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. Pythagoras and his wife are variously stated to have had a total of four children, including a son, Telauges, and three daughters, Damo, Arignote, and Myia.
Pythagoras biography information
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 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 that which was considered divine. Thus many myths were created about Pythagoras: such as Apollo was his father; 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 Laërtius, Porphyry, and Iamblichus for the details on Pythagoras biography. 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 consider the statements based on their inherent probability, but even then, if all the credible stories concerning the history of Pythagoras were supposed true, his range of accomplishments and achievements would be impossibly vast.
Pythagoras achievements and accomplishments
Unfortunately there are no books written by the Greek philosopher Pythagoras that are known to have survived, although forgeries under his name 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. Pythagoras appears as a character in the last book of Ovid's Metamorphoses, where Ovid has him expound upon his philosophical viewpoints. Pythagoras has been quoted as saying, "No man is free who cannot command himself."
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
Pythagoras Pythagorean theorem
Since the fourth century AD, the mathematician Pythagoras has commonly been given credit for the discoveries of 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, a2 + b2 = c2.
While the mathematic 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.
Pythagoras Musical Contributions and discoveries
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."
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. However, it may be that Pythagoras was indeed responsible for discovering these properties of string length.
Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Another belief attributed to Pythagoras was that of the "harmony of the spheres". 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
Pythagoras beliefs on 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.
Other Pythagoras accomplishments and achievements
A major Pythagoras accomplishment was the discovery that music was based on proportional intervals of four. It was his belief that the number system, and therefore the universe system, was based on the sum of these numbers: ten. Pythagoreans swore by the Tetrachtys of the Decad, or ten, rather than by the gods. He assigned roles for the numbers as follows: one was reason, two was opinion, four was justice, five was marriage because it was the sum of the first odd and the first even numbers (one was disregarded), seven was virgin because it neither factors or produces among the numbers one through ten. Odd numbers were masculine and even numbers were feminine.
Pythagorus discovered the theory of mathematical proportions, constructed from three to five geometrical solids. One of his order also discovered irrational numbers, but the idea was unthinkable to Pythagoras, and he had this member executed. He was one of the first to think that the earth was round, that all planets have an axis, and that all the planets travel around one central point. Pythagoras originally identified that point as Earth, but later renounced it for the idea that the planets revolve around a central “fire” that he never identified as the sun. He also believed that the moon was another planet that he called a “counter-Earth” – furthering Pythagoras belief in the Limited-Unlimited.
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.
Pythagorean Brotherhood history
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 here it should be noted that sources indicate that as well as men there were many women among the adherents of Pythagoras), and in some ways a monastery. It was based upon the religious teachings of Pythagoras and was very secretive. The adherents were bound by a vow 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 beliefs and practices.
Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and form an elite circle of followers around himself called Pythagoreans. Very strict rules of conduct governed this cultural center. He opened his school to male and female students alike. Those who joined the inner circle of Pythagoras's society called themselves the Mathematikoi. They lived at the school, owned no personal possessions and were required to assume a vegetarian diet. Other students who lived in neighboring areas were also permitted to attend Pythagoras's school. Known as Akousmatikoi, these students were permitted to eat meat and own personal belongings.
According to Iamblichus, the Pythagoreans followed a structured life of religious teaching, common meals, exercise, reading and philosophical study. Music featured as an essential organizing factor of this life: the disciples would sing hymns to Apollo together regularly; they used the lyre to cure illness of the soul or body; poetry recitations occurred before and after sleep to aid the memory.
Flavius Josephus relates that, according to Hermippus of Smyrna, Pythagoras was familiar with and an admirer of Jewish customs and wisdom. Hermippus is quoted as saying about Pythagoras: "In practicing and repeating these precepts he was imitating and appropriating the doctrines of Jews and Thracians. In fact, it is actually said that that great man introduced many points of Jewish law into his philosophy."
The organization was in some ways a school, in some ways a brotherhood, and in some ways a monastery. It was based upon Pythagoras’ religious teachings and was very secretive. At first, the school was highly concerned with the morality of society. Members were required to live ethically, love one another, share political beliefs, practice pacifism and vegetarianism, and devote themselves to the mathematics of nature.
Pythagoras's followers were commonly called "Pythagoreans." For the most part we remember them as philosophical mathematicians who had an influence on the beginning of axiomatic geometry, which after two hundred years of development was written down by Euclid in The Elements.
The Pythagoreans observed a rule of silence called echemythia, the breaking of which was punishable by death. This was because the Pythagoreans believed that a man's words were usually careless and misrepresented him and that when someone was "in doubt as to what he should say, he should always remain silent". Another rule that they had was to help a man "in raising a burden, but do not assist him in laying it down, for it is a great sin to encourage indolence", and they said "departing from your house, turn not back, for the furies will be your attendants"; this axiom reminded them that it was better to learn none of the truth about mathematics, God, and the universe at all than to learn a little without learning all.
In his biography of Pythagoras (written seven centuries after Pythagoras's time), Porphyry stated that this silence was "of no ordinary kind." The Pythagoreans were divided into an inner circle called the mathematikoi ("mathematicians") and an outer circle called the akousmatikoi ("listeners"). Porphyry wrote "the mathematikoi learned the more detailed and exactly elaborate version of this knowledge, the akousmatikoi (were) those which had heard only the summary headings of his (Pythagoras's) writings, without the more exact exposition." According to Iamblichus, the akosmatikoi were the exoteric disciples who listened to lectures that Pythagoras gave out loud from behind a veil.
The akousmatikoi were not allowed to see Pythagoras and they were not taught the inner secrets of the cult. Instead they were taught laws of behavior and morality in the form of cryptic, brief sayings that had hidden meanings. The akousmatikoi recognized the mathematikoi as real Pythagoreans, but not vice versa. After the murder of Pythagoras and a number of the mathematikoi by the cohorts of Cylon, a resentful disciple, the two groups split from each other entirely, with Pythagoras's wife Theano and their two daughters leading the mathematikoi.
Theano, daughter of the Orphic initiate Brontinus, was a mathematician in her own right. She is credited with having written treatises on mathematics, physics, medicine, and child psychology, although nothing of her writing survives. Her most important work is said to have been a treatise on the principle of the golden mean. In a time when women were usually considered property and relegated to the role of housekeeper or spouse, Pythagoras allowed women to function on equal terms in his society.
The Pythagorean society is associated with prohibitions such as not to step over a crossbar, and not to eat beans. These rules seem like primitive superstition, similar to "walking under a ladder brings bad luck". The abusive epithet mystikos logos ("mystical speech") was hurled at Pythagoras even in ancient times to discredit him. The prohibition on beans could be linked to favism, which is relatively widespread around the Mediterranean.
The key here is that akousmata means "rules", so that the superstitious taboos primarily applied to the akousmatikoi, and many of the rules were probably invented after Pythagoras's death and independent from the mathematikoi (arguably the real preservers of the Pythagorean tradition). The mathematikoi placed greater emphasis on inner understanding than did the akousmatikoi, even to the extent of dispensing with certain rules and ritual practices. For the mathematikoi, being a Pythagorean was a question of innate quality and inner understanding.
There was also another way of dealing with the akousmata — by allegorizing them. We have a few examples of this, one being Aristotle's explanations of them: "'step not over a balance', i.e. be not covetous; 'poke not the fire with a sword', i.e. do not vex with sharp words a man swollen with anger, 'eat not heart', i.e. do not vex yourself with grief," etc. We have evidence for Pythagoreans allegorizing in this way at least as far back as the early fifth century BC. This suggests that the strange sayings were riddles for the initiated.
The Pythagoreans are known for their theory of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. They performed purification rites and followed and developed various rules of living which they believed would enable their soul to achieve a higher rank among the gods.
Much of their mysticism concerning the soul seem inseparable from the Orphic tradition. The Orphics advocated various purificatory rites and practices as well as incubatory rites of descent into the underworld. Pythagoras is also closely linked with Pherecydes of Syros, the man ancient commentators tend to credit as the first Greek to teach a transmigration of souls. Ancient commentators agree that Pherekydes was Pythagoras's most intimate teacher. Pherekydes expounded his teaching on the soul in terms of a pentemychos ("five-nooks", or "five hidden cavities") — the most likely origin of the Pythagorean use of the pentagram, used by them as a symbol of recognition among members and as a symbol of inner health (ugieia).
Pythagoras was interested in music and the Pythagoreans were musicians as well as mathematicians. He wanted to improve the music of his day, which he believed was not harmonious enough and was too chaotic.
Pythagoras 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 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.
Pythagoras 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".
Neopythagoreanism (or Neo-Pythagoreanism) was a Graeco-Alexandrian school of philosophy, reviving Pythagorean doctrines, which became prominent in the 1st and 2nd centuries CE.
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.
Pythagoras academic genealogy
Anaximander, Pherecydes of Samos, Hermodamas of Samos, Thales
Ameinias, Bathyllus, Brontinus (husband of Theano), Calliphon, Cercops, Echecrates, Empedocles, Eurytus, Hippasus, Leon, Lysis of Tarentum, Milon (whose house was used as a Pythagorean meeting place), Parmeniscus, Petron, Philolaus of Croton, Theano (Pythagoras' daughter), Xenophilus of Chaldice, Zalmoxis (Pythagoras' slave)
There is no doubt that Pythagoras of Samos was an influential teacher of his time. Pythagoras' achievements and accomplishments are still debated to this day. Pythagoras discoveries and contributions in the fields of music and mathematics are his gifts to mankind.