The Doctrine of Transmigration in Pythagorean Philosophy, by Dr. James Luchte

v • d • e Greek mathematics Mathematicians Anaxagoras · Anthemius · Archytas · Aristaeus the Elder · Aristarchus · Apollonius · Archimedes · Autolycus · Bion · Boethius · Bryson · Callippus · Carpus · Chrysippus · Cleomedes · Conon · Ctesibius · Democritus · Dicaearchus · Diocles · Diophantus · Dinostratus · Dionysodorus · Domninus · Eratosthenes · Eudemus · Euclid · Eudoxus · Eutocius · Geminus · Heron · Hipparchus · Hippasus · Hippias · Hippocrates · Hypatia · Hypsicles · Isidore of Miletus · Leo the Mathematician · Marinus · Menaechmus · Menelaus · Nicomachus · Nicomedes · Nicoteles · Oenopides · Pappus · Perseus · Philolaus · Philon · Porphyry · Posidonius · Proclus · Ptolemy · Pythagoras · Serenus  · Simplicius · Sosigenes · Sporus · Thales · Theaetetus · Theano · Theodorus · Theodosius · Theon of Alexandria · Theon of Smyrna · Thymaridas · Xenocrates · Zeno of Elea · Zeno of Sidon · Zenodorus Treatises Almagest · Archimedes Palimpsest · Arithmetica · Conics · Elements · On the Sizes and Distances (Aristarchus) · On Sizes and Distances (Hipparchus) · On the Moving Sphere · The Sand Reckoner Centers Academy of Athens · Cyrene · Library of Alexandria Influences Babylonian mathematics · Egyptian mathematics Influenced European mathematics · Indian mathematics · Islamic mathematics Tables Timetable of Greek mathematicians Problems Problem of Apollonius · Squaring the circle · Doubling the cube · Angle trisection

v • d • e Pre-Socratic philosophers Milesian school Thales · Anaximander · Anaximenes Pythagoreanism Pythagoras · Alcmaeon · Hippasus · Philolaus · Archytas Ephesian school Heraclitus Eleatic school Xenophanes · Parmenides · Zeno of Elea · Melissus Pluralist school Anaxagoras · Archelaus · Empedocles Atomist school Leucippus · Democritus Sophism Protagoras · Gorgias · Prodicus · Hippias Others Pherecydes · Hippo · Diogenes of Apollonia

v • d • e Ancient Greece topics Timeline Cycladic civilization · Minoan civilization · Mycenaean civilization · Greek Dark Ages · Archaic period · Classical Greece · Hellenistic Greece · Roman Greece Geography Aegean Sea · Hellespont · Macedonia · Sparta · Athens · Corinth · Thebes · Thermopylae · Antioch · Alexandria · Pergamon · Miletus · Ephesus · Delphi · Delos  · Olympia · Troy · Rhodes · Crete · Peloponnesus · Epirus · Cyprus Life Agriculture · Cuisine · Democracy · Economy · Education · Law · Medicine · Pederasty · Prostitution · Religion · Slavery · Technology · Olympic Games  · Warfare  · Wine People Philosophers Anaxagoras · Anaximander · Anaximenes · Antisthenes · Aristotle · Democritus · Diogenes of Sinope · Epicurus · Empedocles · Heraclitus · Leucippus · Gorgias · Parmenides · Plato · Protagoras · Pythagoras · Socrates · Thales · Zeno Authors Aeschylus · Aesop · Aristophanes · Euripides · Herodotus · Hesiod · Homer · Lucian · Menander · Pindar · Plutarch · Polybius · Sappho · Sophocles · Theognis of Megara · Thucydides · Xenophon Others Alexander the Great · Lycurgus · Leonidas · Alcibiades · Demosthenes · Pericles · Solon · Themistocles · Archimedes · Euclid · Hippocrates · Aspasia · Milo of Croton Buildings Parthenon · Temple of Artemis · Acropolis · Ancient Agora · Temple of Zeus at Olympia · Temple of Hephaestus · Samothrace temple complex Arts Architecture · Coinage · Literature · Music · Pottery · Sculpture · Theatre Language Proto-Greek · Mycenaean  · Homeric · Dialects (Aeolic • Arcadocypriot • Attic • Doric • Ionic • Locrian • Macedonian • Pamphylian) · Koine

Persondata
NAME	Pythagoras
ALTERNATIVE NAMES	Πυθαγόρας (Greek)
SHORT DESCRIPTION	Ionian philosopher
DATE OF BIRTH	circa 570 BC
PLACE OF BIRTH	Samos Island
DATE OF DEATH	circa 495 BC
PLACE OF DEATH

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)