Pythagoras Pre-Socratic philosophy
Bust of Pythagoras of Samos in the Capitoline Museums, Rome
Name	Pythagoras (Πυθαγόρας)
Birth	c. The Pre-Socratic Greek philosophers were active before Socrates or contemporaneously but expounding knowledge developed earlier The Capitoline Museums ( Italian Musei Capitolini) are a group of art and archeological Museums in Piazza del Campidoglio Rome ( Roma ˈroma Roma is the capital city of Italy and Lazio, and is Italy's largest and most populous city with more than 2 580 BC – 572 BC
Death	c. Events and trends 589 BC — Apries succeeds Psammetichus II as king of Egypt. Events and trends 579 BC — Servius Tullius succeeds the assassinated Lucius Tarquinius Priscus as the sixth King of Rome. 500 BC – 490 BC
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" redirects here. Events By place Greece Darius I sends an expedition under Artaphernes and Datis the Mede across Pythagoreanism is a term used for the Esoteric and metaphysical beliefs held by Pythagoras and his followers the Pythagoreans who were much influenced Metaphysics is the branch of Philosophy investigating principles of reality transcending those of any particular science Music is an Art form in which the medium is Sound organized in Time. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Ethics is a major branch of Philosophy, encompassing right conduct and good life Politics Politics is the process by which groups of people make decisions In Mathematics and the Arts two quantities are in the Golden ratio if the Ratio between the sum of those quantities and the larger one is the Pythagorean tuning is a system of Musical tuning in which the Frequency relationships of all intervals are based on the ratio 32. In Mathematics, the Pythagorean theorem ( American English) or Pythagoras' theorem ( British English) is a relation in Euclidean geometry Thales of Miletus According to Bertrand Russell, "Philosophy begins with Thales Anaximander ( Ancient Greek:) (c 610 BC–c 546 BC was a Pre-Socratic Greek philosopher who lived in Miletus See also Pherecydes of Leros Pherecydes of Syros (in Greek: Φερεκύδης was a Greek thinker from the island of Syros Philolaus (ca 480 BC &ndash ca 385 BC Φιλόλαος was a Greek Pythagorean and Presocratic. Alcmaeon ( Gr) of Croton (in Magna Græcia) was one of the most eminent natural philosophers and medical theorists of antiquity Parmenides of Elea ( Greek:, early 5th century BC was an Ancient Greek Philosopher born in Elea, a Greek city on the southern coast of Biography Early life Birth and family Plato was born in Athens Greece Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry Empedocles ( Greek:, ca 490–430 BC was a Greek Pre-Socratic Philosopher and a citizen of Agrigentum, a Greek colony in Hippasus of Metapontum (Ίππασος b c 500 BC in Magna Graecia, was a Greek Philosopher. Johannes Kepler (ˈkɛplɚ ( December 27 1571 &ndash November 15 1630) was a German Mathematician, Astronomer For the Samian statuary of the same name, see Pythagoras (sculptor). Pythagoras of Samos ( Ancient Greek:, fl 5th century BC) was a statuary from Samos whom Pliny the Elder expressly distinguishes

Pythagoras of Samos (Greek: Ὁ Πυθαγόρας ὁ Σάμιος, Pythagoras the Samian, or simply Ὁ Πυθαγόρας; born between 580 and 572 BC, died between 500 and 490 BC) was an Ionian Greek mathematician and founder of the religious movement called Pythagoreanism. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly Events and trends 589 BC — Apries succeeds Psammetichus II as king of Egypt. Events and trends 579 BC — Servius Tullius succeeds the assassinated Lucius Tarquinius Priscus as the sixth King of Rome. Events By place Greece Darius I sends an expedition under Artaphernes and Datis the Mede across The Ionians ( Greek:, Iōnes singular) were one of the three populations into which the Ancient Greeks considered the population of Hellenes to have been The Greeks ( Greek: Έλληνες) are a Nation and Ethnic group native to Greece, Cyprus and neighbouring regions A mathematician is a person whose primary area of study and research is the field of Mathematics. Pythagoreanism is a term used for the Esoteric and metaphysical beliefs held by Pythagoras and his followers the Pythagoreans who were much influenced He is often revered as a great mathematician, mystic and scientist; however some have questioned the scope of his contributions to mathematics and natural philosophy. Herodotus referred to him as "the most able philosopher among the Greeks". Herodotus of Halicarnassus ( Greek: Hēródotos Halikarnāsseús) was a Greek Historian who lived in the 5th century BC ( 484 BC&ndash 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 of benefit to humankind. PYTHIA is a computer simulation program for particle collisions at very high energies (see Event (particle physics) in Particle accelerators Aristippus (Ἀρίστιππος of Cyrene, (c 435-c 356 BCE was the founder of the Cyrenaic school of Philosophy ^[1]

He is best known for the Pythagorean theorem, which bears his name. In Mathematics, the Pythagorean theorem ( American English) or Pythagoras' theorem ( British English) is a relation in Euclidean geometry Known as "the father of numbers", Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language The 6th century BC started the first day of 600 BC and ended the last day of 501 BC. Because legend and obfuscation cloud his work even more than with the other pre-Socratics, one can say little with confidence about his life and teachings. The Pre-Socratic Greek philosophers were active before Socrates or contemporaneously but expounding knowledge developed earlier We do know that Pythagoras and his students believed that everything was related to mathematics and that numbers were the ultimate reality and, through mathematics, everything could be predicted and measured in rhythmic patterns or cycles. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and According to Iamblichus, Pythagoras once said that "number is the ruler of forms and ideas and the cause of gods and demons. "

He was the first man to call himself a philosopher, or lover of wisdom,^[2] and Pythagorean ideas exercised a marked influence on Plato. Biography Early life Birth and family Plato was born in Athens Greece Unfortunately, very little is known about Pythagoras because none of his writings have survived. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors.

Life

Pythagoras was born on Samos, a Greek island in the eastern Aegean, off the coast of Asia Minor. Samos (Σάμος is a Greek island in the North Aegean Sea, south of Chios, north of Patmos and the Dodecanese, and off Anatolia (Anadolu Ανατολία Anatolía) or Asia minor, comprising most of modern Turkey, is the geographic region bounded by the Black He was born to Pythais (his mother, a native of Samos) and Mnesarchus (his father, a Phoenician merchant from Tyre). Phoenicia ( Phoenician: Phoenician nunsvg|12px|נ]]Phoenician nun Tyre ( Arabic صور Ṣūr, Phoenician Phoenician wawsvg|12px|ו]] Ṣur, Hebrew As a young man, he left his native city for Croton, Calabria, in Southern Italy, to escape the tyrannical government of Polycrates. Croton may also refer to a plant genus See Croton (genus. Or to the NY village Croton-on-Hudson. Calabria ( Latin: Brutium) is a region in southern Italy, south of Naples, located at the "toe" of Italy (Italia officially the Italian Republic, (Repubblica Italiana is located on the Italian Peninsula in Southern Europe, and on the two largest In modern usage a tyrant is a single ruler holding absolute power over a State or within an Organization. Polycrates (Πολυκράτης son of Aeaces, was the Tyrant of Samos from c According to Iamblichus, Thales, impressed with his abilities, advised Pythagoras to head to Memphis in Egypt and study with the priests there who were renowned for their wisdom. Thales of Miletus According to Bertrand Russell, "Philosophy begins with Thales Memphis was the ancient capitol of the first nome of Lower Egypt, and of the Old Kingdom of Egypt from its foundation until around 2200 BC and He also was discipled in the temples of Tyre and Byblos in Phoenicia. It may have been in Egypt where he learned some geometric principles which eventually inspired his formulation of the theorem that is now called by his name. In Mathematics, a theorem is a statement proven on the basis of previously accepted or established statements This possible inspiration is presented as an example problem in the Berlin Papyrus. The Berlin Papyrus 6619 commonly known as the Berlin Papyrus is an Ancient Egyptian papyrus document from the Middle Kingdom. Upon his migration from Samos to Croton, Calabria, Italy, Pythagoras established a secret religious society very similar to (and possibly influenced by) the earlier Orphic cult. Croton may also refer to a plant genus See Croton (genus. Or to the NY village Croton-on-Hudson. Calabria ( Latin: Brutium) is a region in southern Italy, south of Naples, located at the "toe" of Italy (Italia officially the Italian Republic, (Repubblica Italiana is located on the Italian Peninsula in Southern Europe, and on the two largest Orphism (more rarely Orphicism) is the name given to a set of religious beliefs and practices in the ancient Greek and Thracian world associated with literature

Bust of Pythagoras, Vatican

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. A bust is a sculpted or cast representation of the upper part of the human figure depicting a person's head and Neck, as well as a variable portion of The Vatican Museums (Musei Vaticani in Viale Vaticano in Rome, inside the Vatican City, are one of the greatest museums in the world since they display works 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 mainly vegetarian diet (meat that could be sacrificed was allowed to be eaten). Vegetarianism is the practice of a diet that excludes Meat (including game and slaughter by-products Fish (including Shellfish and other sea 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. Richard Blackmore, in his book The Lay Monastery (1714), saw in the religious observances of the Pythagoreans, "the first instance recorded in history of a monastic life. "

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. The lyre is a stringed musical instrument well known for its use in Classical Antiquity and later

Flavius Josephus, in his polemical Against Apion, in defence of Judaism against Greek philosophy, mentions that according to Hermippus of Smyrna, Pythagoras was familiar with Jewish beliefs, incorporating some of them in his own philosophy. Josephus (AD 37 – c 100 also known as Yosef Ben Matityahu (Joseph son of Matthias and after he became a Roman citizen, as Titus Flavius Josephus Against Apion (or Contra Apionem) was a polemical work written by Flavius Josephus as a defense of Judaism as a classical religion Judaism (from the Greek Ioudaïsmos, derived from the Hebrew יהודה Yehudah, " Judah " in Hebrew יַהֲדוּת Yahedut Ancient Greek philosophy focused on the role of Reason and Inquiry. Hermippus (Ἕρμιππος of Smyrna, a Peripatetic philosopher surnamed by the ancient writers the Callimachian (ό Καλλιμάχειος from

Towards the end of his life he fled to Metapontum because of a plot against him and his followers by a noble of Croton named Cylon. Metapontum or Metapontium ( Greek:: Thuc Strab and all Greek writers have this form the Latins almost universally Metapontum was an important city He died in Metapontum around 90 years old from unknown causes.

Pythagoreans

Main article: Pythagoreans

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

The organization was in some ways a school, in some ways a brotherhood, and in some ways a monastery. Pythagoreanism is a term used for the Esoteric and metaphysical beliefs held by Pythagoras and his followers the Pythagoreans who were much influenced The School of Athens, or it Scuola di Atene in Italian, is one of the most famous Paintings by the Italian Renaissance artist Raphael Sanzio, usually known by his first name alone (in Italian Raffaello) (April 6 or March 28 1483 – April 6 1520 was an Italian painter and 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 devote themselves to the mathematics of nature.

Pythagoras's followers were commonly called "Pythagoreans". They are generally accepted 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. Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry Euclid's Elements ( Greek:) is a mathematical and geometric Treatise consisting of 13 books written by the Greek

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. (The Secret Teachings of All Ages by Manly P. Hall).

In his biography of Pythagoras (written seven centuries after Pythagoras's time), Porphyry stated that this silence was "of no ordinary kind. Porphyry of Tyre ( Greek:, c AD 233&ndashc 309 was a Phoenician Neoplatonic philosopher " 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 akousmatikoi were the exoteric disciples who listened to lectures that Pythagoras gave out loud from behind a veil. Exoteric refers to knowledge that is outside of and independent from anyone's experience and can be ascertained by anyone

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 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 (Greek Θεανώ born c 546 BCE and lived in the last part of the 6th century BCE was a Greek mathematician

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". Superstition ( Latin superstitio, literally "standing over" derived perhaps from standing in awe used in Latin as a unreasonable or excessive belief 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. Glucose-6-phosphate dehydrogenase deficiency is an X-linked recessive Hereditary disease characterised by abnormally low levels of Glucose-6-phosphate

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. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. 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. Orphism (more rarely Orphicism) is the name given to a set of religious beliefs and practices in the ancient Greek and Thracian world associated with literature 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. See also Pherecydes of Leros Pherecydes of Syros (in Greek: Φερεκύδης was a Greek thinker from the island of Syros 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).

Musical theories and investigations

Pythagoras was very interested in music, and so were his followers. The Pythagoreans were musicians as well as mathematicians. Pythagoras wanted to improve the music of his day, which he believed was not harmonious enough and was too hectic.

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. An anvil is a manufacturing tool made of a hard and massive block of stone or metal used as a support for Chiseling and Hammering other objects such as in " (See Pythagorean tuning. Pythagorean tuning is a system of Musical tuning in which the Frequency relationships of all intervals are based on the ratio 32. )

The Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Pythagoras believed in something called the harmony of the spheres. He believed that the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony. ^[3]

Influence

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). Anaximander ( Ancient Greek:) (c 610 BC–c 546 BC was a Pre-Socratic Greek philosopher who lived in Miletus See also Pherecydes of Leros Pherecydes of Syros (in Greek: Φερεκύδης was a Greek thinker from the island of Syros Thales of Miletus According to Bertrand Russell, "Philosophy begins with Thales Brontinus (Βροντῖνος of Metapontum, was a Pythagorean philosopher who lived at the end of the 6th century BC. Calliphon (or Callipho (Καλλιφῶν was a Greek Philosopher, who probably belonged to the Peripatetic school and lived in the 2nd century BC Cercops (Κέρκωψ One of the oldest Orphic poets called a Pythagorean by Clement of Alexandria and Cicero, was said by Epigenes of Echecrates (pronounced eh-CHEHK-rah-tees was according to Plato, a Pythagorean philosopher from the ancient Greek town of Phlius. Empedocles ( Greek:, ca 490–430 BC was a Greek Pre-Socratic Philosopher and a citizen of Agrigentum, a Greek colony in Eurytus (Εὔρυτος an eminent Pythagorean philosopher lived c Hippasus of Metapontum (Ίππασος b c 500 BC in Magna Graecia, was a Greek Philosopher. Lysis of Taras (Λῦσις (died c 390 BC was a Greek Philosopher. Milo or Milon of Croton (late 6th century BC was a famous ancient Greek athlete Philolaus (ca 480 BC &ndash ca 385 BC Φιλόλαος was a Greek Pythagorean and Presocratic. Theano (Greek Θεανώ born c 546 BCE and lived in the last part of the 6th century BCE was a Greek mathematician Zalmoxis ( Greek Ζάλμοξις, also known as Salmoxis, Σάλμοξις Zamolxis, Ζάμολξις or Samolxis Σάμολξις

Pythagoras is commonly 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. In Mathematics, the Pythagorean theorem ( American English) or Pythagoras' theorem ( British English) is a relation in Euclidean geometry

While the theorem that now bears his name was known and previously utilized by the Babylonians, and Indians, he, or his students, are thought to have constructed the first proof. 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. Biography Early life Birth and family Plato was born in Athens Greece This attribution has stuck, down the centuries up to modern times. ^[4] 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. Marcus Tullius Cicero ( Classical Latin ˈkikeroː usually ˈsɪsərəʊ in English January 3, 106 BC &ndash December 7, 43 BC was a Roman Lucius Mestrius Plutarchus ( Greek: Μέστριος Πλούταρχος c

Today, Pythagoras is revered as a prophet by the Ahl al-Tawhid or Druze faith along with his fellow Greek, Plato. The Druze ( Arabic: درزي derzī or durzī, plural دروز durūz) are a religious community found primarily in Syria, Lebanon The Druze ( Arabic: درزي derzī or durzī, plural دروز durūz) are a religious community found primarily in Syria, Lebanon 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". Heraclitus of Ephesus ( Ancient Greek: &mdash grc-Latn ''Hērákleitos ho Ephésios'' English Heraclitus the Ephesian) (ca Hesiod ( Greek: Hesiodos) was an early Greek Poet and Rhapsode, who presumably lived around 700 BCE Xenophanes of Colophon ( Greek ( 570 – 480 BC was a Greek Philosopher, Poet, and social and religious Critic. ^[5]

Religion and science

Pythagoras’ religious and scientific views were, in his opinion, inseparably interconnected. However, they are looked at separately in the 21st century. Religiously, Pythagoras was a believer of metempsychosis. Reincarnation Metempsychosis is a philosophical term in the Greek language referring to the belief of Transmigration of the soul, especially its Reincarnation 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 was one of the first to propose that the thought processes and the soul were located in the brain and not the heart. 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.

One of Pythagoras' beliefs was that the essence of being is number. Thus, being relies on stability of all things that create the universe. Things like health relied on a stable proportion of elements; too much or too little of one thing causes an imbalance that makes a being unhealthy. Pythagoras viewed thinking as the calculating with the idea numbers. When combined with the Folk theories, the philosophy evolves into a belief that Knowledge of the essence of being can be found in the form of numbers. If this is taken a step further, one can say that because mathematics is an unseen essence, the essence of being is an unseen characteristic that can be encountered by the study of mathematics.

Literary works

No texts by Pythagoras survive, although forgeries under his name — a few of which remain extant — did circulate in antiquity. Classical antiquity (also the classical era or classical period) is a broad term for a long period of cultural History centered on the Mediterranean Critical ancient sources like Aristotle and Aristoxenus cast doubt on these writings. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. For the 1st century physician of Asia Minor see Aristoxenus (physician. 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. Publius Ovidius Naso ( March 20, 43 BC – 17 AD was a Roman poet known to the English -speaking world as Ovid who wrote on many topics including The Metamorphoses by the Roman poet Ovid is a narrative poem Pythagoras has been quoted as saying, "No man is free who cannot command himself. "

Lore

There is another side to Pythagoras, as he became the subject of elaborate legends surrounding his historic persona. Aristotle described Pythagoras as 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. ^[6] 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. Brewer's Dictionary of Phrase and Fable, sometimes referred to simply as Brewer's — is a Reference work containing definitions and explanations of many ^[7]

Another legend, also taken from Brewer's Dictionary, 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. ^[8]

Other accomplishments

The number is irrational.

One of Pythagoras's major accomplishments was the discovery that music was based on proportional intervals of the numbers one through four. He believed 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. Odd numbers were masculine and even were feminine. He discovered the theory of mathematical proportions, constructed from three to five geometrical solids. One of his order, Hippasos, also discovered irrational numbers, but the idea was unthinkable to Pythagoras, and according to one version this member was executed. Hippasus of Metapontum (Ίππασος b c 500 BC in Magna Graecia, was a Greek Philosopher. In Mathematics, an irrational number is any Real number that is not a Rational number — that is it is a number which cannot be expressed as a fraction Pythagoras (or the Pythagoreans) also discovered square numbers. They found that if one took, for example, four small stones and arranged them into a square, each side of the square was not only equivalent to the other, but that when the two sides were multiplied together, they equaled the sum total of stones in the square arrangement, hence the name "Square Root"^[9]. 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. He 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 his belief in the Limited-Unlimited.

Groups influenced by Pythagoras

Influence on Plato

Pythagoras or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of Plato. Biography Early life Birth and family Plato was born in Athens Greece 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. Richard Mervyn Hare ( 21 March 1919  &ndash 29 January 2002) was an English moral philosopher who held the post of White's The Republic ( Greek: / Politeía, meaning "political system" Latin: Res Publica, meaning "public business" or 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". Science (from the Latin scientia, meaning " Knowledge " or "knowing" is the effort to discover, and increase human understanding Morality (from the Latin la moralitas "manner character proper behavior" has three principal meanings c) Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world". The soul, according to many religious and philosophical beliefs is the self-awareness, or Consciousness, unique to a particular living It is probable that both have been influenced by Orphism. Orphism (more rarely Orphicism) is the name given to a set of religious beliefs and practices in the ancient Greek and Thracian world associated with literature ^[10]

Plato's harmonics were clearly influenced by the work of Archytas, a genuine Pythagorean of the third generation, who made important contributions to geometry, reflected in Book VIII of Euclid's Elements. Archytas (Ἀρχύτας 428 BC – 347 BC was an Ancient Greek Philosopher, Mathematician, Astronomer, Statesman, and strategist Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry

Roman influence

In the legends of ancient Rome, Numa Pompilius, the second King of Rome, is said to have studied under Pythagoras. Ancient Rome was a Civilization that grew out of a small agricultural community founded on the Italian Peninsula as early as the 10th century BC Numa Pompilius, according to Legend, was the second King of Rome, succeeding Romulus. This is unlikely, since the commonly accepted dates for the two lives do not overlap.

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. Numerology is any of many Systems Traditions or Beliefs in a mystical or Esoteric relationship between Numbers and physical The Middle East is a Subcontinent with no clear boundaries often used as a synonym to Near East, in opposition to Far East. The 8th-century Muslim alchemist Jabir ibn Hayyan grounded his work in an elaborate numerology greatly influenced by Pythagorean theory. The 8th century is the period from 701 to 800 in accordance with the Julian calendar in the Christian / Common Era. A Muslim (مسلم pronounced Muslim, not Muzlim) is an adherent of the Religion Alchemy a part of the Occult Tradition is both a philosophy and a practice with an ultimately unknown aim involving the improvement of the alchemist as well as the making of For the 12th century astronomer see Jabir ibn Aflah. For the anonymous 14th century Spanish alchemist see Pseudo-Geber.

See also

Notes

References

Primary sources

No primary sources about Pythagoras have survived. This article describes the classical interpretation of Pythagoras, which is based on a small set of texts written between 150 AD and 450 AD. As these texts were written 600 to 1000 years after Pythagoras is said to have lived, their accuracy is uncertain.

It is postulated that the classical Pythagoras did not exist prior to these biographies: many of the discoveries and life details they attributed to Pythagoras may have been those of other Pythagoreans, if not fiction. This would explain the lack of reference to a man Pythagoras until 150 AD, given that he would have been of interest to contemporary philosophers (Aristotle referred to the so-called Pythagoreans). It is suggested that the mathematical significance of the early Pythagoreans (pre 450 BC) has been exaggerated (with the exception of their theory of harmonics), and that the Pythagoreans were an Orphic-like cult with an emphasis on numerology who only later evolved into serious mathematicians as geometry became popular across Greece. Orphism (more rarely Orphicism) is the name given to a set of religious beliefs and practices in the ancient Greek and Thracian world associated with literature Numerology is any of many Systems Traditions or Beliefs in a mystical or Esoteric relationship between Numbers and physical

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. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. 350 BC

Classical secondary sources

Modern secondary sources

External links

• “Other Lives” by M. F. Burnyeat, an article about current Pythagoras scholarship
• Pythagoreanism Web Site
• References for Pythagoras
• Pythagoras, Internet 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
• The Complete Pythagoras, an on-line book containing all survived biographies and Pythagorean fragments.
• Pythagoras and the Pythagoreans, Department of Mathematics, Texas A&M University
• Pythagoras and Pythagoreanism, The Catholic Encyclopedia
• Pythagoreanism Web Article
• Occult conception of Pythagoreanism
• Pythagoras of Samos
• Stanford Encyclopedia of Philosophy entry
• Tetraktys
• Golden Verses of Pythagoras
• Pythagoras on Vegetarianism Quotes from primary source historical literature on Pythagoras' view on Vegetarianism, Justice and Kindness
• Wandering Souls: The Doctrine of Transmigration in Pythagorean Philosophy, by Dr. James Luchte