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132-461: Laërtius must have lived after Sextus Empiricus (c. 200), whom he mentions, and before Stephanus of Byzantium and Sopater of Apamea (c. 500), who quote him. His work makes no mention of Neoplatonism , even though it is addressed to a woman who was "an enthusiastic Platonist". Hence he is assumed to have flourished in the first half of the 3rd century, during the reign of Alexander Severus (222–235) and his successors. The precise form of his name

264-563: A Sonchis of Sais ). According to the Christian theologian Clement of Alexandria ( c.  150  – c.  215  AD), "Pythagoras was a disciple of Sonchis, an Egyptian archprophet, as well as a Plato of Sechnuphis ." Some ancient writers claimed that Pythagoras learned geometry and the doctrine of metempsychosis from the Egyptians. Other ancient writers, however, claimed that Pythagoras had learned these teachings from

396-569: A pseudepigraphal poem. Empedocles , who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical. By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals. The identity of the morning star and evening star was known to the Babylonians over a thousand years earlier. Sizeable Pythagorean communities existed in Magna Graecia, Phlius , and Thebes during

528-515: A Scythian priest of Apollo by the name of Abaris the Hyperborean : Abaris stayed with Pythagoras, and was compendiously taught physiology and theology; and instead of divining by the entrails of beasts, he revealed to him the art of prognosticating by numbers, conceiving this to be a method purer, more divine, and more kindred to the celestial numbers of the Gods. This shouldn't be confused with

660-547: A close friend of Plato and he is quoted in Plato's Republic . Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans. Cicero repeats this statement, remarking that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean"). According to Charles H. Kahn , Plato's middle dialogues, including Meno , Phaedo , and The Republic , have

792-422: A deadly snake bit Pythagoras, he bit it back and killed it. Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans and that he once convinced a notoriously destructive bear to swear that it would never harm a living thing again, and that the bear kept its word. Riedweg suggests that Pythagoras may have personally encouraged these legends, but Gregory states that there

924-412: A different interpretation, according to which Sextus does allow beliefs, so long as they are not derived by reason, philosophy or speculation; a skeptic may, for example, accept common opinions in the skeptic's society. The important difference between the skeptic and the dogmatist is that the skeptic does not hold his beliefs as a result of rigorous philosophical investigation. Diogenes Laërtius and

1056-462: A divine figure, sent by the gods to benefit humankind. Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time. For Pythagoreans, the highest reward a human could attain was for their soul to join in the life of the gods and thus escape the cycle of reincarnation. Two groups existed within early Pythagoreanism:

1188-526: A dozen. Georg Wilhelm Friedrich Hegel (1770–1831) criticized Diogenes Laërtius for his lack of philosophical talent and categorized his work as nothing more than a compilation of previous writers' opinions. Nonetheless, he admitted that Diogenes Laërtius's compilation was an important one given the information that it contained. Hermann Usener (1834–1905) deplored Diogenes Laërtius as a "complete ass" ( asinus germanus ) in his Epicurea (1887). Werner Jaeger (1888–1961) damned him as "that great ignoramus". In

1320-433: A five-year initiation period, during which they were required to remain silent. Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women and female members of Pythagoras's school appear to have played an active role in its operations. Iamblichus provides a list of 235 famous Pythagoreans, seventeen of whom are women. In later times, many prominent female philosophers contributed to

1452-479: A fragment, Aristotle writes that Pythagoras had a golden thigh, which he publicly exhibited at the Olympic Games and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo". Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications. He was supposedly once seen at both Metapontum and Croton at

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1584-489: A golden wreath atop his head and to have worn trousers after the fashion of the Thracians . Diogenes Laërtius presents Pythagoras as having exercised remarkable self-control ; he was always cheerful, but "abstained wholly from laughter, and from all such indulgences as jests and idle stories". Pythagoras was said to have had extraordinary success in dealing with animals. A fragment from Aristotle records that, when

1716-459: A lady of Crete and the daughter of Pythenax and had several children with her. Porphyry writes that Pythagoras had two sons named Telauges and Arignote , and a daughter named Myia, who "took precedence among the maidens in Croton and, when a wife, among married women." Iamblichus mentions none of these children and instead only mentions a son named Mnesarchus after his grandfather. This son

1848-436: A lawgiver. The so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything. According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons, devoid of practical application. They believed that all things were made of numbers. The number one (the monad ) represented

1980-601: A major revival in the first century BC among Middle Platonists , coinciding with the rise of Neopythagoreanism . Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus , Johannes Kepler , and Isaac Newton . Pythagorean symbolism was also used throughout early modern European esotericism , and his teachings as portrayed in Ovid 's Metamorphoses would later influence

2112-537: A new body. This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus. Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur. Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations. Diogenes Laërtius reports an account from Heraclides Ponticus that Pythagoras told people that he had lived four previous lives that he could remember in detail. The first of these lives

2244-489: A person should always put the right sandal on before the left. The exact meanings of these sayings, however, are frequently obscure. Iamblichus preserves Aristotle's descriptions of the original, ritualistic intentions behind a few of these sayings, but these apparently later fell out of fashion, because Porphyry provides markedly different ethical-philosophical interpretations of them: New initiates were allegedly not permitted to meet Pythagoras until after they had completed

2376-405: A popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole hecatomb , to the gods. Cicero rejected this story as spurious because of the much more widely held belief that Pythagoras forbade blood sacrifices. Porphyry attempted to explain the story by asserting that the ox was actually made of dough . The Pythagorean theorem was known and used by

2508-640: A proclivity towards tyranny. Other accounts claim that Pythagoras left Samos because he was so overburdened with public duties in Samos, because of the high estimation in which he was held by his fellow-citizens. He arrived in the Greek colony of Croton (today's Crotone , in Calabria ) in what was then Magna Graecia . All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment. He served as an advisor to

2640-510: A result of Pherecydes's influence. Another story, which may be traced to the Neopythagorean philosopher Nicomachus , tells that, when Pherecydes was old and dying on the island of Delos , Pythagoras returned to care for him and pay his respects. Duris , the historian and tyrant of Samos, is reported to have patriotically boasted of an epitaph supposedly penned by Pherecydes which declared that Pythagoras's wisdom exceeded his own. On

2772-572: A school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem , Pythagorean tuning , the five regular solids , the Theory of Proportions , the sphericity of the Earth , and the identity of the morning and evening stars as the planet Venus . It

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2904-428: A secure basis for philosophy, science, and morality. Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world" and both were probably influenced by Orphism . The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans. Bertrand Russell , in his A History of Western Philosophy , contends that

3036-562: A simplified version known today as " Pythagorean numerology ", involving a variant of an isopsephic technique known – among other names – as pythmenes ' roots ' or ' base numbers ' , by means of which the base values of letters in a word were mathematically reduced by addition or division, in order to obtain a single value from one to nine for the whole name or word; these 'roots' or 'base numbers' could then be interpreted with other techniques, such as traditional Pythagorean attributions. This latter form of numerology flourished during

3168-479: A specific building that was still in use during his own time, appears to be motivated by Samian patriotic interest. Around 530 BC, when Pythagoras was about forty years old, he left Samos. His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos, Riedweg notes that this explanation closely aligns with Nicomachus's emphasis on Pythagoras's purported love of freedom, but that Pythagoras's enemies portrayed him as having

3300-474: A state of ataraxia (roughly, 'peace of mind'). There is some debate as to the extent to which Sextus advocated the suspension of judgement. According to Myles Burnyeat , Jonathan Barnes , and Benson Mates , Sextus advises that we should suspend judgment about virtually all beliefs; that is to say, we should neither affirm any belief as true nor deny any belief as false, since we may live without any beliefs, acting by habit. Michael Frede , however, defends

3432-423: A strong "Pythagorean coloring", and his last few dialogues (particularly Philebus and Timaeus ) are extremely Pythagorean in character. According to R. M. Hare , Plato's Republic may be partially based on the "tightly organised community of like-minded thinkers" established by Pythagoras at Croton. Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are

3564-534: A synthesis of everything Pythagoras had learned from Orpheus, from the Egyptian priests, from the Eleusinian Mysteries , and from other religious and philosophical traditions. Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent. Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros

3696-472: A vow of silence that they would not reveal these symbols to non-members. Those who did not obey the laws of the community were expelled and the remaining members would erect tombstones for them as though they had died. A number of "oral sayings" ( akoúsmata ) attributed to Pythagoras have survived, dealing with how members of the Pythagorean community should perform sacrifices, how they should honor

3828-743: A will to objectivity and fact-checking, Diogenes's works are today seen as generally unreliable from a historical perspective. He is neither consistent nor reliable in some of his reports and some of the details he cites contain obvious errors. Some of them were probably introduced by copyists in the transmission of the text from antiquity, but some errors are undoubtedly due to Diogenes himself. The reliability of Diogenes' sources have also been questioned, since he uses comic poets as sources. Professor Brian Gregor suggests that readers will benefit from modern scholarly assistance while reading Diogenes' biographies, since they are "notoriously unreliable". Some scholars (e.g. Delfim Leão) state that Diogenes' unreliability

3960-583: Is a less competent thinker than those on whom he writes, is less liable to re-formulate statements and arguments, and especially in the case of Epicurus, less liable to interfere with the texts he quotes. He does, however, simplify." Despite his importance to the history of western philosophy and the controversy surrounding him, according to Gian Mario Cao, Diogenes Laërtius has still not received adequate philological attention. Both modern critical editions of his book, by H. S. Long (1964) and by M. Marcovich (1999) have received extensive criticism from scholars. He

4092-563: Is commonly doubted. In his medical work, as reflected by his name, tradition maintains that he belonged to the Empiric school in which Pyrrhonism was popular. However, at least twice in his writings, Sextus seems to place himself closer to the Methodic school . As a skeptic, Sextus Empiricus raised concerns which applied to all types of knowledge. He doubted the validity of induction long before its best known critic David Hume , and raised

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4224-431: Is criticized primarily for being overly concerned with superficial details of the philosophers' lives and lacking the intellectual capacity to explore their actual philosophical works with any penetration. However, according to statements of the 14th-century monk Walter Burley in his De vita et moribus philosophorum , the text of Diogenes seems to have been much fuller than that which we now possess. Although Diogenes had

4356-554: Is dated to the 13th century, and is in the Laurentian Library . The titles for the individual biographies used in modern editions are absent from these earliest manuscripts, however they can be found inserted into the blank spaces and margins of manuscript P by a later hand. There seem to have been some early Latin translations, but they no longer survive. A 10th-century work entitled Tractatus de dictis philosophorum shows some knowledge of Diogenes. Henry Aristippus , in

4488-626: Is devoted to Epicurus, and contains three long letters written by Epicurus, which explain Epicurean doctrines. His chief authorities were Favorinus and Diocles of Magnesia , but his work also draws (either directly or indirectly) on books by Antisthenes of Rhodes , Alexander Polyhistor , and Demetrius of Magnesia , as well as works by Hippobotus , Aristippus , Panaetius , Apollodorus of Athens , Sosicrates , Satyrus , Sotion , Neanthes , Hermippus , Antigonus , Heraclides , Hieronymus , and Pamphila . There are many extant manuscripts of

4620-520: Is impartial to all schools, in the manner of the Pyrrhonists, and he carries the succession of Pyrrhonism further than that of the other schools. At one point, he even seems to refer to the Pyrrhonists as "our school." On the other hand, most of these points can be explained by the way he uncritically copies from his sources. It is by no means certain that he adhered to any school, and he is usually more attentive to biographical details. In addition to

4752-462: Is incomplete and breaks off during the life of Chrysippus . From a table of contents in one of the manuscripts (manuscript P), this book is known to have continued with Zeno of Tarsus , Diogenes , Apollodorus , Boethus , Mnesarchus , Mnasagoras , Nestor , Basilides , Dardanus , Antipater , Heraclides , Sosigenes , Panaetius , Hecato , Posidonius , Athenodorus , another Athenodorus , Antipater , Arius , and Cornutus . The whole of Book X

4884-444: Is known as Pyrrhonian skepticism , which Sextus differentiated from Academic skepticism as practiced by Carneades which, according to Sextus, denies the possibility of knowledge altogether, something that Sextus criticized as being an affirmative belief. Instead, Sextus advocates simply giving up belief; in other words, suspending judgment ( epoché ) about whether or not anything is knowable. Only by suspending judgment can we attain

5016-413: Is mentioned most often. Similar miracle stories were told about both Pythagoras and Pherecydes, including one in which the hero predicts a shipwreck, one in which he predicts the conquest of Messina , and one in which he drinks from a well and predicts an earthquake. Apollonius Paradoxographus , a paradoxographer who may have lived in the second century BC, identified Pythagoras's thaumaturgic ideas as

5148-478: Is no direct evidence of this. Anti-Pythagorean legends were also circulated. Diogenes Laërtes retells a story told by Hermippus of Samos, which states that Pythagoras had once gone into an underground room, telling everyone that he was descending to the underworld. He stayed in this room for months, while his mother secretly recorded everything that happened during his absence. After he returned from this room, Pythagoras recounted everything that had happened while he

5280-461: Is not entirely his responsibility and blame his sources instead. Attribution: Sextus Empiricus Sextus Empiricus ( ‹See Tfd› Greek : Σέξτος Ἐμπειρικός , Sextos Empeirikos ; fl.  mid-late 2nd century AD ) was a Greek Pyrrhonist philosopher and Empiric school physician with Roman citizenship . His philosophical works are the most complete surviving account of ancient Greek and Roman Pyrrhonism , and because of

5412-510: Is the one from Diogenes Laërtius 's Lives and Opinions of Eminent Philosophers . The two later biographies were written by the Neoplatonist philosophers Porphyry and Iamblichus and were partially intended as polemics against the rise of Christianity . The later sources are much lengthier than the earlier ones, and even more fantastic in their descriptions of Pythagoras's achievements. Porphyry and Iamblichus used material from

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5544-605: Is uncertain. The ancient manuscripts invariably refer to a "Laertius Diogenes", and this form of the name is repeated by Sopater and the Suda . The modern form "Diogenes Laertius" is much rarer, used by Stephanus of Byzantium, and in a lemma to the Greek Anthology . He is also referred to as "Laertes" or simply "Diogenes". The origin of the name "Laertius" is also uncertain. Stephanus of Byzantium refers to him as "Διογένης ὁ Λαερτιεύς" ( Diogenes ho Laertieus ), implying that he

5676-539: Is unknown how much of the total work has been lost. The supposed general title of this partially lost work is Skeptical Treatises' ( Σκεπτικὰ Ὑπομνήματα / Skeptika Hypomnēmata ). An influential Latin translation of Sextus's Outlines was published by Henricus Stephanus in Geneva in 1562, and this was followed by a complete Latin Sextus with Gentian Hervet as translator in 1569. Petrus and Jacobus Chouet published

5808-777: The Protrepticus . Aristotle's disciples Dicaearchus , Aristoxenus , and Heraclides Ponticus (who all lived in the 3rd century BC) also wrote on the same subject. Most of the major sources on Pythagoras's life are from the Roman period , by which point, according to the German classicist Walter Burkert , "the history of Pythagoreanism was already   ... the laborious reconstruction of something lost and gone." Three ancient biographies of Pythagoras have survived from late antiquity, all of which are filled primarily with myths and legends. The earliest and most respectable of these

5940-467: The Babylonians and Indians centuries before Pythagoras, but he may have been the first to introduce it to the Greeks. Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof . Burkert rejects this suggestion as implausible, noting that Pythagoras was never credited with having proved any theorem in antiquity. Furthermore, the manner in which

6072-639: The Byzantine era , and was first attested among the Gnostics of the second century AD. By that time, isopsephy had developed into several different techniques that were used for a variety of purposes; including divination, doctrinal allegory, and medical prognosis and treatment. 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

6204-492: The Celts and Iberians . Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers. Some identify Hermodamas of Samos as a possible tutor. Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer . Others credit Bias of Priene , Thales, or Anaximander (a pupil of Thales). Other traditions claim

6336-620: The Lives , although none of them are especially old, and they all descend from a common ancestor, because they all lack the end of Book VII. The three most useful manuscripts are known as B, P, and F. Manuscript B ( Codex Borbonicus ) dates from the 12th century, and is in the National Library of Naples . Manuscript P ( Paris ) is dated to the 11th/12th century, and is in the Bibliothèque nationale de France . Manuscript F ( Florence )

6468-623: The Lives and Opinions of Eminent Philosophers in Book 2 of his Libri della famiglia and modeled his own autobiography on Diogenes Laërtius's Life of Thales . Diogenes Laërtius's work has had a complicated reception in modern times. The value of his Lives and Opinions of Eminent Philosophers as an insight into the private lives of the Greek sages led the French Renaissance philosopher Michel de Montaigne (1533–1592) to exclaim that he wished that, instead of one Laërtius, there had been

6600-414: The Lives, Diogenes refers to another work that he had written in verse on famous men, in various metres, which he called Epigrammata or Pammetros (Πάμμετρος). The work by which he is known, Lives and Opinions of Eminent Philosophers ( ‹See Tfd› Greek : Βίοι καὶ γνῶμαι τῶν ἐν φιλοσοφίᾳ εὐδοκιμησάντων ; Latin : Vitae Philosophorum ), was written in Greek and professes to give an account of

6732-689: The Magi in Persia or even from Zoroaster himself. Diogenes Laërtius asserts that Pythagoras later visited Crete , where he went to the Cave of Ida with Epimenides . The Phoenicians are reputed to have taught Pythagoras arithmetic and the Chaldeans to have taught him astronomy. By the third century BC, Pythagoras was already reported to have studied under the Jews as well. Contradicting all these reports,

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6864-526: The Suda report that Sextus Empiricus wrote ten books on Pyrrhonism. The Suda also says Sextus wrote a book Ethica . Sextus Empiricus's three surviving works are the Outlines of Pyrrhonism ( Πυῤῥώνειοι ὑποτυπώσεις , Pyrrhōneioi hypotypōseis , thus commonly abbreviated PH ), and two distinct works preserved under the same title, Adversus Mathematicos ( Πρὸς μαθηματικούς , Pros mathematikous , commonly abbreviated "AM" or "M" and known as Against Those in

6996-466: The mathematikoi ("learners") and the akousmatikoi ("listeners"). The akousmatikoi are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings; whereas the mathematikoi are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific. Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed

7128-834: The planets move according to mathematical equations and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras developed the numerological and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly Philolaus of Croton . Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy , and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or he may have escaped to Metapontum and died there. Pythagoras influenced Plato, whose dialogues , especially his Timaeus , exhibit Pythagorean teachings. Pythagorean ideas on mathematical perfection also impacted ancient Greek art . His teachings underwent

7260-514: The regress argument against all forms of reasoning: Those who claim for themselves to judge the truth are bound to possess a criterion of truth. This criterion, then, either is without a judge's approval or has been approved. But if it is without approval, whence comes it that it is trustworthy? For no matter of dispute is to be trusted without judging. And, if it has been approved, that which approves it, in turn, either has been approved or has not been approved, and so on ad infinitum . This view

7392-707: The "Italian" begins with Pythagoras and ends with Epicurus . The Socratic school , with its various branches, is classed with the Ionic; while the Eleatics and Pyrrhonists are treated under the Italic. He also includes his own poetic verse, albeit pedestrian, about the philosophers he discusses. The work contains incidental remarks on many other philosophers, and there are useful accounts concerning Hegesias , Anniceris , and Theodorus ( Cyrenaics ); Persaeus (Stoic); and Metrodorus and Hermarchus (Epicureans). Book VII

7524-429: The 12th century, is known to have translated at least some of the work into Latin, and in the 14th century an unknown author made use of a Latin translation for his De vita et moribus philosophorum (attributed erroneously to Walter Burley ). The first printed editions were Latin translations. The first, Laertii Diogenis Vitae et sententiae eorum qui in philosophia probati fuerunt (Romae: Giorgo Lauer, 1472), printed

7656-617: The Babylonians employed 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. Pythagoras's biographers state that he also was the first to identify the five regular solids and that he was the first to discover the Theory of Proportions . According to legend, Pythagoras discovered that musical notes could be translated into mathematical equations when he passed blacksmiths at work one day and heard

7788-679: The Disciplines, or Against the Mathematicians ). Adversus Mathematicos is incomplete as the text references parts that are not in the surviving text. Adversus Mathematicos also includes mentions of three other works which did not survive: The surviving first six books of Adversus Mathematicos are commonly known as Against the Professors . Each book also has a traditional title; although none of these titles except Pros mathematikous and Pyrrhōneioi hypotypōseis are found in

7920-444: The Egyptian priests at Diospolis (Thebes), and that he was the only foreigner ever to be granted the privilege of taking part in their worship. The Middle Platonist biographer Plutarch ( c.  46  – c.  120  AD) writes in his treatise On Isis and Osiris that, during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of Heliopolis (meanwhile Solon received lectures from

8052-469: The Greek text for the first time in 1621. Stephanus did not publish it with his Latin translation either in 1562 or in 1569, nor was it published in the reprint of the latter in 1619. Sextus's Outlines were widely read in Europe during the 16th, 17th and 18th centuries, and had a profound effect on Michel de Montaigne , David Hume and Georg Wilhelm Friedrich Hegel , among many others. Another source for

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8184-527: The Pythagoreans during one of their meetings, either in the house of Milo or in some other meeting-place. Accounts of the attack are often contradictory and many probably confused it with the later anti-Pythagorean rebellions, such as the one in Metapontum in 454 BC. The building was apparently set on fire, and many of the assembled members perished; only the younger and more active members managed to escape. Sources disagree regarding whether Pythagoras

8316-659: The Renaissance, French philosophy has been continuously influenced by Sextus: Montaigne in the 16th century, Descartes , Blaise Pascal , Pierre-Daniel Huet and François de La Mothe Le Vayer in the 17th century, many of the "Philosophes", and in recent times controversial figures such as Michel Onfray , in a direct line of filiation between Sextus' radical skepticism and secular or even radical atheism. Pythagoras Pythagoras of Samos ( Ancient Greek : Πυθαγόρας ; c.  570  – c.  495  BC)

8448-527: The age of 40, which would give a date of birth around 570 BC. Pythagoras's name led him to be associated with Pythian Apollo ( Pūthíā ); Aristippus of Cyrene in the 4th century BC explained his name by saying, "He spoke [ ἀγορεύω , agoreúō ] the truth no less than did the Pythian [ πυθικός puthikós ]". During Pythagoras's formative years, Samos was a thriving cultural hub known for its feats of advanced architectural engineering, including

8580-525: The ancient world. His home town is unknown (at best uncertain, even according to a hypothesis that Laertius refers to his origin). A disputed passage in his writings has been used to suggest that it was Nicaea in Bithynia . It has been suggested that Diogenes was an Epicurean or a Pyrrhonist . He passionately defends Epicurus in Book 10, which is of high quality and contains three long letters attributed to Epicurus explaining Epicurean doctrines. He

8712-527: The arguments they contain against the other Hellenistic philosophies , they are also a major source of information about those philosophies. Little is known about Sextus Empiricus. He likely lived in Alexandria , Rome , or Athens . His Roman name, Sextus , implies he was a Roman citizen. The Suda , a 10th-century Byzantine encyclopedia, states that he was the same person as Sextus of Chaeronea , as do other pre-modern sources, but this identification

8844-431: The boys' "raging willfulness" was quelled. The Pythagoreans also placed particular emphasis on the importance of physical exercise ; therapeutic dancing , daily morning walks along scenic routes , and athletics were major components of the Pythagorean lifestyle. Moments of contemplation at the beginning and end of each day were also advised. Pythagorean teachings were known as "symbols" ( symbola ) and members took

8976-566: The building of the Tunnel of Eupalinos , and for its riotous festival culture. It was a major center of trade in the Aegean where traders brought goods from the Near East . According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions. Pythagoras's early life also coincided with the flowering of early Ionian natural philosophy . He

9108-568: The circulation of Sextus's ideas was Pierre Bayle 's Dictionary . The legacy of Pyrrhonism is described in Richard Popkin 's The History of Skepticism from Erasmus to Descartes and High Road to Pyrrhonism . The transmission of Sextus's manuscripts through antiquity and the Middle Ages is reconstructed by Luciano Floridi 's Sextus Empiricus, The Recovery and Transmission of Pyrrhonism (Oxford: Oxford University Press , 2002). Since

9240-463: The city of Metapontum , where they took shelter in the temple of the Muses and died there of starvation after forty days without food. Another tale recorded by Porphyry claims that, as Pythagoras's enemies were burning the house, his devoted students laid down on the ground to make a path for him to escape by walking over their bodies across the flames like a bridge. Pythagoras managed to escape, but

9372-413: The development of Neopythagoreanism . Pythagoreanism also entailed a number of dietary prohibitions. It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beans and the meat of non-sacrificial animals such as fish and poultry. Both of these assumptions, however, have been contradicted. Pythagorean dietary restrictions may have been motivated by belief in

9504-449: The doctrine of metempsychosis . Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet. Eudoxus of Cnidus , a student of Archytas, writes, "Pythagoras was distinguished by such purity and so avoided killing and killers that he not only abstained from animal foods, but even kept his distance from cooks and hunters." Other authorities contradict this statement. According to Aristoxenus , Pythagoras allowed

9636-420: The earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras. The Athenian rhetorician Isocrates ( c.  436  – c.  338  BC) was the first to describe Pythagoras as having visited Egypt. Aristotle ( c.  384  – c.  322  BC) wrote a treatise On the Pythagoreans , which no longer exists. Some of it may be preserved in

9768-399: The early fourth century BC. Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia. According to later tradition, Archytas was elected as strategos ("general") seven times, even though others were prohibited from serving more than a year. Archytas was also a renowned mathematician and musician. He was

9900-531: The elites in Croton and gave them frequent advice. Later biographers tell fantastical stories of the effects of his eloquent speeches 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. Diogenes Laërtius states that Pythagoras "did not indulge in the pleasures of love" and that he cautioned others to only have sex "whenever you are willing to be weaker than yourself". According to Porphyry, Pythagoras married Theano ,

10032-418: The exact details of Pythagoras's teachings are uncertain, it is possible to reconstruct a general outline of his main ideas. Aristotle writes at length about the teachings of the Pythagoreans, but without mentioning Pythagoras directly. One of Pythagoras's main doctrines appears to have been metempsychosis , the belief that all souls are immortal and that, after death, a soul is transferred into

10164-476: The exclusion of outsiders. Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans . One Pythagorean maxim was " koinà tà phílōn " ("All things in common among friends"). Both Iamblichus and Porphyry provide detailed accounts of the organization of the school, although the primary interest of both writers is not historical accuracy, but rather to present Pythagoras as

10296-478: The fields of music , astronomy , and medicine . Since at least the first century BC, 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 is equal [to the sum of] the squares of the two other sides" —that is, a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} . According to

10428-465: The first to teach that the Earth was spherical , the first to divide the globe into five climatic zones , and the first to identify the morning star and the evening star as the same celestial object (now known as Venus ). Of the two philosophers, Parmenides has a much stronger claim to having been the first and the attribution of these discoveries to Pythagoras seems to have possibly originated from

10560-399: The format and content of Laertius's work into English, but Stanley compiled his book from a number of classical biographies of philosophers. The first complete English translation was a late 17th-century translation by ten different persons. A better translation was made by Charles Duke Yonge (1853), but although this was more literal, it still contained many inaccuracies. The next translation

10692-461: The gods, how they should "move from here", and how they should be buried. Many of these sayings emphasize the importance of ritual purity and avoiding defilement. For instance, a saying which Leonid Zhmud concludes can probably be genuinely traced back to Pythagoras himself forbids his followers from wearing woolen garments. Other extant oral sayings forbid Pythagoreans from breaking bread, poking fires with swords, or picking up crumbs and teach that

10824-490: The grounds of all these references connecting Pythagoras with Pherecydes, Riedweg concludes that there may well be some historical foundation to the tradition that Pherecydes was Pythagoras's teacher. Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis. Before 520 BC, on one of his visits to Egypt or Greece, Pythagoras might have met Thales of Miletus , who would have been around fifty-four years older than him. Thales

10956-420: The historian Herodotus of Halicarnassus ( c.  484  – c.  420  BC), who describes him as one of the greatest Greek teachers and states that Pythagoras taught his followers how to attain immortality . The accuracy of the works of Herodotus is controversial. The writings attributed to the Pythagorean philosopher Philolaus of Croton ( c.  470  – c.  385  BC) are

11088-411: The influence of Pythagoras on Plato and others was so great that he should be considered the most influential philosopher of all time. He concludes that "I do not know of any other man who has been as influential as he was in the school of thought." A revival of Pythagorean teachings occurred in the first century BC when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed

11220-809: The late 1150s, which has since been lost or destroyed. Geremia da Montagnone used this translation as a source for his Compedium moralium notabilium ( c.  1310 ) and an anonymous Italian author used it as a source for work entitled Liber de vita et moribus philosophorum (written c. 1317–1320), which reached international popularity in the Late Middle Ages . The monk Ambrogio Traversari (1386–1439) produced another Latin translation in Florence between 1424 and 1433, for which far better records have survived. The Italian Renaissance scholar, painter, philosopher, and architect Leon Battista Alberti (1404–1472) borrowed from Traversari's translation of

11352-424: The late twentieth and early twenty-first centuries, however, scholars have managed to partially redeem Diogenes Laertius's reputation as a writer by reading his book in a Hellenistic literary context. Nonetheless, modern scholars treat Diogenes's testimonia with caution, especially when he fails to cite his sources. Herbert S. Long warns: "Diogenes has acquired an importance out of all proportion to his merits because

11484-513: The lives and opinions of the Greek philosophers. Although it is at best an uncritical and unphilosophical compilation, its value, as giving us an insight into the private lives of the Greek sages, led Montaigne to write that he wished that instead of one Laërtius there had been a dozen. On the other hand, modern scholars have advised that we treat Diogenes' testimonia with care, especially when he fails to cite his sources: "Diogenes has acquired an importance out of all proportion to his merits because

11616-628: The loss of many primary sources and of the earlier secondary compilations has accidentally left him the chief continuous source for the history of Greek philosophy". Diogenes divides his subjects into two "schools" which he describes as the Ionian/Ionic and the Italian/Italic; the division is somewhat dubious and appears to be drawn from the lost doxography of Sotion . The biographies of the "Ionian school" begin with Anaximander and end with Clitomachus , Theophrastus and Chrysippus ;

11748-563: The loss of many primary sources and of the earlier secondary compilations has accidentally left him the chief continuous source for the history of Greek philosophy." Robert M. Strozier offers a somewhat more positive assessment of Diogenes Laertius's reliability, noting that many other ancient writers attempt to reinterpret and expand on the philosophical teachings they describe, something which Diogenes Laërtius rarely does. Strozier concludes, "Diogenes Laertius is, when he does not conflate hundreds of years of distinctions, reliable simply because he

11880-439: The lost writings of Aristotle's disciples (Dicaearchus, Aristoxenus, and Heraclides) and material taken from these sources is generally considered to be the most reliable. There is not a single detail in the life of Pythagoras that stands uncontradicted. But it is possible, from a more or less critical selection of the data, to construct a plausible account. Herodotus , Isocrates , and other early writers agree that Pythagoras

12012-459: The manuscripts. Adversus Mathematicos I–VI is sometimes distinguished from Adversus Mathematicos VII–XI by using another title, Against the Dogmatists ( Πρὸς δογματικούς , Pros dogmatikous ) and then the remaining books are numbered as I–II, III–IV, and V, despite the fact that it is commonly inferred that what we have is just part of a larger work whose beginning is missing and it

12144-480: The modern vegetarian movement. No authentic writings of Pythagoras have survived, and almost nothing is known for certain about his life. The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical . The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by the Greek philosopher Xenophanes of Colophon ( c.  570  – c.  478  BC), who had been one of his contemporaries. In

12276-711: The mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphic Mysteries . The Neoplatonists wrote of a "sacred discourse" Pythagoras had written on the gods in the Doric Greek dialect, which they believed had been dictated to Pythagoras by the Orphic priest Aglaophamus upon his initiation to the orphic Mysteries at Leibethra . Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship. Iamblichus describes Pythagoreanism as

12408-401: The neighboring colony of Sybaris in 510 BC. After the victory, some prominent citizens of Croton proposed a democratic constitution , which the Pythagoreans rejected. The supporters of democracy, headed by Cylon and Ninon, the former of whom is said to have been irritated by his exclusion from Pythagoras's brotherhood, roused the populace against them. Followers of Cylon and Ninon attacked

12540-451: The novelist Antonius Diogenes , writing in the second century BC, reports that Pythagoras discovered all his doctrines himself by interpreting dreams . The third-century AD Sophist Philostratus claims that, in addition to the Egyptians, Pythagoras also studied under sages or gymnosophists in India . Iamblichus expands this list even further by claiming that Pythagoras also studied with

12672-499: The number philosophy attributed to him was really an innovation by Philolaus. According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics. Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, proofless arithmetic , but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics. Both Plato and Isocrates state that, above all else, Pythagoras

12804-415: The origin of all things and the number two (the dyad ) represented matter. The number three was an "ideal number" because it had a beginning, middle, and end and was the smallest number of points that could be used to define a plane triangle, which they revered as a symbol of the god Apollo . The number four signified the four seasons and the four elements . The number seven was also sacred because it

12936-481: The permanent reality behind superficial appearances. Early Archaic sculpture represents life in simple forms, and may have been influenced by the earliest Greek natural philosophies. The Greeks generally believed that nature expressed itself in ideal forms and was represented by a type ( εἶδος ), which was mathematically calculated. When dimensions changed, architects sought to relay permanence through mathematics. Maurice Bowra believes that these ideas influenced

13068-507: The poem, Xenophanes describes Pythagoras interceding on behalf of a dog that is being beaten, professing to recognize in its cries the voice of a departed friend. Alcmaeon of Croton ( fl.   c.  450  BC), a doctor who lived in Croton at around the same time Pythagoras lived there, incorporates many Pythagorean teachings into his writings and alludes to having possibly known Pythagoras personally. The poet Heraclitus of Ephesus (fl.   c.  500  BC), who

13200-549: The priestess Aristoclea ( Aristokleia ). Ancient authorities furthermore note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphic or Cretan mysteries , or the Delphic oracle . Porphyry repeats an account from Antiphon , who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle". Here, Samians debated matters of public concern. Supposedly,

13332-666: The result of confusion with a different man named Pythagoras, who was an athletics trainer. Diogenes Laërtius records Milo's wife's name as Myia. Iamblichus mentions Theano as the wife of Brontinus of Croton. Diogenes Laërtius states that the same Theano was Pythagoras's pupil and that Pythagoras's wife Theano was her daughter. Diogenes Laërtius also records that works supposedly written by Theano were still extant during his own lifetime and quotes several opinions attributed to her. These writings are now known to be pseudepigraphical . Pythagoras's emphasis on dedication and asceticism are credited with aiding in Croton's decisive victory over

13464-673: The rise of a "new" Pythagoreanism in Alexandria . At around the same time, Neopythagoreanism became prominent. The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings. The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy and probably understood the soul as a "kind of mathematical harmony". The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory. Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines. Greek sculpture sought to represent

13596-425: The same time . When Pythagoras crossed the river Kosas (the modern-day Basento ), "several witnesses" reported that they heard it greet him by name. In Roman times, a legend claimed that Pythagoras was the son of Apollo. According to Muslim tradition , Pythagoras was said to have been initiated by Hermes (Egyptian Thoth ). Pythagoras was said to have dressed all in white. He is also said to have borne

13728-451: The school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach. Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends. Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos, but cautions that Antiphon's account, which makes reference to

13860-493: The sound of their hammers clanging against the anvils. Thinking that the sounds of the hammers were beautiful and harmonious, except for one, he rushed into the blacksmith shop and began testing the hammers. He then realized that the tune played when the hammer struck was directly proportional to the size of the hammer and therefore concluded that music was mathematical. In ancient times, Pythagoras and his contemporary Parmenides of Elea were both credited with having been

13992-573: The ten books into paragraphs of equal length, and progressively numbered them, providing the system still in use today. The first critical edition of the entire text, by H.S. Long in the Oxford Classical Texts , was not produced until 1964; this edition was superseded by Miroslav Marcovich 's Teubner edition, published between 1999 and 2002. A new edition, by Tiziano Dorandi , was published by Cambridge University Press in 2013. Thomas Stanley's 1656 History of Philosophy adapts

14124-439: The theory of Pythagoras and his students, who believed that "all things are numbers". During the sixth century BC, the number philosophy of the Pythagoreans triggered a revolution in Greek sculpture. Greek sculptors and architects attempted to find the mathematical relation ( canon ) behind aesthetic perfection. Possibly drawing on the ideas of Pythagoras, the sculptor Polykleitos wrote in his Canon that beauty consists in

14256-477: The tradition linking Pythagoras to the tetractys is probably genuine. Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton . In his landmark study Lore and Science in Ancient Pythagoreanism , Walter Burkert argues that Pythagoras was a charismatic political and religious teacher, but that

14388-525: The translation of Ambrogio Traversari (whose manuscript presentation copy to Cosimo de' Medici was dated February 8, 1433) and was edited by Elio Francesco Marchese. The Greek text of the lives of Aristotle and Theophrastus appeared in the third volume of the Aldine Aristotle in 1497. The first edition of the whole Greek text was that published by Hieronymus Froben in 1533. The Greek/Latin edition of 1692 by Marcus Meibomius divided each of

14520-421: The two approaches were compatible. The study of mathematics and music may have been connected to the worship of Apollo. The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body. One anecdote of Pythagoras reports that when he encountered some drunken youths trying to break into the home of a virtuous woman, he sang a solemn tune with long spondees and

14652-426: The use of all kinds of animal food except the flesh of oxen used for ploughing , and rams . According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices and established a diet for athletes dependent on meat. Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure. In

14784-562: Was a contemporary of the philosophers Anaximander , Anaximenes , and the historian Hecataeus , all of whom lived in Miletus , across the sea from Samos. Pythagoras is traditionally thought to have received most of his education in the Near East. Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures. Like many other important Greek thinkers, Pythagoras

14916-466: Was a native of Samos , descending from a geomoroi family. Apollonius of Tyana , gives her name as Pythaïs. Iamblichus tells the story that the Pythia prophesied to her while she was pregnant with him that she would give birth to a man supremely beautiful, wise, and beneficial to humankind. As to the date of his birth, Aristoxenus stated that Pythagoras left Samos in the reign of Polycrates , at

15048-544: Was a philosopher, scientist, mathematician, and engineer, also known for a special case of the inscribed angle theorem . Pythagoras's birthplace, the island of Samos , is situated in the Northeast Aegean Sea not far from Miletus . Diogenes Laërtius cites a statement from Aristoxenus (fourth century BC) stating that Pythagoras learned most of his moral doctrines from the Delphic priestess Themistoclea . Porphyry agrees with this assertion but calls

15180-605: Was an ancient Ionian Greek philosopher , polymath , and the eponymous founder of Pythagoreanism . His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato , Aristotle , and, through them, the West in general. Knowledge of his life is clouded by legend; modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded

15312-557: Was as Aethalides the son of Hermes , who granted him the ability to remember all his past incarnations. Next, he was incarnated as Euphorbus , a minor hero from the Trojan War briefly mentioned in the Iliad . He then became the philosopher Hermotimus , who recognized the shield of Euphorbus in the temple of Apollo. His final incarnation was as Pyrrhus, a fisherman from Delos . One of his past lives, as reported by Dicaearchus ,

15444-505: Was as a beautiful courtesan. Another belief attributed to Pythagoras was that of the " harmony of the spheres ", which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony. According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together. In his philosophical dialogue Protrepticus , Aristotle has his literary double say: When Pythagoras

15576-492: Was asked [why humans exist], he said, "to observe the heavens", and he used to claim that he himself was an observer of nature, and it was for the sake of this that he had passed over into life. Pythagoras was said to have practiced divination and prophecy . The earliest mentions of divination by isopsephy in Greek literature associate it with Pythagoras; he was viewed as the founder of this practice. According to his biographer, Iamblichus, he taught his method of divination to

15708-667: Was born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime, mocked Pythagoras as a clever charlatan, remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, and selecting from these writings he manufactured a wisdom for himself—much learning, artful knavery." The Greek poets Ion of Chios ( c.  480  – c.  421  BC) and Empedocles of Acragas ( c.  493  – c.  432  BC) both express admiration for Pythagoras in their poems. The first concise description of Pythagoras comes from

15840-483: Was by Robert Drew Hicks (1925) for the Loeb Classical Library , although it is slightly bowdlerized . A new translation by Pamela Mensch was published by Oxford University Press in 2018. Another by Stephen White was published by Cambridge University Press in 2020. Henricus Aristippus , the archdeacon of Catania , produced a Latin translation of Diogenes Laërtius's book in southern Italy in

15972-427: Was credited with devising the tetractys , the triangular figure of four rows which add up to the perfect number, ten. The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance. Iamblichus, in his Life of Pythagoras , states that the tetractys was "so admirable, and so divinised by those who understood [it]," that Pythagoras's students would swear oaths by it. Andrew Gregory concludes that

16104-457: Was gone, convincing everyone that he had really been in the underworld and leading them to trust him with their wives. Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field. Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem , as well as discoveries in

16236-463: Was known as the founder of a new way of life. The organization Pythagoras founded at Croton was called a "school", but, in many ways, resembled a monastery . 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 members of the sect shared all their possessions in common and were devoted to each other to

16368-470: Was present when the attack occurred and, if he was, whether or not he managed to escape. In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes. According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape, leading a small group of followers to the nearby city of Locris , where they pleaded for sanctuary, but were denied. They reached

16500-445: Was raised by Pythagoras's appointed successor Aristaeus and eventually took over the school when Aristaeus was too old to continue running it. Suda writes that Pythagoras had 4 children (Telauges, Mnesarchus, Myia and Arignote). The wrestler Milo of Croton was said to have been a close associate of Pythagoras and was credited with having saved the philosopher's life when a roof was about to collapse. This association may have been

16632-449: Was related to mathematics and that numbers were important, but it is debated to what extent, if at all, he actually contributed to mathematics or natural philosophy . The teaching most securely identified with Pythagoras is the "transmigration of souls" or metempsychosis , which holds that every soul is immortal and, upon death, enters into a new body . He may have also devised the doctrine of musica universalis , which holds that

16764-419: Was said that he was the first man to call himself a philosopher ("lover of wisdom") and that he was the first to divide the globe into five climatic zones . Classical historians debate whether Pythagoras made these discoveries, and many of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras

16896-654: Was said to have studied in Egypt . By the time of Isocrates in the fourth century BC, Pythagoras's reputed studies in Egypt were already taken as fact. The writer Antiphon , who may have lived during the Hellenistic Era, claimed in his lost work On Men of Outstanding Merit , used as a source by Porphyry, that Pythagoras learned to speak Egyptian from the Pharaoh Amasis II himself, that he studied with

17028-496: Was so despondent at the deaths of his beloved students that he committed suicide. A different legend reported by both Diogenes Laërtius and Iamblichus states that Pythagoras almost managed to escape, but that he came to a fava bean field and refused to run through it, since doing so would violate his teachings, so he stopped instead and was killed. This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself. Although

17160-693: Was the native of some town, perhaps the Laerte in Caria (or another Laerte in Cilicia ). Another suggestion is that one of his ancestors had for a patron a member of the Roman family of the Laërtii . The prevailing modern theory is that "Laertius" is a nickname (derived from the Homeric epithet Diogenes Laertiade , used in addressing Odysseus ) used to distinguish him from the many other people called Diogenes in

17292-455: Was the number of planets and the number of strings on a lyre, and because Apollo's birthday was celebrated on the seventh day of each month. They believed that odd numbers were masculine , that even numbers were feminine , and that the number five represented marriage, because it was the sum of two and three. Ten was regarded as the "perfect number" and the Pythagoreans honored it by never gathering in groups larger than ten. Pythagoras

17424-405: Was the son of Mnesarchus, and that he was born on the Greek island of Samos in the eastern Aegean . According to these biographers, Pythagoras's father was not born on the island, although he got naturalized there, but according to Iamblichus he was a native of the island. He is said to have been a gem-engraver or a wealthy merchant but his ancestry is disputed and unclear. His mother

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