Pythagoras of Samos (
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[2] Ancient Greek:
Πυθαγόρας ὁ Σάμιος Pythagóras ho Sámios “Pythagoras the
Samian”, or simply
Πυθαγόρας; Πυθαγόρης in
Ionian Greek; c. 570 – c. 495 BC)
[3][4] was an
Ionian Greek philosopher,
mathematician, and founder of the religious movement called
Pythagoreanism. 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, and might have travelled widely in his youth, visiting
Egypt and other places seeking knowledge. Around 530 BC, he moved to
Croton, in
Magna Graecia, 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. Pythagorean meeting-places were burned and Pythagoras was forced to flee the city. He is said to have died in
Metapontum.
Pythagoras made influential contributions to
philosophy and
religion in the late 6th century BC. He is often revered as a great
mathematician,
mystic, and
scientist and is best known for the
Pythagorean theorem which bears his name. However, because legend and obfuscation cloud his work even more than that of the other
pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to
mathematics or
natural philosophy. 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,
[5] and Pythagorean ideas exercised a marked influence on
Plato, and through him, all of
Western philosophy.
Biographical sources
Accurate facts about the life of Pythagoras are so few that most information concerning him is untrustworthy, making it nearly 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.
[6] 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 the same time.
[7] 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 biographical details. Aristotle had written a separate work on the Pythagoreans, which unfortunately has not survived.
[8] His disciples
Dicaearchus,
Aristoxenus, and
Heraclides Ponticus had written on the same subject. These writers, late as they are, were among the best sources from whom Porphyry and Iamblichus drew, while still adding some legendary accounts and their own inventions to the mix. 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.
[9]
Life
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.
[10] 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.
[11] A late source gives his mother's name as Pythais.
[12]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.
[13]
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 and
Oriental. We find mentioned as his instructors
Creophylus,
[14] Hermodamas of Samos,
[15] Bias,
[14] Thales,
[14] Anaximander,
[16] and
Pherecydes of Syros.
[17] He is said too, to have been taught by a
Delphicpriestess named
Themistoclea, who introduced him to the principles of
ethics.
[18][19] 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.
[20] Of the various claims regarding his Greek teachers, Pherecydes is mentioned most often.
Diogenes Laërtius reported that Pythagoras had undertaken extensive travels, having not only visited
Egypt but also "journeyed among the
Chaldaeans and
Magi", for the purpose of collecting all available knowledge and especially to learn information concerning the secret or mystic cults of the gods.
[21] Plutarch asserted in his book
On Isis and Osiris that during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of
Heliopolis.
[22] Other ancient writers asserted his visit to Egypt.
[23] 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.
[24]
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,
[25] or the
Delphic oracle.
[26]
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;
[27] and
Xenophanes claimed that he believed in the
transmigration of souls.
[28] 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.
[29] In his book
The Life of Apollonius of Tyana,
Philostratus wrote that Pythagoras knew not only who he was himself, but also who he had been.
[30]
Many mathematical and scientific discoveries were attributed to Pythagoras, including
his famous theorem,
[31] as well as discoveries in the field of
music,
[32]astronomy,
[33] and
medicine.
[34] 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,
[35] and he was said to have practised
divination and
prophecy.
[36] 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.
[37]
Croton on the southern coast of Magna Graecia (Southern Italy), to which Pythagoras ventured after feeling overburdened in Samos.
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 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.
[38] 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.
[39]
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 science and mathematics, or the secret religious doctrines and usages which were undoubtedly prominent in the Pythagorean system, and may have been connected with the worship of Apollo.
[40] Temperance of all kinds seems to have been strictly urged. There is disagreement among the biographers as to whether Pythagoras forbade all animal food,
[41] or only certain types.
[42] The club was in practice at once "a philosophical school, a religious brotherhood, and a political association."
[43]
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 seems 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.
[44] 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,
[45] others that he fled first to
Tarentum, and that, being driven from there, he escaped to
Metapontum, and there starved himself to death.
[46] His tomb was shown at Metapontum in the time of
Cicero.
[47]
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 are known to have survived, 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 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).
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.
There are good reasons to believe that Pythagoras never dealt with Mathematics
at all.
[48] Therefore, although the mathematical ideas exposed below circulated among the Pythagoreans, they may well not be due to Pythagoras himself.
Pythagorean theorem
A visual proof of the Pythagorean theorem
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 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 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.
[49] 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.
[50] 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 and other instruments in Pythagorean tuning
According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when he passed blacksmiths at work one day and thought that the sounds emanating from their anvils 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 the sounds were produced by looking at their tools. He discovered that it was because the
hammers 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), and not to hammer weight.
[51][52] However, it may be that Pythagoras was indeed responsible for discovering the 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". Thus the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony.
[53]
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 immortal. His ideas of reincarnation were influenced by ancient Greek religion.
Heraclides Ponticus reports the story that Pythagoras claimed that he had lived four previous lives that he could remember in detail.
[54] One of his past lives, as reported by
Aulus Gellius, was as a beautiful courtesan.
[55] According to
Xenophanes, Pythagoras heard the cry of his dead friend in the bark of a dog.
[56]
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 (Egyptian
Thoth).
[57] According to accounts of Aristotle and others, some ancients believed that he had the ability to travel through space and time and to communicate with animals and plants.
[58] 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.[59]
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.[60]
Pythagoreans
Both
Plato and
Isocrates affirm that, above all else, Pythagoras was famous for leaving behind him a way of life.
[61] 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.
[62]
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),
[63] 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.
[64]
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.
[65] 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.
[66] Thus the Pythagoreans were divided into an inner circle called the
mathematikoi ("learners") and an outer circle called the
akousmatikoi ("listeners").
[67] Iamblichus describes them in terms of
esoterikoi and
exoterikoi (or alternatively
Pythagoreioi and
Pythagoristai),
[68] 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.
[69]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.
[70] Other authorities contradict the statement. According to
Aristoxenus,
[71] he allowed the use of all kinds of animal food except the flesh of
oxen used for
ploughing, and
rams.
[72] There is a similar discrepancy as to the prohibition of
fish and
beans.
[73] 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.
[74]
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.
[75] Iamblichus (apparently on the authority of
Aristoxenus)
[76] 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.
[77]There were even stories of secret symbols, by which members of the sect could recognise each other, even if they had never met before.
[78]
Influence
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, this influence consists of three points: (1) 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. (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 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.
[79]
Aristotle claimed that the philosophy of Plato closely followed the teachings of the Pythagoreans,
[80] and Cicero repeats this claim:
Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean").
[81] Bertrand Russell, 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.
