Pythagŏras in Harpers Dictionary of Classical Antiquities (1898)
A celebrated Greek philosopher, a native of Samos, and the son of Mnesarchus, who was either a merchant, or, according to others, an engraver of signets. The date of his birth is uncertain; but all authorities agree that he flourished in the times of Polycrates and Tarquinius Superbus (B.C. 540-510). He studied in his own country under Creophilus, Pherecydes of Syros, and others, and is said to have visited Egypt and many countries of the East for the purpose of acquiring knowledge. We have not much trustworthy evidence, either as to the kind and amount of knowledge which he acquired, or as to his definite philosophical views. It is certain, however, that he believed in the transmigration of souls; and he is said to have pretended that he had been Euphorbus, the son of Panthoüs, in the Trojan War, as well as various other characters. He is further said to have discovered the propositions that the triangle inscribed in a semicircle is right-angled; that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the sides. There is a celebrated story of his having discovered the arithmetical relations of the musical scale by observing accidentally the various sounds produced by hammers of different weights striking upon an anvil, and suspending by strings weights equal to those of the different hammers. The retailers of the story of course never took the trouble to verify the experiment, or they would have discovered that different hammers do not produce different sounds from the same anvil, any more than different clappers do from the same bell. Discoveries in astronomy are also attributed to Pythagoras. There can be little doubt that he paid great attention to arithmetic, and its application to weights, measures, and the theory of music. Apart from all direct testimony, however, it may safely be affirmed that the very remarkable influence exerted by Pythagoras, and even the fact that he was made the hero of so many marvellous stories, proves him to have been a man both of singular capabilities and of great acquirements. It may also be affirmed with safety that the religious element was the predominant one in the character of Pythagoras, and that religious ascendancy in connection with a certain mystic religious system was the object which he chiefly laboured to secure. It was this religious element which made the profoundest impression upon his contemporaries. They regarded him as standing in a peculiarly close connection with the gods. The Crotoniats even identified him with the Hyperborean Apollo. And, without viewing him as an impostor, we may easily believe that he himself, to some extent, shared the same views. He pretended to divination and prophecy; and he appears as the revealer of a mode of life calculated to raise his disciples above the level of mankind, and to recommend them to the favour of the gods. No certainty can be arrived at as to the length of time spent by Pythagoras in Egypt or the East, or as to his residence and efforts in Samos or other Grecian cities, before he settled at Crotona in Italy. He probably removed to Crotona because he found it impossible to realize his schemes in his native country while under the tyranny of Polycrates. The reason why he selected Crotona as the sphere of his operations it is impossible to ascertain; but soon after his arrival in that city he attained extensive influence, and gained over great numhers to enter into his views. His adherents were chiefly of the noble and wealthy classes. Three hundred of these were formed into a select brotherhood or club, bound by a sort of vow to Pythagoras and each other, for the purpose of cultivating the religious and ascetic observances enjoined by their master, and of studying his religious and philosophical theories. Everything that was done and taught among the members was kept a profound secret from all without its pale. It was an old Pythagorean maxim, that everything was not to be told to everybody. There were also gradations among the members themselves, as in the distinction of ἀκουσματικοί or "hearers" as contrasted with μαθηματικοί or esoteric students. In the admission of candidates Pythagoras is said to have placed great reliance on his physiognomical discernment. If admitted, they had to pass through a period of probation, in which their powers of maintaining silence were especially tested, as well as their general temper, disposition, and mental capacity. As regards the nature of the esoteric instruction to which only the most approved members of the fraternity were admitted, some have supposed that it had reference to the political views of Pythagoras. Others have maintained, with greater probability, that it related mainly to the orgies, or secret religious doctrines and usages, which undoubtedly formed a prominent feature in the Pythagorean system, and were peculiarly connected with the worship of Apollo. There were some outward peculiarities of an ascetic kind in the mode of life to which the members of the brotherhood were subjected. Some represent him as forbidding all animal food; but all the members cannot have been subjected to this prohibition, since the athletic Milo, for instance, could not possibly have dispensed with animal food. According to some ancient authorities, he allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and rams. There is a similar discrepancy as to the prohibition of fish and beans. But temperance of all kinds seems to have been strictly enjoined. It is also stated that they had common meals, resembling the Spartan syssitia, at which they met in companies of ten. Considerable importance seems to have been attached to music and gymnastics in the daily exercises of the disciples. Their whole discipline is represented as tending to produce a lofty serenity and self-possession, regarding the exhibition of which various anecdotes were current in antiquity. Among the best ascertained features of the brotherhood are the devoted attachment of the members to each other, and their sovereign contempt for those who did not belong to their ranks. It appears that they had some secret conventional symbols, by which members of the fraternity could recognize each other, even if they had never met before. Clubs similar to that at Crotona were established at Sybaris, Metapontum, Tarentum, and other cities of Magna Graecia. The institutions of Pythagoras were certainly not intended to withdraw those who adopted them from active exertion, that they might devote themselves exclusively to religious and philosophical contemplations. He rather aimed at the production of a calm bearing and elevated tone of character, through which those trained in the discipline of the Pythagorean life should exhibit in their personal and social capacities a reflection of the order and harmony of the universe. Whether he had any distinct political designs in the foundation of his brotherhood is doubtful; but it was perfectly natural, even without any express design on his part, that a club such as the Three Hundred of Crotona should gradually come to mingle political with other objects, and, by the facilities afforded by their secret and compact organization, should speedily gain extensive political influence. That this influence should be decisively on the side of aristocracy or oligarchy resulted naturally both from the nature of the Pythagorean institutions, and from the rank and social position of the members of the brotherhood. Through them, of course, Pythagoras himself exercised a large amount of indirect influence over the affairs both of Crotona and of other Italian cities. This Pythagorean brotherhood or order resembled in many respects the one founded by Loyola. It is easy to understand how this aristocratical and exclusive club would excite the jealousy and hostility not only of the democratical party in Crotona, but also of a considerable number of the opposite faction. The hatred which they had excited speedily led to their destruction. The populace of Crotona rose against them; and an attack was made upon them while assembled either in the house of Milo, or in some other place of meeting. The building was set on fire, and many of the assembled members perished; only the more active escaped. Similar commotions ensued in the other cities of Magna Graecia in which Pythagorean clubs had been formed. As an active and organized brotherhood, the Pythagorean Order was everywhere suppressed; but the Pythagoreans still 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.
Respecting 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, and that, being driven thence, he escaped to Metapontum, and there starved himself to death. His tomb was shown at Metapontum in the time of Cicero. According to some accounts, Pythagoras married Theano , a lady of Crotona, and had a daughter Damo, and a son Telauges, or, according to others, two daughters, Damo and Myia ; while other notices seem to imply that he had a wife and a daughter grown up when he came to Crotona. When we come to inquire what were the philosophical or religious opinions held by Pythagoras himself, we are met at the outset by the difficulty that even the authors from whom we have to draw possessed no authentic records bearing upon the age of Pythagoras himself. If Pythagoras ever wrote anything, his writings perished with him, or not long after. The probability is that he wrote nothing. Everything current under his name in antiquity is spurious. It is all but certain that Philolaüs was the first who published the Pythagorean doctrines, at any rate in a written form. (See Philolaüs.) Still there was so marked a peculiarity running through the Pythagorean philosophy that there can be little question as to the germs of the system, at any rate, having been derived from Pythagoras himself. Pythagoras resembled the philosophers of the Ionic school, who undertook to solve, by means of a single primordial principle, the vague problem of the origin and constitution of the universe as a whole. His predilection for mathematical studies led him to trace the origin of all things to number, his theory being suggested, or at all events confirmed, by the observation of various numerical relations, or analogies to them, in the phenomena of the universe. Musical principles likewise played almost as important a part in the Pythagorean system as mathematical or numerical ideas. We find running through the entire system the idea that order, or harmony of relation, is the regulating principle of the whole universe. The intervals between the heavenly bodies were supposed to be determined according to the laws and relations of musical harmony. Hence arose the celebrated doctrine of the harmony of the spheres; for the heavenly bodies, in their motion, could not but occasion a certain sound or note, depending on their distances and velocities; and as these were determined by the laws of harmonical intervals, the notes altogether formed a regular musical scale or harmony. This harmony, however, we do not hear, either because we have been accustomed to it from the first, and have never had an opportunity of contrasting it with stillness, or because the sound is so powerful as to exceed our capacities for hearing. The ethics of the Pythagoreans consisted more in ascetic practice, and maxims for the restraint of the passions, especially of anger, and the cultivation of the power of endurance, than in scientific theory. What of the latter they had was, as might be expected, intimately connected with their numbertheory. Happiness consisted in the science of the perfection of the virtues of the soul, or in the perfect science of numbers. Likeness to the Deity was to be the object of all our endeavours, man becoming better as he approaches the gods, who are the guardians and guides of men. Great importance was attached to the influence of music in controlling the force of the passions. Self-examination was strongly insisted on. The transmigration of souls was viewed apparently in the light of a process of purification. Souls under the dominion of sensuality either passed into the bodies of animals, or, if incurable, were thrust down into Tartarus to meet with expiation or condign punishment. The pure were exalted to higher modes of life, and at last attained to incorporeal existence. As regards the fruits of this system of training or belief, it is interesting to remark, that wherever we have notices of distinguished Pythagoreans, we usually hear of them as men of great uprightness, conscientiousness, and self-restraint, and as capable of devoted and enduring friendship. (See Archytas; Damon; and Phintias.) Existing works that bear the name of Pythagoras are spurious. See Günther, Carmen Aureum (Breslau, 1816); Schneeberger, Die goldenen Sprüche des Pythagoras (Münnerstadt, 1862). On the life of Pythagoras, see the Eng. version of the life by Iamblichus made by Taylor (London, 1818); and, in general, Ritter, Geschichte der Pythagorischen Philosophie (Hamburg, 1826); Brandis, Ueber die Zahlenlehre der Pythagoreer und Platoniker in the Rheinisches Museum for 1828; Gladisch, Die Pythagoreer (Posen, 1841); Grote, History of Greece, vol. iv. pp. 525-551; Langel, Pythagore, in the Revue des Deux Mondes for 1864, pp. 969-989; Rathgeber, Grossgriechenland und Pythagoras (Gotha, 1866); Baltzer, Pythagoras der Weise von Samos (Nordhausen, 1868); Chaignet, Pythagore et la Philosophie Pythagorienne (Paris, 1873); Gow, Short History of Mathematics (London, 1884); Zeller, The Pre-Socratic Schools (Eng. trans. 1882); and the article Philosophia.
Pythagoras in Wikipedia
Pythagoras of Samos (Greek: Ὁ Πυθαγόρας ὁ Σάμιος, O Pythagoras o Samios, "Pythagoras the Samian", or simply Ὁ Πυθαγόρας; c. 570-c. 495 BC) 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, 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. He had a teacher named Themistoclea, who introduced him to the principles of ethics. 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 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. 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, and through him, all of Western philosophy.
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 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. With the exception of a few remarks by Xenophanes, Heraclitus, Herodotus, Plato, Aristotle, and Isocrates, we are mainly dependent on Diogenes Laertius, Porphyry, and Iamblichus for the biographical details. Aristotle had written a separate work on the Pythagoreans, which unfortunately has not survived. 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, 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.
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. 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. A late source gives his mother's name as Pythais. 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.
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, Hermodamas, Bias, Thales, Anaximander, and Pherecydes of Syros. 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. 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. The journey to Babylon is possible, and not very unlikely. 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. . 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 or Cretan mysteries, or the Delphic oracle.
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; and Xenophanes claimed that he believed in the transmigration of souls. 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.
Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem, as well as discoveries in the field of music, astronomy, 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, and he was said to have practised divination and prophecy. 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.
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. 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 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. 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, others that he fled first to Tarentum, and that, being driven from there, he escaped to Metapontum, and there starved himself to death. His tomb was shown at Metapontum in the time of Cicero.
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.
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.
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
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. 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. 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
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 were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on."
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.
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 lives that he could remember in detail, and, according to Xenophanes, Pythagoras heard the cry of his dead friend in the bark of a dog.
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). 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'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.
Both Plato and Isocrates affirm that, above all else, Pythagoras was famous for leaving behind him a way of life. 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.
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. On the other hand, it seems certain that there were many women among the adherents of Pythagoras.
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. This may have been due to the doctrine of metempsychosis. Other authorities contradict the statement. According to Aristoxenus, he allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and rams. There is a similar discrepancy as to the prohibition of fish and beans. 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.
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. Iamblichus (apparently on the authority of Aristoxenus) 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. 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.
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, 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.
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. Today, Pythagoras is revered as a prophet by the Ahl al-Tawhid or Druze faith along with his fellow Greek, Plato.