Who is Pythagoras: Learn about the life and legacy of this ancient Greek philosopher, mathematician, and founder of Pythagoreanism, known for his famous theorem and contributions to mathematics and philosophy.
Pythagoras: The Enigmatic Greek Philosopher and Mathematician
Pythagoras, an ancient Ionian Greek philosopher, was the eponymous founder of Pythagoreanism, a school of thought that combined political and religious teachings. Born on the island of Samos, he was the son of Mnesarchus, a gem-engraver. Although shrouded in legend, his life and work have had a profound impact on Western philosophy, influencing the likes of Plato and Aristotle.
The details of his education and influences remain a topic of debate among modern scholars. Around 530 BC, Pythagoras traveled to Croton, southern Italy, where he established a secretive, communal school with an ascetic lifestyle. This way of life included dietary restrictions, such as vegetarianism, though its extent is contested.
Pythagoras is most famously associated with metempsychosis, the belief in the transmigration of souls, which posits that each soul is immortal and reincarnates into a new body upon death. Another doctrine attributed to him is musica universalis, the idea that celestial bodies move according to mathematical equations, creating an inaudible harmony.
Despite the uncertainty surrounding his contributions to mathematics and natural philosophy, Pythagoras is credited with numerous discoveries, such as the Pythagorean theorem, Pythagorean tuning, and the five regular solids. Furthermore, he is believed to have been the first to refer to himself as a philosopher and to categorize the globe into five climatic zones.
While it is unclear whether Pythagoras himself made these discoveries, it is evident that his teachings have had a lasting impact. The Middle Ages saw the revival of Pythagorean thought, which went on to influence great scientists like Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. His ideas also shaped ancient Greek art and had a resurgence in Middle Platonism.
In conclusion, Pythagoras of Samos was a renowned Greek philosopher and mathematician whose teachings and ideas have left an indelible mark on the fields of mathematics, philosophy, and natural sciences. Although much of his life remains shrouded in mystery, his legacy has endured through the ages, influencing generations of thinkers and shaping the course of Western thought.
The Elusive Legacy of Pythagoras: Sources and Controversies
There are no authentic writings of Pythagoras that have survived, and very little is known for certain about his life. The earliest sources on his life are brief, ambiguous, and often satirical. Xenophanes of Colophon, one of his contemporaries, wrote a satirical poem about him after his death. Other early sources, such as Alcmaeon of Croton and Heraclitus of Ephesus, offer conflicting accounts of Pythagoras's life and teachings, with Heraclitus mocking him as a clever charlatan.
Greek poets Ion of Chios and Empedocles of Acragas expressed admiration for Pythagoras in their works. Historian Herodotus of Halicarnassus described him as a significant Greek sage and credited him with teaching his followers about immortality. However, the accuracy of Herodotus's works is controversial. The earliest texts discussing the numerological and musical theories attributed to Pythagoras are by Philolaus of Croton, a fifth-century BC philosopher.
Aristotle wrote a treatise on the Pythagoreans, which has been lost, and his disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus also wrote on the subject. Most major sources on Pythagoras's life come from the Roman period, and according to German classicist Walter Burkert, by this time, the history of Pythagoreanism had already become a challenging reconstruction of something lost and gone.
Three ancient biographies of Pythagoras have survived from late antiquity, primarily filled with myths and legends. The most respected of these is from Diogenes Laërtius's Lives and Opinions of Eminent Philosophers. Neoplatonist philosophers Porphyry and Iamblichus also wrote biographies, partially intended as polemics against the rise of Christianity. These later sources are lengthier and more fantastic in their descriptions of Pythagoras's achievements. Porphyry and Iamblichus used material from the lost writings of Aristotle's disciples, and information taken from these sources is generally considered the most reliable.
Pythagoras of Samos: The Early Years and Birth of a Philosopher
Pythagoras, one of the most famous and controversial ancient Greek philosophers, was born on the Greek island of Samos in the eastern Aegean. According to Herodotus and Isocrates, Pythagoras was the son of Mnesarchus, a gem-engraver or wealthy merchant, who was naturalized on the island. However, Iamblichus claimed that Mnesarchus was a native of Samos. Pythagoras' mother was a native of Samos, and her name was Pythaïs. During his formative years, Samos was a thriving cultural hub known for its advanced architectural engineering, riotous festival culture, and major center of trade in the Aegean.
Pythagoras was born at a time when early Ionian natural philosophy was flourishing. He was a contemporary of the philosophers Anaximander, Anaximenes, and the historian Hecataeus, all of whom lived in Miletus, across the sea from Samos. According to Aristoxenus, Pythagoras left Samos in the reign of Polycrates, at the age of 40, which would give a date of birth around 570 BC. Pythagoras' name led him to be associated with Pythian Apollo. Aristippus of Cyrene explained his name by saying, "He spoke the truth no less than did the Pythian."
Despite the controversies surrounding his ancestry, Pythagoras was prophesied by the Pythia to his mother while she was pregnant with him. The Pythia prophesied that she would give birth to a man supremely beautiful, wise, and beneficial to humankind. This prophecy came true, as Pythagoras would go on to become an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism.
Pythagoras's Education and Cultural Influences
Pythagoras is said to have received much of his education from various cultures in the Near East. While ancient writers, such as Isocrates and Antiphon, claimed that Pythagoras studied in Egypt and learned to speak Egyptian from Pharaoh Amasis II himself, other writers asserted that he had learned these teachings from the Magi in Persia or even from Zoroaster himself. Pythagoras was also reputed to have studied under the Phoenicians, the Chaldeans, the Jews, the Celts, the Iberians, and even the gymnosophists in India.
Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by Levantine and Mesopotamian cultures, and Pythagoras was said to have studied in Egypt like many other important Greek thinkers. Pythagoras's education and cultural influences are an essential aspect of understanding his philosophical and mathematical contributions to Western philosophy and mathematics.
Pythagoras's Education and Influences
Pythagoras is known for his contributions to mathematics, philosophy, and mysticism. While he is traditionally believed to have received most of his education in the Near East and Egypt, modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures. Pythagoras was said to have studied under a variety of native Greek thinkers, including Hermodamas of Samos, Bias of Priene, Thales, and Anaximander. Additionally, he may have met Thales of Miletus on one of his visits to Egypt or Greece.
Pythagoras's birthplace, the island of Samos, is situated in the Northeast Aegean Sea not far from Miletus. Some traditions credit the mythic bard Orpheus as Pythagoras's teacher, and 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. Pythagoras and Pherecydes of Syros also appear to have shared similar views on the soul and the teaching of metempsychosis. Overall, Pythagoras's teachings were influenced by a diverse range of sources, including Greek thinkers, Near Eastern and Egyptian cultures, and Orphism.
Pythagoras' Life and Work: Leaving Samos and Founding a School in Croton
According to Porphyry, Pythagoras founded a school known as the "semicircle" while still on the island of Samos. The school provided a forum for Samians to debate matters of public concern and gained such renown that the brightest minds in all of Greece came to hear Pythagoras teach. However, Christoph Riedweg cautions that the account may be motivated by Samian patriotic interest. Around the age of forty, Pythagoras left Samos and arrived in Croton, a Greek colony in Magna Graecia.
His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos, but Pythagoras's enemies portrayed him as having a proclivity towards tyranny. All sources agree that Pythagoras quickly acquired great political influence in Croton and served as an advisor to the elites there. He gave them frequent advice and, through his eloquent speeches, led 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.
Pythagoras' Family and Relationships: Marriage, Children, and Associates
According to Diogenes Laërtius and Porphyry, Pythagoras did not indulge in sexual pleasures and advised others to be cautious in having sex. However, Porphyry states that Pythagoras married Theano, a lady from Crete, and had several children with her, including two sons named Telauges and Arignote, and a daughter named Myia. Iamblichus only mentions a son named Mnesarchus who eventually took over Pythagoras' school when Aristaeus was too old to continue running it. Milo of Croton, a famous wrestler, was said to have been a close associate of Pythagoras and was credited with having saved the philosopher's life.
Confusion arose when another man named Pythagoras, who was an athletics trainer, was also mentioned. Diogenes Laërtius records that Milo's wife was named Myia, while Iamblichus mentions Theano as the wife of Brontinus of Croton. Interestingly, Diogenes Laërtius states that Pythagoras' wife Theano was also her daughter and that works supposedly written by Theano were still extant during his own lifetime, though these writings are now known to be pseudepigraphical.
Pythagoras and the Fall of the Pythagoreans in Croton
Pythagoras's teachings of dedication and asceticism are credited with aiding in Croton's victory over the neighboring colony of Sybaris in 510 BC. However, after the victory, the Pythagoreans rejected a proposal for a democratic constitution, which led to a rebellion by supporters of democracy, headed by Cylon and Ninon. They attacked the Pythagoreans during one of their meetings, either in the house of Milo or in some other meeting-place, and the building was set on fire. Many of the assembled members perished, and only the younger and more active members managed to escape.
Sources disagree regarding whether Pythagoras was present when the attack occurred and, if he was, whether or not he managed to escape. Some accounts suggest that he was not present as he was on Delos tending to the dying Pherecydes. Others suggest that he was present 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 the city of Metapontum, where they took shelter in the temple of the Muses and died there of starvation after forty days without food.
Porphyry recorded a legend that claims Pythagoras's 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 he was so despondent at the deaths of his beloved students that he committed suicide. Another legend reported by both Diogenes Laërtius and Iamblichus states that Pythagoras almost managed to escape but refused to run through a fava bean field, violating his teachings, and was killed.
The fall of the Pythagoreans in Croton was a significant event in Pythagorean history and marks the end of the school's influence in southern Italy.
Pythagoras Teachings
Pythagoras and His Teachings on Metempsychosis
Pythagoras is an ancient Greek philosopher, mathematician, and the eponymous founder of Pythagoreanism. While the details of his teachings are uncertain, it is possible to reconstruct a general outline of his main ideas. 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 a new body. This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus. Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations.
Pythagoras is said to have lived four previous lives, which he remembered in detail, according to an account from Heraclides Ponticus reported by Diogenes Laërtius. Pythagoras's past lives include being Aethalides, the son of Hermes; Euphorbus, a minor hero from the Trojan War; the philosopher Hermotimus; and Pyrrhus, a fisherman from Delos. Another past life of Pythagoras, as reported by Dicaearchus, was as a beautiful courtesan. However, nothing whatsoever is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur.
Pythagoras and his Spiritual Beliefs
Pythagoras, an ancient Greek philosopher and mathematician, is known for his contributions to mathematics and philosophy, but he also held spiritual beliefs that influenced his teachings. One of these beliefs was the "harmony of the spheres," which posited that the planets and stars move according to mathematical equations that correspond to musical notes, producing an inaudible symphony. Pythagoras also believed in metempsychosis, the transfer of the soul to a new body after death.
Pythagoras was said to have practiced divination and prophecy and would enter an enclosed space, typically a cave, for a spiritual practice called "smoke trapping." This involved lighting a fire until noxious fumes filled the room, and inhaling the smoke to induce vivid hallucinations, often of divine geometric shapes and patterns. Pythagoras also believed that observing the heavens was the purpose of human existence and that he himself was an observer of nature.
In his travels throughout Greece, Pythagoras appeared as a religious or priestly figure, or as a lawgiver. According to Porphyry, Pythagoras taught that the seven Muses were the seven planets singing together. While much of Pythagoras's spiritual beliefs remain uncertain, his influence on philosophy and mathematics is still felt today.
Numerology and Mysticism in Pythagoreanism
According to Aristotle, the Pythagoreans held a mystical belief in numbers, considering them the fundamental building blocks of the universe and all things within it. They believed that the number one represented the origin of all things, while the number two represented matter. The number three was considered ideal because it had a beginning, middle, and end and was the smallest number of points needed to define a plane triangle, which was revered as a symbol of the god Apollo. The number four signified the four seasons and the four elements, and the number seven was sacred because it was the number of planets and the number of strings on a lyre, as well as the day of Apollo's birthday. Odd numbers were considered masculine, while even numbers were considered feminine, and the number five represented marriage because it was the sum of two and three. The perfect number was ten, and the Pythagoreans never gathered in groups larger than ten, honoring it as a symbol of mystical importance.
The tetractys, a triangular figure of four rows that add up to the perfect number ten, was credited to Pythagoras and regarded as of utmost mystical importance. However, modern scholars debate whether Pythagoras himself developed the numerological teachings or if they were innovations of the later Pythagorean philosopher Philolaus of Croton.
Some scholars argue that Pythagoras never dealt with numbers and made no noteworthy contribution to mathematics, with the only math the Pythagoreans engaged in being simple, proofless arithmetic. Nonetheless, the Pythagoreans' numerological beliefs contributed significantly to the beginnings of mathematics.
Pythagoreanism
The Pythagorean Way of Life: A Religious and Philosophical Community
According to both Plato and Isocrates, Pythagoras was known as the founder of a new way of life that went beyond mere philosophy. The organization he founded in Croton was called a "school," but in many ways, it resembled a monastic community. The adherents were bound by a vow to Pythagoras and to each other, for the purpose of pursuing religious and ascetic observances, as well as studying his religious and philosophical theories. The members of the sect shared all their possessions in common and were devoted to each other, excluding outsiders. Pythagorean maxims included "All things in common among friends."
Two groups existed within early Pythagoreanism: the mathematikoi or "learners," and the akousmatikoi or "listeners." The latter are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings, while the former were seen as more intellectual, modernist, rationalist, and scientific. However, there was probably not a sharp distinction between them, and many Pythagoreans probably believed the two approaches were compatible. The study of mathematics and music may have been connected to the worship of Apollo, and music was seen as a purification for the soul, just as medicine was for the body.
The Pythagoreans 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. Both Iamblichus and Porphyry provide detailed accounts of the organization of the school, although their primary interest was not historical accuracy but rather to present Pythagoras as a divine figure, sent by the gods to benefit humankind.
Overall, Pythagoras's legacy was not just in mathematics but also in creating a community of followers devoted to a way of life focused on philosophy, religion, and asceticism.
Pythagorean Teachings: Symbols, Sayings, and Dietary Restrictions
Pythagorean teachings were shrouded in secrecy and were known as "symbols." Members of the Pythagorean community took a vow of silence not to reveal these symbols to non-members. Pythagoreanism also entailed a number of dietary prohibitions, which may have been motivated by the belief in the doctrine of metempsychosis. Pythagoras enforced a strictly vegetarian diet, according to some ancient writers, while other authorities contradict this statement. Pythagorean dietary restrictions also included a prohibition against the consumption of fava beans and the meat of non-sacrificial animals such as fish and poultry.
The Pythagorean community had a strict code of conduct, and those who did not obey the laws of the community were expelled. A number of "oral sayings" attributed to Pythagoras have survived, dealing with how members of the Pythagorean community should perform sacrifices, how they should honor 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.
New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five-year initiation period, during which they were required to remain silent. Female members of Pythagoras's school played an active role in its operations, and many prominent female philosophers contributed to the development of Neopythagoreanism.
Pythagoras: The Legend and Myths Surrounding the Greek Philosopher
Pythagoras, an ancient Greek mathematician and philosopher, was not only known for his groundbreaking contributions to mathematics and philosophy, but also for the elaborate legends and myths that surrounded him during his lifetime. According to Aristotle, Pythagoras was a supernatural figure and wonder-worker who exhibited a golden thigh at the Olympic Games as proof of his identity as the "Hyperborean Apollo". Pythagoras was also said to have dressed in all white, borne a golden wreath atop his head, and had extraordinary success in dealing with animals. He was reportedly able to convince a bull not to eat fava beans and a destructive bear to swear that it would never harm a living thing again.
While some scholars speculate that Pythagoras may have personally encouraged these legends, there is no direct evidence to support this claim. Anti-Pythagorean legends were also circulated, such as the story of Pythagoras descending to the underworld and convincing others of his journey upon his return. Despite the mythical elements surrounding his life, Pythagoras remains one of the most famous and controversial ancient Greek philosophers, often called the first "true" mathematician and the eponymous founder of Pythagoreanism.
Pythagoras Discoveries
Pythagoras and his Mathematical Contributions: Examining the Legend of the Pythagorean Theorem
Pythagoras is widely known for his mathematical discoveries, particularly the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. However, classical historians debate whether Pythagoras himself made any significant contributions to mathematics. Many discoveries, including the Pythagorean theorem, were attributed to him, and he was said to have identified the five regular solids and discovered the Theory of Proportions. Despite this, the Babylonians and Indians knew and used the Pythagorean theorem centuries before Pythagoras, but he may have been the first to introduce it to the Greeks.
The legend states that after he discovered the theorem, Pythagoras sacrificed an ox or a hecatomb to the gods, but this story has been rejected by some historians. While Pythagoras was never credited with having proved any theorem in antiquity, some have suggested that he or his students may have constructed the first proof. Nevertheless, Pythagoras's contributions to mathematics remain a subject of debate.
Pythagoras and the Mathematical Harmony of Music
According to legend, Pythagoras, an ancient Greek mathematician and philosopher, discovered the mathematical relationships behind musical notes. As the story goes, he was passing by a blacksmith shop and was struck by the harmonious sounds of the hammers striking the anvils, except for one discordant note. Curious, he entered the shop and began experimenting with the different hammers. He soon discovered that the sound produced by each hammer was directly proportional to its size. This realization led him to conclude that music is mathematical, and that there is a fundamental harmony between the world of numbers and the world of sound.
Pythagoras is often considered the first "true" mathematician, and his contributions to the field are still studied today. He is best known for his eponymous theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. However, Pythagoras was not just interested in mathematics. He founded a philosophical and religious movement known as Pythagoreanism, which explored the connections between numbers, music, and the cosmos.
Pythagoras believed that the universe was ordered and that everything in it was governed by mathematical principles. This belief extended to the human soul, which he believed was made up of mathematical harmony. Pythagoreanism was also influenced by vegetarianism and the idea of reincarnation. Pythagoras and his followers saw themselves as seekers of knowledge and wisdom, and their ideas had a profound impact on Western philosophy and science.
While Pythagoras may not have been the first to discover the mathematical relationships behind music, his legend has endured as a symbol of the fundamental connection between numbers and the natural world. His insights into the harmony of the universe and the human soul continue to inspire thinkers and scholars to this day.
Pythagoras and the Spherical Earth: Separating Fact from Fiction
According to legend, Pythagoras and his contemporary Parmenides of Elea were both credited with being the first to teach that the Earth was spherical, to divide the globe into five climatic zones, and to identify the morning star and evening star as the same celestial object. However, the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem, and Parmenides has a much stronger claim to having been the first.
Additionally, by the end of the fifth century BC, the fact that the Earth was spherical 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. This article explores the historical accuracy of Pythagoras' supposed contributions to our understanding of the shape of the Earth and celestial bodies, and separates fact from fiction.
Pythagoreanism and Its Influence on Philosophy
The Pythagorean philosophy, founded by the ancient Greek mathematician and philosopher Pythagoras, had a significant influence on philosophy and science throughout history. Pythagorean communities existed in various regions of Greece, including Magna Graecia, Phlius, and Thebes during the early fourth century BC. The Pythagorean philosopher Archytas was a highly influential figure in the politics of the city of Tarentum in Magna Graecia, as well as a renowned mathematician and musician who was a close friend of Plato. The philosophy of Plato, a student of Pythagoreanism, was heavily influenced by the teachings of the Pythagoreans.
Pythagorean ideas and concepts continued to be influential in philosophy and science even after the decline of the Pythagorean school in the fifth century BC. Neopythagoreanism became prominent in the first century BC, and its followers, such as Apollonius of Tyana and Moderatus of Gades, sought to emulate Pythagoras and live by Pythagorean teachings. The mathematician and musicologist Nicomachus and the philosopher Numenius of Apamea likewise expanded on Pythagorean numerology and music theory. The Pythagorean philosophy had a profound impact on the development of philosophy, mathematics, and science and continues to be studied and appreciated today.
Pythagorean Numerology and its Influence on Greek Sculpture and Architecture
Greek sculpture aimed to convey the timeless essence of reality beyond surface appearances. Early Archaic sculpture represented life in simple forms, possibly influenced by the earliest Greek natural philosophies. The Greeks believed that nature expressed itself in ideal forms, mathematically calculated as a type (εἶδος). Greek architects attempted to convey permanence through mathematics by seeking the mathematical relation (canon) behind aesthetic perfection. The number philosophy of the Pythagoreans triggered a revolution in Greek sculpture during the sixth century BC. Sculptors and architects sought to find the mathematical canon behind aesthetic perfection, possibly drawing on Pythagorean ideas. Polykleitos, a sculptor, believed that beauty consists in the proportion of the interrelation of parts with one another and with the whole. Greek architectural orders were constructed by mathematical relations, and the ratio 2:1 was the generative ratio of the Doric order.
The oldest known building designed according to Pythagorean teachings is the Porta Maggiore Basilica, built underground during the reign of the Roman emperor Nero as a secret place of worship for Pythagoreans. The basilica was built according to Pythagorean numerology, with each table in the sanctuary providing seats for seven people. The emperor Hadrian's Pantheon in Rome was also built based on Pythagorean numerology, with the temple's circular plan, central axis, hemispherical dome, and alignment with the four cardinal directions symbolizing Pythagorean views on the order of the universe. The single oculus at the top of the dome symbolized the monad and the sun-god Apollo, while the twenty-eight ribs extending from the oculus symbolized the moon, and the five coffered rings beneath the ribs represent the marriage of the sun and moon.
Pythagorean numerology had a significant influence on Greek sculpture and architecture, with its emphasis on mathematical canon and proportion. The belief that all things are numbers, as espoused by Pythagoras and his students, influenced Polykleitos and other sculptors to seek the mathematical relation behind aesthetic perfection. The basilica and the Pantheon are examples of Pythagorean numerology in architecture, showcasing the influence of Pythagorean ideas on the design of buildings.
Early Christian admiration for Pythagoras: his moral teachings, wisdom, and belief in the soul's immortality
The ancient Greek philosopher Pythagoras, known for his contributions to mathematics, philosophy, and mysticism, also gained respect among early Christians for his moral teachings and wisdom. Eusebius, a bishop of Caesarea, praised Pythagoras for his rule of silence, frugality, morality, and wise teachings in his Against Hierokles. In another work, Eusebius even compared Pythagoras to Moses. Church Father Jerome praised Pythagoras for his wisdom in one of his letters, and credited him with the belief in the immortality of the soul which he suggests Christians inherited from him. While Augustine of Hippo rejected Pythagoras's teaching of metempsychosis, he otherwise expressed admiration for him. In On the Trinity, Augustine lauded Pythagoras for his humility in calling himself a "lover of wisdom" rather than a "sage," and in another passage, defended Pythagoras's reputation by arguing that he certainly never taught the doctrine of metempsychosis.
Pythagoras in the Middle Ages: Founder of Mathematics and Music
During the Middle Ages, Pythagoras was highly esteemed for his contributions to mathematics and music, which were two of the Seven Liberal Arts. He appeared in numerous medieval depictions, in illuminated manuscripts and in relief sculptures on the portal of the Cathedral of Chartres. Pythagoras's influence was not limited to the arts, however, as his philosophical ideas also gained prominence during this time.
The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe, which led William of Conches (c. 1080–1160) to declare that Plato was Pythagorean. In the 1430s, the Camaldolese friar Ambrose Traversari translated Diogenes Laërtius's Lives and Opinions of Eminent Philosophers from Greek into Latin, and in the 1460s, the philosopher Marsilio Ficino translated Porphyry and Iamblichus's Lives of Pythagoras into Latin as well, thereby allowing them to be read and studied by western scholars.
In 1494, the Greek Neopythagorean scholar Constantine Lascaris published The Golden Verses of Pythagoras, translated into Latin, with a printed edition of his Grammatica, thereby bringing them to a widespread audience. In 1499, he published the first Renaissance biography of Pythagoras in his work Vitae illustrium philosophorum siculorum et calabrorum, issued in Messina. Pythagoras's ideas continued to inspire scholars throughout the Middle Ages and the Renaissance, cementing his place as one of the most influential thinkers in history.
Pythagoras' Influence on Modern Science: Copernicus, Kepler, Newton, and Einstein
Pythagoras' impact on the development of mathematics, music, and philosophy is well-known, but his influence on modern science is often overlooked. This article explores the Pythagorean influence on several prominent scientists, including Copernicus, Kepler, Newton, and Einstein.
Copernicus, in his groundbreaking book "On the Revolution of the Heavenly Spheres," cites Pythagoreans as the most important influence on his heliocentric model of the universe. Kepler considered himself a Pythagorean and believed in the doctrine of musica universalis. He attributed his discovery of the laws of planetary motion to Pythagorean teachings, as expressed in his book "Harmonices Mundi." Newton firmly believed in the Pythagorean doctrine of mathematical harmony and order in the universe and even attributed the discovery of the Law of Universal Gravitation to Pythagoras. Einstein also recognized the value of Pythagorean thought in scientific inquiry and argued that logical simplicity is an indispensable tool for scientific research.
Pythagorean ideas about the fundamental nature of reality and the mathematical order of the universe continue to resonate with scientists and thinkers today. Through the centuries, Pythagoras' legacy has persisted, influencing and inspiring scientists and philosophers alike.
Pythagoreanism and its Influence on Early Modern European Esotericism
Pythagoreanism, the philosophy and mathematical teachings of Pythagoras and his followers, has had a significant impact on European esotericism. Johannes Reuchlin, a German humanist scholar, synthesized Pythagoreanism with Christian theology and Jewish Kabbalah, arguing that Pythagoras was a kabbalist. Heinrich Cornelius Agrippa, in his three-volume treatise De Occulta Philosophia, called Pythagoras a "religious magi" and described his mystical numerology as operating on a supercelestial level.
The Freemasons modeled their society on the community founded by Pythagoras, and Rosicrucianism and Robert Fludd also used Pythagorean symbolism. John Dee, Adam Weishaupt, and even Wolfgang Amadeus Mozart were all heavily influenced by Pythagorean ideology, particularly the teaching that all things are made of numbers. Sylvain Maréchal, in his six-volume biography The Voyages of Pythagoras, declared that all revolutionaries in all time periods are the "heirs of Pythagoras".
Pythagorean Numerology in Literature and Philosophy
Throughout history, Pythagorean numerology has played a significant role in literature and philosophy. Dante Alighieri, the author of the Divine Comedy, was fascinated by Pythagorean numerology and incorporated it into his descriptions of Hell, Purgatory, and Heaven. He believed that Pythagoras saw unity as good and plurality as evil, and the number eleven and its multiples are found throughout the Divine Comedy.
Transcendentalists such as Henry David Thoreau were also impacted by Pythagorean numerology, using it as a guide for living a model life. Thoreau's views on nature may have been influenced by the Pythagorean idea of images corresponding to archetypes, and his magnum opus, Walden, explores the Pythagorean teaching of musica universalis. Overall, Pythagorean numerology continues to influence and inspire thinkers and artists to this day.
Frequently Asked Questions
Can any triangle other than the right angle triangle hold the Pythagorean theorem?
No, the Pythagorean theorem only holds for right-angled triangles. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is a fundamental theorem in Euclidean geometry and has numerous applications in mathematics, science, and engineering. However, it does not apply to any other type of triangle.
What role did Pythagoras play in the history of math?
Pythagoras was an ancient Greek mathematician and philosopher who is often called the first "true" mathematician. He is best known for the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
This theorem is one of the most famous and important results in mathematics and is used in a variety of fields, including physics, engineering, and geometry. Pythagoras is also credited with the development of the concept of proof and the creation of a mathematical community that would eventually become known as the Pythagoreans. The Pythagoreans made many important contributions to mathematics, including the discovery of irrational numbers, the development of musical theory, and the study of proportion and harmony.
Pythagoras himself is also credited with many other mathematical and philosophical ideas, such as the belief in the transmigration of souls and the importance of vegetarianism. His contributions to mathematics and philosophy have had a lasting impact on Western thought and continue to be studied and admired today.
Pythagoras Quotes
Here are some of Pythagoras’s most famous quotes.
Be silent or let thy words be worth more than silence.
No one is free who has not obtained the empire of himself.
Educate the children and it won't be necessary to punish the men.
To see more Pythagoras quotes, we recommend visiting the Pythagoras Quote section in Quotes Analysis.
We hope we have been helpful to you in this "Who is Pythagoras" article, and we hope you have a better understanding of who this amazing scientist and philosopher is!
