Pythagoras of Samos (Ancient Greek: Πυθαγόρας; about 570–495 BC) was an ancient Greek philosopher, expert in many areas, and the founder of a movement called Pythagoreanism. His teachings about politics and religion were widely known in Magna Graecia and influenced later thinkers like Plato and Aristotle, who in turn shaped Western philosophy. Scholars today disagree about where Pythagoras studied and who influenced him, but most agree he traveled to Croton in southern Italy around 530 BC. There, he started a school where students were said to take oaths of secrecy and live together in a simple, strict way of life.
In ancient times, Pythagoras was credited with important discoveries in math and science, such as the Pythagorean theorem, the theory of musical scales, the five regular solids, the theory of proportions, the idea that Earth is a sphere, the recognition that the morning and evening stars are the planet Venus, and the division of Earth into five climate zones. He was also the first person to call himself a "philosopher," meaning "lover of wisdom." Historians debate whether Pythagoras made these discoveries himself or if they were done by his followers or others, like Hippasus and Philolaus.
The idea most clearly linked to Pythagoras is the belief in the "transmigration of souls," or metempsychosis, which means that souls are immortal and move into new bodies after death. He may also have introduced the idea of "musica universalis," the belief that planets move in mathematical patterns that create a silent, musical harmony. After Croton defeated Sybaris around 510 BC, Pythagoras's followers faced conflict with supporters of democracy. Their meeting places were destroyed, and Pythagoras may have been killed or escaped to Metapontum, where he might have died.
Pythagoras influenced Plato, whose writings, especially Timaeus, show Pythagorean ideas. His teachings were revived in the first century BC by Middle Platonists and became central to Neopythagoreanism. Throughout the Middle Ages, Pythagoras was seen as a great philosopher, and his ideas affected scientists like Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbols also appeared in early modern European esoteric traditions, and his ideas, as described by Ovid in Metamorphoses, later inspired the modern vegetarian movement.
Life
No real writings by Pythagoras have survived, and very little is known for sure about his life. The earliest records about Pythagoras, written by Xenophanes, Heraclitus, Empedocles, Ion of Chios, and Herodotus, are short, unclear, and sometimes humorous. The main sources about Pythagoras’s life are three biographies from late ancient times, written by Diogenes Laërtius, Porphyry, and Iamblichus. These biographies are mostly filled with myths and stories that become more exaggerated the farther they are from Pythagoras’s time. However, Porphyry and Iamblichus also used some information from earlier writings by Aristotle’s students, Dicaearchus, Aristoxenus, and Heraclides Ponticus, from the 4th century BC. This information, when it can be identified, is usually considered the most reliable.
— Walter Burkert, 1972
Herodotus and Isocrates both say that Pythagoras was the son of Mnesarchus and was born on the Greek island of Samos in the eastern Aegean Sea. Mnesarchus was either a gem engraver or a wealthy merchant, but his background is unclear. Apollonius of Tyana wrote that Pythagoras’s mother was Pythaïs, a woman who was said to be related to Ancaeus, the mythical founder of Samos. Iamblichus wrote that the Pythia, a priestess at the temple of Apollo, predicted while Pythaïs was pregnant that she would give birth to a man who would be extremely wise, beautiful, and helpful to people. Iamblichus also believed Pythagoras’s mother was related to Ancaeus. About his birth date, Aristoxenus said Pythagoras left Samos when Polycrates ruled the island, at age 40, which would place his birth around 570 BC. Pythagoras’s name was linked to Pythian Apollo (Pūthíā). Aristippus of Cyrene, writing in the 4th century BC, explained the name by saying, “He spoke the truth as much as the Pythian [puthikós].”
During Pythagoras’s youth, Samos was a busy cultural center known for advanced engineering, such as the Tunnel of Eupalinos, and for lively festivals. It was a major trading hub in the Aegean Sea, where traders brought goods from the Near East. Christiane L. Joost-Gaugier suggests these traders likely brought ideas and traditions from the Near East as well. Pythagoras’s early life also overlapped with the rise of early Ionian natural philosophy. He was a contemporary of philosophers Anaximander and Anaximenes and the historian Hecataeus, all of whom lived in Miletus, across the sea from Samos.
Modern scholars have shown that Archaic Greek culture was influenced by Levantine and Mesopotamian cultures. This influence was recognized by later Classical and Hellenistic writers, who claimed Pythagoras learned unusual beliefs from travels to distant lands. The belief in metempsychosis, or the reincarnation of the soul after death, which Herodotus and Diogenes Laertius attributed to the Egyptians, led to stories that Pythagoras learned the Egyptian language from Pharaoh Amasis II and studied with Egyptian priests in Diospolis (Thebes), where he was the only foreigner allowed to participate in their worship. Other ancient writers said Pythagoras learned teachings from the Magi in Persia or even from Zoroaster. The Phoenicians are said to have taught him arithmetic, and the Chaldeans taught him astronomy. By the third century BC, it was reported that Pythagoras studied under the Jews. By the third century AD, Philostratus wrote that Pythagoras studied with sages or gymnosophists in India, and Iamblichus said he also studied with the Celts and Iberians.
Ancient sources also say Pythagoras studied under various Greek thinkers. Diogenes Laërtius wrote that Pythagoras visited Crete and went to the Cave of Ida with Epimenides. Some suggest Hermodamas of Samos may have been his teacher. Hermodamas was part of the Samian tradition of rhapsodic poetry, and his father, Creophylos, was said to have hosted Homer’s rival poet. Others credit Bias of Priene, Thales, or Anaximander (a student of Thales) as teachers. Some traditions say the mythic bard Orpheus was Pythagoras’s teacher, linking Pythagoreanism to the Orphic Mysteries. Neoplatonists wrote about a “sacred discourse” Pythagoras wrote in the Doric Greek dialect, which they believed was dictated to him by the Orphic priest Aglaophamus after his initiation into the Orphic Mysteries at Leibethra. Iamblichus said Orpheus was the model for Pythagoras’s speech, spiritual attitude, and worship. Iamblichus described Pythagoreanism as a mix of ideas from Orpheus, Egyptian priests, the Eleusinian Mysteries, and other traditions. However, the novelist Antonius Diogenes, writing in the second century BC, said Pythagoras discovered all his teachings by interpreting dreams. Riedweg notes that while these stories are fanciful, Pythagoras’s teachings were clearly influenced by Orphism.
Of the Greek sages said to have taught Pythagoras, Pherecydes of Syros is most often mentioned. Similar miracle stories are told about both Pythagoras and Pherecydes, including one where they predict a shipwreck, one where they predict the conquest of Messina, and one where they drink from a well and predict an earthquake. Apollonius Paradoxographus, a paradoxographer who may have lived in the second century BC, said Pythagoras’s ideas about miracles came from Pherecydes’s influence. Another story, possibly from the Neopythagorean philosopher Nicomachus, says that when Pherecydes was old and dying on Delos, Pythagoras returned to care for him. Duris, a historian and tyrant of Samos, is said to have proudly claimed that Pherecydes wrote an epitaph stating Pythagoras’s wisdom surpassed his own. Because of these connections, Riedweg concludes there may be some truth to the tradition that Pherecydes taught Pythagoras. Pythagoras and Pherecydes also seem to have shared similar views on the soul and the teaching of metempsychosis.
Porphyry repeats an account from Antiphon, who said that while still on Samos, Pythagoras founded a school called the “semicircle.” Here, Samians debated public issues. The school became so famous that the brightest minds in Greece came to Samos to hear Pythagoras teach. Pythagoras himself lived in a secret cave
Teachings
The exact details of Pythagoras's teachings are not fully known, but we can create a general outline of his main ideas. Aristotle wrote extensively about the beliefs of the Pythagoreans, but he did not mention Pythagoras directly. One of Pythagoras's main beliefs was metempsychosis, the idea that souls are immortal and that after death, a soul moves into a new body. This belief is mentioned by Xenophanes, Ion of Chios, and Herodotus. The earliest record of Pythagoras's belief in metempsychosis comes from a satirical poem written by Xenophanes of Colophon, who lived around the same time as Pythagoras. In the poem, Xenophanes describes Pythagoras trying to help a dog that was being beaten, claiming he recognized the dog's cries as those of a friend who had died. However, nothing is known about how Pythagoras believed metempsychosis happened.
Empedocles wrote in a poem that Pythagoras might have claimed to remember his past lives. Diogenes Laërtius reported that Heraclides Ponticus said Pythagoras told people he had lived four previous lives and could remember them clearly. His first life was as Aethalides, the son of Hermes, who gave him the ability to remember all his past lives. Next, he was Euphorbus, a minor hero from the Trojan War mentioned briefly in the Iliad. Then, he became Hermotimus, a philosopher who recognized Euphorbus's shield in a temple. His last life was as Pyrrhus, a fisherman from Delos. Another life, as noted by Dicaearchus, was as a beautiful courtesan.
Another belief connected to Pythagoras was the "harmony of the spheres," which suggested that planets and stars move according to mathematical rules that match musical notes, creating an invisible symphony. Porphyry wrote that Pythagoras taught the seven Muses were actually the seven planets singing together.
Modern scholars usually credit these ideas to Philolaus of Croton, a later Pythagorean philosopher. His writings are the earliest to describe the numerological and musical theories later attributed to Pythagoras. Walter Burkert, in his study Lore and Science in Ancient Pythagoreanism, argued that Pythagoras was a religious and political teacher, but the mathematical ideas linked to him were developed by Philolaus. Burkert claimed Pythagoras did not study numbers or make important mathematical discoveries. The Pythagoreans only used basic arithmetic, but these simple calculations helped start the field of mathematics. Later followers credited Pythagoras with creating the tetractys, a triangular shape with four rows that total ten, considered a sacred symbol. Iamblichus wrote that the tetractys was so important to Pythagoras's followers that they swore oaths by it.
This should not be confused with a simpler version called "Pythagorean numerology," which uses a method called isopsephic technique, also known as pythmenes' roots or base numbers. This method involves adding or dividing the numerical values of letters in a word to get a single number from one to nine.
Pythagoreanism
Both Plato and Isocrates say that Pythagoras was most famous for creating a new way of life. The group he founded in Croton was called a "school," but it was similar to a monastery. Members made promises to follow Pythagoras and support each other, aiming to live religiously and study his teachings. They shared all their possessions and focused only on each other, not outsiders. Ancient records describe Pythagoreans eating meals together, like the Spartans. A Pythagorean rule was "koinà tà phílōn" ("All things in common among friends"). Iamblichus and Porphyry wrote about the school's organization, but their main goal was to show Pythagoras as a god-sent figure, not to provide exact historical details. Iamblichus, in particular, compared the "Pythagorean Way of Life" to Christian monastic groups of his time. For Pythagoreans, the greatest goal was for the soul to join the gods and escape reincarnation.
Early Pythagoreanism had two groups: the mathematikoi ("learners") and the akousmatikoi ("listeners"). Scholars often say the akousmatikoi focused on mysticism and religious ideas, while the mathematikoi were more intellectual and scientific. Gregory warns that the differences between these groups may not have been clear, and many Pythagoreans likely saw both approaches as useful. The study of math and music may have been linked to worshiping Apollo. Pythagoreans believed music purified the soul, like medicine purified the body. One story says Pythagoras calmed rowdy youths by singing a solemn song. Physical activity, such as dancing, walking, and athletics, was important in their lifestyle. They also practiced daily reflection at the start and end of each day.
Pythagorean teachings were called "symbols" (symbola), and members promised to keep these secret from outsiders. Those who broke community rules were expelled, and others would mark their graves as if they had died. Many "oral sayings" (akoúsmata) attributed to Pythagoras survived, covering rituals, honoring gods, and burial practices. These sayings often stressed purity and avoiding pollution. Others warned against eating bread, using swords to light fires, or picking up crumbs, and taught to put the right sandal on first. The meanings of these rules are often unclear. Iamblichus explains some of Aristotle's original ritual purposes, but later writers like Porphyry gave different interpretations.
New members were not allowed to meet Pythagoras until after five years of silence. Sources say Pythagoras treated women respectfully, and women in his school may have had active roles. Iamblichus lists 235 famous Pythagoreans, 17 of whom were women. Later, many female philosophers helped shape Neopythagoreanism.
Pythagoreanism also included dietary rules. Some say Pythagoras banned eating fava beans and meat from non-sacrificial animals like fish and poultry. However, these claims are debated. Some believe the rules were tied to the belief in reincarnation, while others suggest they were linked to a genetic condition called favism, common in the Mediterranean. Some ancient writers claim Pythagoras avoided all animal foods, even avoiding cooks and hunters. Others disagree, saying he allowed meat except from certain animals like oxen and rams. Heraclides Ponticus notes Pythagoras ate meat from sacrifices and provided meat-based diets for athletes.
Legends
During his lifetime, Pythagoras became the subject of detailed stories that praised him highly. Aristotle described Pythagoras as a person with amazing abilities and a figure almost like a supernatural being. In one piece of writing, Aristotle mentions that Pythagoras had a golden thigh, which he displayed at the Olympic Games and showed to Abaris the Hyperborean as proof that he was the "Hyperborean Apollo." It is said that a priest of Apollo gave Pythagoras a magical arrow, which he used to travel long distances and perform special cleansing ceremonies. He was reportedly seen in both Metapontum and Croton at the same time. When Pythagoras crossed the river Kosas (now called Basento), several witnesses claimed they heard the river greet him by name. In Roman times, a legend stated that Pythagoras was the son of Apollo.
Pythagoras was said to wear only white clothing. He also wore a golden wreath on his head and trousers in the style of the Thracians. He was believed to have had great success in interacting with animals. A record from Aristotle describes how a deadly snake bit Pythagoras, but he bit the snake back and killed it. Both Porphyry and Iamblichus wrote that Pythagoras once convinced a bull not to eat fava beans and once persuaded a very destructive bear to promise it would never harm living things again, and the bear kept its promise. Riedweg suggests that Pythagoras may have encouraged these stories, but Gregory points out there is no direct proof of this.
Attributed discoveries
Although Pythagoras is most well-known today for a mathematical rule called the Pythagorean theorem, some historians argue that he may not have discovered it himself. Many discoveries in math, music, astronomy, and medicine were said to belong to Pythagoras. For more than 2,000 years, people have believed that Pythagoras discovered the Pythagorean theorem, which is a rule in geometry stating that "in a right triangle, the square of the longest side (called the hypotenuse) equals the sum of the squares of the other two sides." This can be written as a² + b² = c². A story claims that Pythagoras celebrated this discovery by offering a sacrifice to the gods, possibly a large number of oxen. However, some ancient writers, like Cicero, doubted this story because Pythagoras was said to oppose blood sacrifices. Another writer, Porphyry, suggested that the "ox" might have been made of dough instead.
The Pythagorean theorem was already used by the Babylonians and Indians long before Pythagoras lived. A scholar named Burkert argued that Pythagoras likely had no role in proving the theorem, as no ancient records credit him with doing so. Another scholar, Riedweg, noted that there is no evidence that Pythagoras or his followers created a logical proof for the theorem. The way the Babylonians used the theorem suggests they understood its general rule, but no proof has been found in ancient writings.
According to a story, Pythagoras discovered a connection between music and math when he heard blacksmiths working. He noticed that the sounds made by their hammers were harmonious, except for one. He tested the hammers and realized that the pitch of the sound depended on the size of the hammer, showing that music and math were related.
In ancient times, Pythagoras and Parmenides of Elea were both said to have been the first to teach that Earth is round, to divide the world into five climate zones, and to recognize that the morning star and evening star are the same object (now known as Venus). However, Parmenides has stronger evidence for these claims, and some believe the credit for these discoveries was mistakenly given to Pythagoras. A later thinker, Empedocles, who lived after Pythagoras and Parmenides, also knew Earth was round. By the late 5th century BC, most Greek scholars accepted that Earth was spherical.
Later influence in antiquity
Many Pythagorean communities lived in Magna Graecia, Phlius, and Thebes during the early fourth century BC. At the same time, the Pythagorean philosopher Archytas had a major influence on the politics of Tarentum in Magna Graecia. Later tradition says Archytas was elected as a military leader, or "strategos," seven times, even though others were not allowed to serve longer than a year. Archytas was also a famous mathematician and musician. He was a close friend of Plato, and his words appear in Plato's Republic. Aristotle said Plato's philosophy was strongly influenced by the teachings of the Pythagoreans. Cicero repeated this, writing that "They say Plato learned all things Pythagorean." According to Charles H. Kahn, Plato's middle dialogues, such as Meno, Phaedo, and The Republic, show strong "Pythagorean coloring," and his later dialogues, like Philebus and Timaeus, are very similar to Pythagorean ideas.
The poet Heraclitus of Ephesus (active around 500 BC), who lived near Samos and may have lived during Pythagoras's time, criticized Pythagoras, calling him a "clever charlatan" and saying he "selected from these writings he manufactured a wisdom for himself—much learning, artful knavery." Alcmaeon of Croton (active around 450 BC), a doctor who lived in Croton at the same time as Pythagoras, included many Pythagorean ideas in his writings and may have known Pythagoras personally. The Greek poets Ion of Chios (c. 480–c. 421 BC) and Empedocles of Acragas (c. 493–c. 432 BC) both praised Pythagoras in their poems.
According to R. M. Hare, Plato's Republic may be based on the "group of like-minded thinkers" that Pythagoras created in Croton. Plato may have also borrowed from Pythagoras the idea that mathematics and abstract thought provide a strong foundation for philosophy, science, and morality. Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world" and were likely influenced by Orphism. The philosopher Frederick Copleston said Plato probably learned his tripartite theory of the soul from the Pythagoreans.
A revival of Pythagorean teachings happened in the first century BC when Middle Platonist philosophers like Eudorus and Philo of Alexandria promoted a "new" Pythagoreanism in Alexandria. Around the same time, Neopythagoreanism became important. The first-century AD philosopher Apollonius of Tyana tried to follow Pythagoras's example and live by Pythagorean teachings. The Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean ideas about numbers and may have believed the soul was a "kind of mathematical harmony." The Neopythagorean mathematician and musicologist Nicomachus also expanded on Pythagorean numerology and music theory. Numenius of Apamea explained Plato's teachings using Pythagorean ideas.
The oldest known building designed using Pythagorean teachings is the Porta Maggiore Basilica, a hidden underground church built during the reign of the Roman emperor Nero as a secret place for Pythagoreans to worship. The church was built underground because of the Pythagorean focus on secrecy and a legend that Pythagoras lived in a cave on Samos. The church's apse faces east and its atrium faces west to honor the rising sun. It has a narrow entrance leading to a small pool where people could purify themselves. The building follows Pythagorean numerology, with each table in the sanctuary seating seven people. Three aisles lead to a single altar, symbolizing the three parts of the soul approaching the unity of Apollo. The apse shows the poet Sappho jumping from Leucadian cliffs, holding her lyre, while Apollo stands below, reaching up to protect her, representing Pythagorean ideas about the soul's immortality. The sanctuary's interior is mostly white, as the Pythagoreans considered white a sacred color.
The Pantheon in Rome, built by Emperor Hadrian, was also designed using Pythagorean numerology. Its circular shape, central axis, dome, and alignment with the four cardinal directions reflect Pythagorean views of the universe's order. The single opening at the top of the dome represents the "monad" and the sun-god Apollo. The 28 ribs below symbolize the moon, as 28 was the number of months in the Pythagorean lunar calendar. The five coffered rings beneath the ribs represent the union of the sun and moon.
Many early Christians respected Pythagoras. Eusebius, a bishop of Caesarea (c. 260–c. 340 AD), praised Pythagoras in his work Against Hierokles for his silence, simplicity, moral strength, and wise teachings. Eusebius also compared Pythagoras to Moses. In one letter, the Church Father Jerome (c. 347–c. 420 AD) praised Pythagoras's wisdom and credited him with teaching the immortality of the soul, which Jerome said Christians inherited from him. Augustine of Hippo (354–430 AD) rejected Pythagoras's idea of the soul being reborn in different bodies without naming him, but otherwise admired him. In On the Trinity, Augustine praised Pythagoras for calling himself a "lover of wisdom" instead of a "sage." Augustine also defended Pythagoras's reputation, saying he never taught the idea of the soul being reborn.
Influence after antiquity
During the Middle Ages, Pythagoras was seen as the creator of mathematics and music, two subjects included in the Seven Liberal Arts. He was often shown in medieval art, such as in beautifully decorated books and carvings on the entrance of the Cathedral of Chartres. The only work by Plato that survived in Latin in western Europe was Timaeus, which led William of Conches (c. 1080–1160) to say that Plato was influenced by Pythagoras. In the 1430s, a friar named Ambrose Traversari translated Lives and Opinions of Eminent Philosophers by Diogenes Laërtius from Greek into Latin. Later, in the 1460s, Marsilio Ficino translated Lives of Pythagoras by Porphyry and Iamblichus into Latin, allowing western scholars to study these works. In 1494, a Greek scholar named Constantine Lascaris published The Golden Verses of Pythagoras in Latin, along with a printed edition of his Grammatica, making these texts widely available. In 1499, Lascaris wrote the first Renaissance biography of Pythagoras in his book Vitae illustrium philosophorum siculorum et calabrorum, published in Messina.
In the preface of his book On the Revolution of the Heavenly Spheres (1543), Nicolaus Copernicus mentioned several Pythagoreans as key influences on his idea that the Earth orbits the Sun. He did not mention Aristarchus of Samos, a non-Pythagorean astronomer who had proposed a similar model centuries earlier, to emphasize that his work was closely connected to Pythagorean ideas. Johannes Kepler believed he was a Pythagorean. He studied the Pythagorean idea of musica universalis, which led him to discover the laws of planetary motion. He named his book on this topic Harmonices Mundi (Harmonics of the World), after the Pythagorean teaching that inspired him. Kepler also called Pythagoras the "grandfather" of all Copernicans.
Albert Einstein believed that a scientist could also be a "Platonist or a Pythagorean" if they valued logical simplicity in their research. The philosopher Alfred North Whitehead said that "Plato and Pythagoras were closer to modern science than Aristotle, because they were mathematicians, while Aristotle was the son of a doctor." By this view, Whitehead said that Einstein and other scientists followed the traditions of Pythagoras.
A fictional version of Pythagoras appears in Book XV of Ovid's Metamorphoses, where he urges his followers to eat only plants. Arthur Golding's 1567 English translation of Metamorphoses made Pythagoras well-known to English speakers during the early modern period. John Donne's Progress of the Soul discussed ideas from Pythagoras's speech, and Michel de Montaigne quoted it three times in his work Of Cruelty to argue against mistreating animals. John Dryden included a version of the scene with Pythagoras in his 1700 work Fables, Ancient and Modern, and John Gay's 1726 fable Pythagoras and the Countryman repeated its themes, linking eating meat with tyranny. Lord Chesterfield said he became a vegetarian after reading Pythagoras's speech in Metamorphoses. Before the word "vegetarianism" was created in the 1840s, people who avoided meat were called "Pythagoreans."
During the early modern period, European mystical traditions used Pythagorean ideas. Johannes Reuchlin, a German scholar, combined Pythagorean teachings with Christian beliefs and Jewish Kabbalah, saying that both were influenced by the traditions of Moses. In his work De verbo mirifico (1494), Reuchlin compared the Pythagorean symbol of the tetractys to the divine name YHWH, assigning symbolic meanings to its letters based on Pythagorean ideas.
Heinrich Cornelius Agrippa's influential book De Occulta Philosophia described Pythagoras as a "religious magi" and said that his mystical use of numbers connected to a high heavenly realm. Freemasons modeled their society after the group Pythagoras founded in Croton. Rosicrucianism used Pythagorean symbols, and Robert Fludd (1574–1637) believed his musical writings were inspired by Pythagoras. John Dee was strongly influenced by Pythagorean ideas, especially the belief that everything is made of numbers.
Transcendentalists studied ancient writings about Pythagoras to learn how to live a meaningful life. Henry David Thoreau was influenced by Thomas Taylor's translations of Life of Pythagoras by Iamblichus and Pythagoric Sayings by Stobaeus. Thoreau's ideas about nature may have been shaped by the Pythagorean belief that images reflect perfect forms. The Pythagorean idea of musica universalis appears often in Thoreau's major work, Walden.