Pythagoras of Samos (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC) was an Ionian Greek philosopher and polymath, widely recognized as the eponymous founder of Pythagoreanism. His political and religious doctrines gained considerable prominence in Magna Graecia, profoundly influencing the philosophies of Plato and Aristotle, and, through them, the trajectory of Western thought. While contemporary scholars dispute the specifics of Pythagoras's education and influences, there is general consensus that he journeyed to Croton in southern Italy around 530 BC, where he established a school whose initiates were reportedly bound by oaths of secrecy and adhered to a communal, ascetic way of life.
Pythagoras of Samos (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC) 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, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle.
In antiquity, Pythagoras was credited with numerous mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the identification of the five regular solids, the theory of proportions, the concept of the Earth's sphericity, the recognition of the morning and evening stars as the planet Venus, and the division of the globe into five climatic zones. He is also reputedly the first individual to adopt the title "philosopher" ("lover of wisdom"). Historians, however, debate the extent to which Pythagoras personally made these discoveries and pronouncements, as some attributed achievements may have originated earlier or been developed by his associates or successors, such as Hippasus and Philolaus.
The doctrine most reliably associated with Pythagoras is the "transmigration of souls," or metempsychosis, which posits the immortality of every soul and its subsequent entry into a new body upon death. He may also have formulated the concept of musica universalis, which theorizes that planets move according to precise mathematical ratios, thereby generating an inaudible cosmic symphony. Following Croton's decisive victory over Sybaris around 510 BC, Pythagoras's adherents clashed with proponents of democracy, leading to the burning of their meeting houses. Pythagoras may have perished during this persecution, or he might have escaped to Metapontum, where he subsequently died.
Pythagoras significantly influenced Plato, whose dialogues (particularly Timaeus) demonstrate clear Pythagorean concepts. A substantial resurgence of his teachings occurred in the first century BC among Middle Platonists, coinciding with the emergence of Neopythagoreanism. Pythagoras maintained his esteemed status as a great philosopher throughout the Middle Ages, and Pythagoreanism exerted influence on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was also widely adopted within early modern European esotericism, and his doctrines, as depicted in Ovid's Metamorphoses, later contributed to the modern vegetarian movement.
Life
No authentic writings by Pythagoras have endured, rendering definitive knowledge about his life exceptionally scarce. The earliest extant sources concerning Pythagoras, from Xenophanes, Heraclitus, Empedocles, Ion of Chios, and Herodotus, are concise, ambiguous, and frequently satirical. The primary biographical accounts of Pythagoras stem from three late antique works by Diogenes Laërtius, Porphyry, and Iamblichus; these are largely replete with myths and legends, becoming progressively longer and more fantastical in their descriptions of Pythagoras's accomplishments the further removed they are from his historical period. Nevertheless, Porphyry and Iamblichus incorporated some material derived from earlier 4th-century BC writings by Aristotle's students Dicaearchus, Aristoxenus, and Heraclides Ponticus, which, when identifiable, is generally considered the most reliable.
Early life
No aspect of Pythagoras's life remains undisputed; however, a critically selective examination of available information allows for the construction of a plausible biographical narrative.
Herodotus and Isocrates concur that Pythagoras was the son of Mnesarchus, born on the Greek island of Samos in the eastern Aegean. Mnesarchus is variously identified as a gem-engraver or a prosperous merchant, though his ancestral origins remain contentious and obscure. Apollonius of Tyana records Pythagoras's mother as Pythaïs, reportedly a descendant of Ancaeus, the legendary founder of Samos. Iamblichus recounts a prophecy delivered to Pythaïs by the Pythia during her pregnancy, foretelling the birth of a man of exceptional beauty, wisdom, and benefit to humanity; Iamblichus also affirmed her descent from Ancaeus. Regarding his birth date, Aristoxenus asserted that Pythagoras departed Samos during Polycrates' reign at the age of 40, suggesting a birth year around 570 BC. Pythagoras's nomenclature fostered an association with Pythian Apollo (Pūthíā); Aristippus of Cyrene, in the 4th century BC, elucidated the name by stating, "He spoke [ἀγορεύω, agoreúō] the truth no less than did the Pythian [πυθικός, puthikós]".
During Pythagoras's developmental period, Samos functioned as a flourishing cultural nexus, distinguished by its sophisticated architectural engineering, exemplified by the construction of the Tunnel of Eupalinos, and its vibrant festival traditions. As a prominent Aegean trade hub, Samos received goods from the Near East. Christiane L. Joost-Gaugier posits that these merchants almost certainly introduced Near Eastern concepts and customs. Concurrently, Pythagoras's early life coincided with the emergence of early Ionian natural philosophy. He was a contemporary of the philosophers Anaximander and Anaximenes, and the historian Hecataeus, all residents of Miletus, situated across the sea from Samos.
Documented Journeys
Contemporary scholarship indicates that Archaic Greek culture was profoundly shaped by Levantine and Mesopotamian civilizations. This influence appears to have been acknowledged by Classical and Hellenistic authors, who frequently ascribed many of Pythagoras's distinctive and unorthodox doctrines to his extensive travels to distant regions, where he purportedly acquired knowledge directly from various peoples. The concept of metempsychosis, or the transmigration of the soul post-mortem, which Herodotus and Diogenes Laertius attributed to the Egyptians, inspired an intricate narrative: Pythagoras allegedly mastered the Egyptian language from Pharaoh Amasis II and subsequently studied with Egyptian priests in Diospolis (Thebes), becoming the sole foreigner ever permitted to participate in their religious rites. Conversely, other ancient authors asserted that Pythagoras acquired these teachings from the Magi in Persia, or even from Zoroaster himself. The Phoenicians are also credited with instructing Pythagoras in arithmetic, while the Chaldeans are said to have taught him astronomy. By the third century BC, reports emerged that Pythagoras had also studied among the Jews. Furthermore, by the third century AD, Philostratus documented Pythagoras's studies with sages or gymnosophists in India, and Iamblichus additionally claimed his tutelage under the Celts and Iberians.
Purported Greek Instructors
Historical accounts indicate that Pythagoras also pursued studies under various indigenous Greek intellectuals. Diogenes Laërtius claims Pythagoras subsequently traveled to Crete, where he entered the Cave of Ida accompanied by Epimenides. Hermodamas of Samos is sometimes identified as a potential instructor. Hermodamas embodied the native Samian rhapsodic heritage, and his father, Creophylos, was reportedly the host of Homer, a rival poet. Alternative accounts attribute his instruction to Bias of Priene, Thales, or Anaximander, a student of Thales. Further traditions posit the mythical bard Orpheus as Pythagoras's preceptor, thereby linking him to the Orphic Mysteries. Neoplatonists documented a "sacred discourse" on deities, composed by Pythagoras in the Doric Greek dialect, which they contended was dictated to him by the Orphic priest Aglaophamus during his initiation into the Orphic Mysteries at Leibethra. Iamblichus attributed Pythagoras's rhetorical style, spiritual disposition, and devotional practices to the influence of Orpheus. Iamblichus characterized Pythagoreanism as an amalgamation of knowledge Pythagoras acquired from Orpheus, Egyptian priests, the Eleusinian Mysteries, and various other religious and philosophical traditions. Conversely, the second-century BC novelist Antonius Diogenes asserted that Pythagoras independently formulated all his doctrines through dream interpretation. Riedweg notes that, despite the imaginative nature of these narratives, Orphism undeniably exerted a significant influence on Pythagoras's doctrines.
Among the numerous Greek sages purported to have instructed Pythagoras, Pherecydes of Syros is the most frequently cited. Both Pythagoras and Pherecydes were subjects of comparable miraculous narratives, such as one where the protagonist foretells a shipwreck, another predicting the subjugation of Messina, and a third in which he consumes water from a well and forecasts an earthquake. Apollonius Paradoxographus, a paradoxographer potentially active in the second century BC, attributed Pythagoras's thaumaturgical concepts to the influence of Pherecydes. A separate account, possibly originating from the Neopythagorean philosopher Nicomachus, recounts Pythagoras's return to the island of Delos to attend to Pherecydes during his old age and final illness, demonstrating his reverence. Duris, the Samian historian and tyrant, reportedly made a patriotic claim regarding an epitaph purportedly written by Pherecydes, which proclaimed Pythagoras's wisdom to surpass his own. Considering these numerous references linking Pythagoras to Pherecydes, Riedweg infers that the tradition identifying Pherecydes as Pythagoras's instructor likely possesses some historical basis. Furthermore, Pythagoras and Pherecydes seemingly held analogous perspectives on the soul and the doctrine of metempsychosis.
In Croton
Porphyry reiterates an account from Antiphon, who stated that Pythagoras established a school called the "semicircle" while still residing on Samos. Within this institution, Samian citizens engaged in discussions regarding public affairs. Allegedly, the school achieved such prominence that leading intellectuals from across Greece journeyed to Samos to attend Pythagoras's lectures. Pythagoras himself resided in a secluded cave, where he pursued private study and periodically engaged in discussions with a select group of intimate companions. Christoph Riedweg, a German scholar specializing in early Pythagoreanism, suggests the possibility of Pythagoras having taught on Samos; however, he warns that Antiphon's narrative, which references a particular edifice still extant in his era, seems influenced by Samian patriotic sentiment.
Around 530 BC, at approximately forty years of age, Pythagoras departed from Samos. Later admirers asserted that his departure was motivated by disagreement with the tyranny of Polycrates in Samos; Riedweg observes that this explanation aligns closely with Nicomachus's emphasis on Pythagoras's alleged commitment to liberty, although Pythagoras's adversaries portrayed him as having an inclination towards authoritarianism. Conversely, other accounts suggest Pythagoras left Samos due to being overwhelmed by civic responsibilities, stemming from the high regard in which he was held by his fellow citizens. He subsequently arrived in the Greek colony of Croton (modern Crotone, in Calabria), located within what was then Magna Graecia. All historical sources concur that Pythagoras possessed charisma and rapidly acquired significant political influence in his new environment. He served as an advisor to the elites in Croton, offering them frequent counsel. Later biographers recount apocryphal narratives detailing the profound impact of his eloquent speeches, which purportedly led the people of Croton to abandon their luxurious and corrupt lifestyles in favor of the more austere philosophical framework he introduced.
Family and Friends
Suda records that Pythagoras had four children: Telauges, Mnesarchus, Myia, and Arignote. Diogenes Laertius, furthermore, documents him as having two brothers, Eunomus the elder and Tyrrhenus the second. Milo of Croton, a renowned wrestler, is reported to have been a close associate of Pythagoras and is attributed with saving the philosopher's life during an imminent roof collapse. This particular association, however, may have potentially resulted from a misidentification with a different individual named Pythagoras, who was an athletics trainer.
Death
Pythagoras's emphasis on dedication and asceticism is attributed with contributing to Croton's conclusive triumph over the neighboring colony of Sybaris in 510 BC. Following this victory, certain prominent citizens of Croton advocated for a democratic governmental structure, a proposal rejected by the Pythagoreans. Supporters of democracy, led by Cylon and Ninon—with Cylon reportedly irritated by his exclusion from Pythagoras's brotherhood—incited public opposition against the Pythagoreans. Followers of Cylon and Ninon subsequently attacked the Pythagoreans during one of their meetings, either at Milo's residence or another designated gathering place. Accounts of this assault are frequently inconsistent, and many narratives likely conflated it with later anti-Pythagorean rebellions, such as the one in Metapontum in 454 BC. The building was reportedly ignited, and many of the assembled members succumbed; only the younger and more active individuals successfully evaded capture.
Historical accounts diverge concerning whether Pythagoras was present during the attack and, if so, whether he managed to escape. In some narratives, Pythagoras was absent from the meeting when the Pythagoreans were assaulted, as he was on Delos attending to the ailing Pherecydes. According to an alternative account from Dicaearchus, Pythagoras was present at the meeting and successfully escaped, leading a small contingent of followers to the nearby city of Locris, where they sought asylum but were refused. They then reached the city of Metapontum, where they sought refuge in the temple of the Muses and perished from starvation after forty days without sustenance. Another tale recorded by Porphyry asserts that, as Pythagoras's adversaries were burning the house, his dedicated disciples reportedly formed a human bridge over the flames with their bodies to facilitate his escape. Pythagoras managed to escape but was so overwhelmed by the loss of his beloved students that he ended his own life. A distinct legend, documented by both Diogenes Laërtius and Iamblichus, posits that Pythagoras nearly escaped but encountered a fava bean field and declined to traverse it, deeming such an act a transgression of his doctrines; consequently, he halted and was killed. This particular story is believed to have originated with the writer Neanthes, who reportedly attributed it to subsequent Pythagoreans rather than to Pythagoras personally.
Teachings
Metempsychosis
While the precise specifics of Pythagoras's doctrines remain elusive, a broad conceptual framework of his core tenets can be reconstructed. Aristotle extensively discusses Pythagorean teachings, though he does not explicitly name Pythagoras. A prominent doctrine attributed to Pythagoras is metempsychosis, which posits the immortality of all souls and their transmigration into new bodies following death. This particular teaching is cited by Xenophanes, Ion of Chios, and Herodotus. The earliest textual evidence for Pythagoras's belief in metempsychosis originates from a satirical poem, likely composed posthumously by the Greek philosopher Xenophanes of Colophon (c. 570 – c. 478 BC), a contemporary of Pythagoras. In this work, Xenophanes depicts Pythagoras intervening to protect a beaten dog, claiming to discern the voice of a deceased friend within its cries. Nevertheless, the precise nature or operational mechanism of Pythagoras's conception of metempsychosis remains entirely unknown.
Empedocles, in one of his poetic works, suggests that Pythagoras might have asserted the capacity to recollect his prior incarnations. Diogenes Laërtius, citing Heraclides Ponticus, records that Pythagoras informed others of having experienced four previous lives, which he could recall with specificity. The initial incarnation was as Aethalides, son of Hermes, who bestowed upon him the faculty of remembering all his past existences. Subsequently, he was embodied as Euphorbus, a lesser hero of the Trojan War, briefly referenced in the Iliad. He then assumed the identity of the philosopher Hermotimus, who reportedly identified Euphorbus's shield within the temple of Apollo. His ultimate recorded incarnation was as Pyrrhus, a fisherman originating from Delos. Additionally, Dicaearchus reported one of his past lives as a beautiful courtesan.
Numerology
A further doctrine ascribed to Pythagoras is the concept of the "harmony of the spheres," which posited that celestial bodies, including planets and stars, operate in accordance with mathematical ratios. These ratios were believed to correlate with musical intervals, thereby generating an inaudible cosmic symphony. Porphyry indicates that Pythagoras asserted the seven Muses represented the seven planets engaged in a collective celestial song.
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.
Contemporary scholarship generally attributes these mathematical and philosophical advancements to Philolaus of Croton (c. 470 – c. 385 BC), a later Pythagorean philosopher. His surviving textual fragments represent the earliest documented accounts of the numerological and musical theories subsequently associated with Pythagoras. In his seminal work, Lore and Science in Ancient Pythagoreanism, Walter Burkert contends that while Pythagoras functioned as an influential political and religious instructor, the numerical philosophy ascribed to him was, in fact, an innovation introduced by Philolaus. Burkert posits that Pythagoras did not engage with numbers in any substantial way, nor did he make any significant contributions to the field of mathematics. Burkert further asserts that the sole mathematical activity undertaken by the Pythagoreans involved rudimentary, unproven arithmetic, yet these arithmetical insights were crucial to the nascent stages of mathematics. Subsequent Pythagoreans credited Pythagoras with the invention of the tetractys, a triangular arrangement of four rows summing to the "perfect" number ten. The Pythagoreans considered the tetractys a symbol of profound mystical significance. Iamblichus, in his Life of Pythagoras, records that the tetractys was "so admirable, and so divinised by those who understood [it]," that Pythagoras's disciples would invoke it in their oaths.
It is imperative to distinguish this from a contemporary, simplified practice termed "Pythagorean numerology," which employs a variation of an isopsephic method. This technique is also referred to as pythmenes, 'roots', or 'base numbers', and involves the mathematical reduction of the base values of letters within a word, through addition or division, to yield a single numerical value between one and nine for the entire name or term.
Pythagoreanism
Communal Lifestyle
Plato and Isocrates both assert that Pythagoras was primarily recognized as the originator of a distinct lifestyle. The institution established by Pythagoras in Croton, though termed a "school," bore significant resemblances to a monastic community. Its adherents committed themselves through vows to Pythagoras and to one another, dedicating themselves to religious and ascetic practices, alongside the study of his theological and philosophical doctrines. Members of this sect practiced communal ownership of possessions and maintained a strong mutual devotion, often to the exclusion of those outside the group. Historical accounts indicate that Pythagoreans shared communal meals, mirroring the Spartan custom. A notable Pythagorean maxim was "koinà tà phílōn," which translates to "All things are common among friends." While Iamblichus and Porphyry offer elaborate descriptions of the school's structure, their principal aim was not historical precision but rather to portray Pythagoras as a divine emissary sent to humanity by the gods. Iamblichus specifically framed the "Pythagorean Way of Life" as a pagan counterpart to the Christian monastic orders prevalent during his era. Pythagoreans believed that the ultimate human achievement was for the soul to assimilate into the divine existence, thereby transcending the cycle of reincarnation.
Early Pythagoreanism comprised two distinct factions: the mathematikoi, or "learners," and the akousmatikoi, or "listeners." Scholars traditionally characterize the akousmatikoi as adherents to older mystical, numerological, and religious doctrines, while the mathematikoi are typically viewed as a more intellectual, modernist group, distinguished by their rationalist and scientific inclinations. Gregory, however, advises against assuming a rigid division between these groups, suggesting that many Pythagoreans likely perceived their approaches as complementary. The pursuit of mathematics and music might have been intrinsically linked to the veneration of Apollo. Pythagoreans held that music served as a catharsis for the soul, analogous to medicine's role in purifying the body. An anecdote recounts that Pythagoras, upon encountering intoxicated youths attempting to trespass into a virtuous woman's residence, sang a solemn melody featuring extended spondees, which reportedly subdued their "raging willfulness." Furthermore, Pythagoreans significantly emphasized physical exercise; therapeutic dance, daily morning perambulations through picturesque landscapes, and athletic pursuits constituted vital elements of their lifestyle. Daily periods of contemplation, both at the commencement and conclusion of the day, were also recommended.
Prohibitions and Regulations
Pythagorean doctrines were referred to as "symbols" (symbola), and initiates swore an oath of silence, pledging not to disclose these symbols to outsiders. Members who failed to adhere to the community's statutes faced expulsion, with the remaining adherents erecting tombstones for them as if they had perished. Several "oral sayings" (akoúsmata) ascribed to Pythagoras persist, outlining proper conduct for Pythagorean community members regarding sacrifices, divine veneration, their "departure from this life," and burial rites. A significant portion of these maxims underscores the imperative of ritual purity and the avoidance of contamination. Additional surviving oral traditions prohibit Pythagoreans from breaking bread, stirring fires with swords, or gathering crumbs, and instruct individuals to always don the right sandal prior to the left. Nevertheless, the precise interpretations of these pronouncements often remain ambiguous. Iamblichus records Aristotle's accounts of the initial, ritualistic purposes underlying some of these sayings; however, these interpretations seemingly became obsolete, as Porphyry offers distinctly different ethical-philosophical explanations for them:
Reportedly, new initiates were not granted an audience with Pythagoras until they had successfully completed a five-year probationary period, during which strict silence was mandated. Historical sources suggest that Pythagoras held remarkably progressive views concerning women, and female members of his school evidently participated actively in its functioning. Iamblichus enumerates 235 notable Pythagoreans, including seventeen women. Subsequently, numerous distinguished female philosophers significantly advanced the evolution of Neopythagoreanism.
Pythagoreanism incorporated various dietary restrictions. While it is generally accepted that Pythagoras prohibited the consumption of fava beans and the flesh of non-sacrificial animals, including fish and poultry, these claims have also faced contradiction. The rationale behind Pythagorean dietary rules might stem from the belief in metempsychosis, or alternatively, from the genetic prevalence of favism, an enzyme deficiency anemia common in the Mediterranean region. Certain ancient authors portray Pythagoras as advocating a strictly vegetarian lifestyle. Eudoxus of Cnidus, a pupil of Archytas, noted that "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." However, other sources present conflicting accounts. Aristoxenus, for instance, stated that Pythagoras permitted all animal foods except the meat of oxen used for plowing and rams. Heraclides Ponticus further claimed that Pythagoras consumed sacrificial meat and devised a meat-based diet for athletes.
Legends
During his lifetime, Pythagoras became the focus of extensive hagiographic legends. Aristotle characterized Pythagoras as a miracle worker and a figure possessing supernatural attributes. In one fragment, Aristotle recounts that Pythagoras possessed a golden thigh, which he publicly displayed at the Olympic Games and presented to Abaris the Hyperborean as evidence of his identity as the "Hyperborean Apollo." Reportedly, an Apollo priest bestowed upon Pythagoras a magical arrow, enabling him to traverse vast distances by flight and conduct ritual purifications. He was also purportedly observed simultaneously in both Metapontum and Croton. Furthermore, when Pythagoras traversed the Kosas River (now known as the Basento), multiple witnesses reportedly heard the river address him by name. By the Roman era, a legend asserted that Pythagoras was the son of Apollo.
Pythagoras is traditionally depicted as wearing entirely white attire. He is also described as having worn a golden wreath on his head and trousers in the Thracian style. Furthermore, Pythagoras was reputed to possess exceptional abilities in interacting with animals. An Aristotelian fragment documents an instance where, upon being bitten by a venomous snake, Pythagoras retaliated by biting and killing it. Both Porphyry and Iamblichus recount that Pythagoras once convinced a bull to refrain from consuming fava beans and successfully persuaded a notoriously destructive bear to pledge never to harm a living creature again, a vow the bear reportedly upheld. While Riedweg posits that Pythagoras might have personally fostered these legends, Gregory asserts a lack of direct evidence to support this claim.
Attributed Discoveries
In Mathematics
While Pythagoras is predominantly recognized today for his purported mathematical breakthroughs, classical historians debate the extent of his actual significant contributions to the discipline. Numerous mathematical and scientific advancements, including the renowned theorem bearing his name, alongside discoveries in music, astronomy, and medicine, have been ascribed to Pythagoras. From at least the first century BC, Pythagoras has been widely credited with the discovery of the Pythagorean theorem, a geometric principle asserting that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides"—expressed as . A prevalent legend suggests that following this discovery, Pythagoras offered an ox, or potentially an entire hecatomb, as a sacrifice to the deities. Cicero, however, dismissed this narrative as fallacious, citing the more widely accepted belief that Pythagoras prohibited blood sacrifices. Porphyry sought to reconcile the story by contending that the ox in question was, in fact, fashioned from dough.
The Pythagorean theorem was utilized by both Babylonian and Indian civilizations centuries prior to Pythagoras. Burkert dismisses any association of Pythagoras with the theorem, highlighting that no ancient sources attribute its proof to him. Riedweg further emphasizes that "there is certainly no reason to suppose that either Pythagoras himself or any early Pythagorean could have provided a deductive proof of the theorem". The Babylonian application of Pythagorean numbers suggests their understanding of the principle's general applicability and the existence of some form of proof, though this evidence remains undiscovered in the largely unpublished cuneiform records.
In Music
A popular legend attributes Pythagoras's discovery of the mathematical basis of musical notes to an encounter with blacksmiths. Reportedly, while passing their workshop, he observed the harmonious sounds produced by their hammers striking anvils, with one exception. Intrigued, he entered the shop to investigate the hammers. He subsequently deduced that the pitch generated by each hammer was directly proportional to its size, leading him to conclude that music possessed an inherent mathematical structure.
In Astronomy
Historically, Pythagoras and his contemporary, Parmenides of Elea, were both credited with pioneering the concepts that the Earth is spherical, that the globe is divisible into five climatic zones, and that the morning and evening stars are a single celestial body (now identified as Venus). However, Parmenides presents a significantly stronger claim to these initial discoveries, with the attribution to Pythagoras potentially stemming from a pseudepigraphal poem. Empedocles, who resided in Magna Graecia shortly after Pythagoras and Parmenides, was also aware of the Earth's spherical nature. By the close of the fifth century BC, this understanding had become universally accepted among Greek intellectuals.
Later Influence in Antiquity
On Greek Philosophy
Substantial Pythagorean communities flourished in Magna Graecia, Phlius, and Thebes during the early fourth century BC. Concurrently, Archytas, a Pythagorean philosopher, exerted significant political influence in the city of Tarentum, also in Magna Graecia. Subsequent traditions assert that Archytas was elected as strategos ("general") on seven occasions, despite regulations prohibiting others from serving for more than one year. Archytas was also an esteemed mathematician and musician, maintaining a close friendship with Plato and being quoted in Plato's Republic. Aristotle posits that Plato's philosophical framework was profoundly shaped by Pythagorean doctrines. Cicero reiterates this assertion, noting that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean"). Charles H. Kahn suggests that Plato's middle dialogues, such as Meno, Phaedo, and The Republic, exhibit a pronounced "Pythagorean coloring," while his later dialogues, notably Philebus and Timaeus, are distinctly Pythagorean in nature.
Heraclitus of Ephesus (fl. c. 500 BC), a poet born near Samos and potentially a contemporary of Pythagoras, derided Pythagoras as an astute charlatan, stating: "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." Alcmaeon of Croton (fl. c. 450 BC), a physician who resided in Croton concurrently with Pythagoras, integrated numerous Pythagorean doctrines into his works and hinted at a potential personal acquaintance with Pythagoras. Furthermore, the Greek poets Ion of Chios (c. 480 – c. 421 BC) and Empedocles of Acragas (c. 493 – c. 432 BC) both conveyed their admiration for Pythagoras within their poetic compositions.
R. M. Hare suggests that Plato's Republic might have been partly influenced by the "tightly organised community of like-minded thinkers" established by Pythagoras in Croton. Furthermore, Plato may have adopted from Pythagoras the concept that mathematics and abstract reasoning provide a robust foundation for philosophy, science, and ethics. Both Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world" and were likely influenced by Orphism. Frederick Copleston, a historian of philosophy, posits that Plato probably derived his tripartite theory of the soul from Pythagorean thought.
The first century BC witnessed a resurgence of Pythagorean doctrines, as Middle Platonist philosophers like Eudorus and Philo of Alexandria celebrated the emergence of a "new" Pythagoreanism in Alexandria. Concurrently, Neopythagoreanism gained prominence. Apollonius of Tyana, a first-century AD philosopher, endeavored to emulate Pythagoras and adhere to Pythagorean principles. Moderatus of Gades, a later first-century Neopythagorean philosopher, elaborated on Pythagorean number philosophy, likely conceiving the soul as a "kind of mathematical harmony." Similarly, the Neopythagorean mathematician and musicologist Nicomachus further developed Pythagorean numerology and music theory. Numenius of Apamea interpreted Platonic teachings through the lens of Pythagorean doctrines.
Regarding Art and Architecture
The Porta Maggiore Basilica, a subterranean structure erected during Emperor Nero's reign, stands as the earliest known edifice designed in accordance with Pythagorean principles, serving as a clandestine place of worship for Pythagoreans. Its underground construction reflected the Pythagorean emphasis on secrecy and alluded to the legend of Pythagoras secluding himself in a Samian cave. The basilica's apse is oriented eastward and its atrium westward, honoring the rising sun. A narrow entrance leads to a small pool for initiates' purification rituals. The building's design also incorporates Pythagorean numerology; each table within the sanctuary accommodates seven individuals. Three aisles converge on a single altar, symbolizing the soul's three components striving towards the unity of Apollo. The apse features a depiction of the poet Sappho leaping from the Leucadian cliffs, clutching her lyre, with Apollo positioned below, extending his right hand in a protective gesture, thereby symbolizing Pythagorean doctrines concerning the soul's immortality. The sanctuary's interior is predominantly white, a color held sacred by Pythagoreans.
Emperor Hadrian's Pantheon in Rome similarly incorporated Pythagorean numerology in its construction. The temple's circular layout, central axis, hemispherical dome, and orientation towards the four cardinal directions collectively symbolize Pythagorean cosmological perspectives on universal order. The singular oculus at the dome's apex represents the monad and the sun-god Apollo. The twenty-eight ribs radiating from the oculus symbolize the moon, corresponding to the number of months in the Pythagorean lunar calendar. The five coffered rings situated beneath these ribs denote the symbolic union of the sun and moon.
Early Christian Perspectives
Numerous early Christians held Pythagoras in high esteem. Eusebius (c. 260 – c. 340 AD), the bishop of Caesarea, commends Pythagoras in his Against Hierokles for his adherence to silence, his frugality, his "extraordinary" moral conduct, and his sagacious doctrines. Elsewhere, Eusebius draws a comparison between Pythagoras and Moses. The Church Father Jerome (c. 347 – c. 420 AD), in one of his epistles, praises Pythagoras for his wisdom, and in another, attributes to him the belief in the soul's immortality, suggesting it was a concept inherited by Christians. Augustine of Hippo (354–430 AD) repudiated Pythagoras's doctrine of metempsychosis, albeit without direct attribution, yet otherwise conveyed admiration for him. In On the Trinity, Augustine applauds Pythagoras's humility in designating himself a philosophos, or "lover of wisdom," rather than a "sage." In a separate passage, Augustine defends Pythagoras's legacy, asserting that Pythagoras unequivocally did not teach the doctrine of metempsychosis.
Post-Antiquity Influence
During the Medieval Period
Throughout the Middle Ages, Pythagoras held a revered status as the originator of mathematics and music, disciplines integral to the Seven Liberal Arts. His image frequently appeared in medieval art, including illuminated manuscripts and the relief sculptures adorning the portal of Chartres Cathedral. The Timaeus, Plato's sole dialogue available in Latin translation in Western Europe, prompted William of Conches (c. 1080–1160) to assert Plato's Pythagorean affiliation. The 1430s saw the Camaldolese friar Ambrose Traversari translate Diogenes Laërtius's Lives and Opinions of Eminent Philosophers from Greek into Latin. Subsequently, in the 1460s, the philosopher Marsilio Ficino rendered Porphyry and Iamblichus's Lives of Pythagoras into Latin, making these texts accessible to Western scholars. In 1494, the Greek Neopythagorean scholar Constantine Lascaris published a Latin translation of The Golden Verses of Pythagoras, alongside a printed edition of his Grammatica, thus disseminating these works to a broader readership. He further contributed in 1499 by publishing the inaugural Renaissance biography of Pythagoras, titled Vitae illustrium philosophorum siculorum et calabrorum, which was issued in Messina.
Modern Scientific Perspectives
In the preface to his seminal work, On the Revolution of the Heavenly Spheres (1543), Nicolaus Copernicus acknowledged several Pythagoreans as primary influences on his heliocentric model of the universe. Notably, he intentionally omitted Aristarchus of Samos, a non-Pythagorean astronomer who had formulated a complete heliocentric model in the fourth century BC, in an apparent effort to present his own model as fundamentally Pythagorean. Johannes Kepler, similarly, identified as a Pythagorean. His adherence to the Pythagorean concept of musica universalis motivated his quest for the underlying mathematical equations, which ultimately led to his formulation of the laws of planetary motion. Kepler's book on this topic, Harmonices Mundi (Harmonics of the World), was named in homage to the Pythagorean doctrine that inspired him. He further characterized Pythagoras as the "grandfather" of all Copernicans.
Albert Einstein posited that a scientist could be considered "a Platonist or a Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research." The English philosopher Alfred North Whitehead contended that "In a sense, Plato and Pythagoras stand nearer to modern physical science than does Aristotle. The two former were mathematicians, whereas Aristotle was the son of a doctor." Based on this assessment, Whitehead asserted that Einstein and other contemporary scientists of his caliber were "following the pure Pythagorean tradition."
Perspectives on Vegetarianism
Book XV of Ovid's Metamorphoses features a fictionalized depiction of Pythagoras, who delivers a discourse advocating for a strict vegetarian diet among his adherents. Arthur Golding's 1567 English translation of Ovid's Metamorphoses was instrumental in popularizing Pythagoras among English-speakers during the early modern era. John Donne's Progress of the Soul explores the implications of the doctrines presented in this speech, while Michel de Montaigne cited the speech at least three times in his treatise "Of Cruelty" to articulate his moral opposition to animal mistreatment. John Dryden incorporated a translation of the scene involving Pythagoras into his 1700 work Fables, Ancient and Modern. Similarly, John Gay's 1726 fable "Pythagoras and the Countryman" reemphasizes these central themes, associating carnivorism with tyranny. Lord Chesterfield documented that his adoption of vegetarianism was prompted by reading Pythagoras's speech within Ovid's Metamorphoses. Prior to the coinage of the term vegetarianism in the 1840s, individuals adhering to a vegetarian diet were commonly known as "Pythagoreans" in English.
Influence on Western Esotericism
Early modern European esoteric traditions significantly incorporated Pythagorean teachings. The German humanist scholar Johannes Reuchlin (1455–1522) integrated Pythagoreanism with Christian theology and Jewish Kabbalah, positing that both Kabbalah and Pythagoreanism originated from Mosaic tradition, thereby classifying Pythagoras as a kabbalist. In his 1494 dialogue, De verbo mirifico, Reuchlin drew a parallel between the Pythagorean tetractys and the ineffable divine name YHWH, attributing symbolic significance to each of the tetragrammaton's four letters in accordance with Pythagorean mystical principles.
Heinrich Cornelius Agrippa's widely recognized and influential three-volume treatise, De Occulta Philosophia, identifies Pythagoras as a "religious magi" and posits that his mystical numerology functions on a supercelestial plane, a theological concept referring to a sublime celestial domain prevalent in that era. The Freemasons intentionally structured their society based on the community established by Pythagoras in Croton. Rosicrucianism incorporated Pythagorean symbolism, a practice also adopted by Robert Fludd (1574–1637), who attributed the inspiration for his musical compositions to Pythagoras. John Dee was profoundly influenced by Pythagorean philosophy, especially the doctrine asserting that all phenomena are fundamentally composed of numbers.
On Literature
Transcendentalist thinkers consulted the ancient texts titled Lives of Pythagoras as instructional guides for exemplary living. Henry David Thoreau was significantly affected by Thomas Taylor's translations of Iamblichus's Life of Pythagoras and Stobaeus's Pythagoric Sayings; furthermore, his perspectives on nature might have been shaped by the Pythagorean concept of images corresponding to archetypes. The Pythagorean doctrine of musica universalis constitutes a recurrent motif throughout Thoreau's seminal work, magnum opus, Walden.
List of Items Named After Pythagoras
- List of things named after Pythagoras
- The maxim Ex pede Herculem, meaning "from his foot, [we can measure] Hercules," originates from an apocryphal narrative asserting that Pythagoras calculated Hercules's height by extrapolating from the length of a racecourse at Pisae.
- The Pythagorean cup refers to a novelty drinking vessel featuring a concealed siphon mechanism, traditionally ascribed to Pythagoras.
- Pythagorean means encompass the arithmetic mean, the geometric mean, and the harmonic mean, all of which are purportedly subjects of Pythagoras's study.
Notes
Citations
Bibliography
Classical Sources
Modern Secondary Sources
- Pythagoras, as featured on the BBC program In Our Time.
- Huffman, Carl. "Pythagoras." In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174.{{cite encyclopedia}}: CS1 maint: overridden setting (link)
- "Pythagoras and the Pythagoreans, Fragments and Commentary," by Arthur Fairbanks, from the Hanover Historical Texts Project, Hanover College Department of History.
- "Pythagoras and the Pythagoreans," archived on March 9, 2009, at the Wayback Machine, from the Department of Mathematics, Texas A&M University.
- "Pythagoras and Pythagoreanism," as presented in The Catholic Encyclopedia.
- A collection of works by or concerning Pythagoras, available through the Internet Archive.
- Works authored by Pythagoras, accessible via LibriVox (public domain audiobooks) .