Pythagoreanism is the body of teachings and way of life associated with Pythagoras of Samos, who founded a community at Croton in southern Italy around 530 BCE. It combined religious doctrines such as the transmigration of souls with the conviction that number and harmony underlie the cosmos, and it profoundly shaped Plato, later Platonism and Western esoteric traditions.
Pythagoreanism at a glance
| Founder | Pythagoras of Samos (c. 570-490 BCE) |
|---|---|
| Founded | Croton, southern Italy, c. 530 BCE |
| Key figures | Philolaus, Archytas of Tarentum, later Nicomachus and Iamblichus |
| Core doctrines | Transmigration of souls, cosmic harmony, the importance of number |
| Divisions | Akousmatikoi ("listeners") and mathematikoi ("learners") |
| Later revival | Neopythagoreanism, from the 1st century BCE |
Pythagoras and the early community
Pythagoras left the island of Samos and settled at Croton in Magna Graecia around 530 BCE. There he founded a community whose members shared a disciplined way of life and exercised considerable political influence in several Greek cities of southern Italy. He wrote nothing, and almost everything said about him comes from later sources, above all the biographies by Diogenes Laertius, Porphyry and Iamblichus, written many centuries after his death. Modern scholars therefore distinguish carefully between Pythagoras himself and the later school that bore his name.
Around the middle of the fifth century BCE, violent reactions against the Pythagorean societies broke out in several cities, and their meeting houses were attacked. Many members fled, and by about 400 BCE the main centers of the movement had moved to places such as Tarentum and to mainland Greece.
Membership reportedly included women as well as men, and later sources name several female Pythagoreans, among them Theano, traditionally described as the wife or pupil of Pythagoras. Ancient writers also claimed that the community kept its doctrines secret and that disclosure to outsiders was forbidden, which helps explain why reliable early evidence is so scarce.
Two currents: listeners and learners
Ancient reports describe a division among the followers. The akousmatikoi, or "listeners," preserved the akousmata, short oral sayings that prescribed ritual and ethical conduct, such as abstaining from beans or observing rules about sacrifice and dress. The mathematikoi, or "learners," claimed a deeper understanding and pursued mathematics, astronomy and music. Each group regarded itself as the true heir of Pythagoras.
Several practices are widely attributed to the school: silence and self-examination, communal friendship, and dietary restrictions. The famous avoidance of meat was linked to belief in the kinship of all living beings, although ancient sources disagree about how strict it was.
Number, harmony and the cosmos
The best-known Pythagorean idea is that number and proportion explain the order of the world. Tradition credits the school with discovering that the main musical intervals correspond to simple ratios: the octave to 2:1, the fifth to 3:2 and the fourth to 4:3. From this grew the notion of a harmony of the heavens, the "music of the spheres" produced by the movements of the celestial bodies.
The tetractys, a triangle of ten points arranged in rows of one, two, three and four, served as a sacred symbol and was invoked in an oath. Philolaus of Croton, the first Pythagorean whose writings survive in fragments, taught that the cosmos is composed of "limiters" and "unlimiteds" held together by harmony, and he removed the earth from the center of the universe in favor of a central fire. Archytas of Tarentum, a friend of Plato, developed mathematical theories of proportion and mechanics.
The so-called Pythagorean theorem was known to Babylonian mathematicians long before, and historians doubt that Pythagoras himself proved it. Aristotle's claim that the Pythagoreans held things to "be" numbers has also been debated, since it does not match Philolaus's own fragments.
The soul and the Pythagorean life
Pythagoras was remembered above all for teaching that the soul is immortal and passes into new bodies after death, a doctrine known as metempsychosis and closely related to ideas found in Orphism. The goal of the Pythagorean life was the purification of the soul through study, music, moral discipline and ritual purity. Later legend associated Pythagoras with Apollo and credited him with miraculous powers, stories that reveal how he became a semi-divine sage in later memory. For the wider history of these ideas, see reincarnation.
Neopythagoreanism and legacy
From the first century BCE a revival known as Neopythagoreanism blended Pythagorean themes with Platonic and Stoic thought. Figures associated with it include Nigidius Figulus in Rome, the wandering sage Apollonius of Tyana, Nicomachus of Gerasa, whose Introduction to Arithmetic became a standard textbook, and Numenius of Apamea. By the third century CE these currents had merged into Neoplatonism, and Iamblichus wrote a work on the Pythagorean way of life.
Pythagorean ideas passed into medieval education through the quadrivium of arithmetic, geometry, music and astronomy. Copernicus cited the Pythagoreans in support of a moving earth, and Kepler sought musical harmonies in planetary motion. In esoteric traditions the Pythagorean reverence for number lives on in numerology, which modern science treats as a symbolic practice without predictive validity.
Related entries
Frequently asked questions
What did the Pythagoreans believe?
The Pythagoreans believed that the soul is immortal and is reborn in new bodies, that the cosmos is ordered by number and harmony, and that a disciplined life of study, music, self-examination and ritual purity could purify the soul. Many also followed dietary rules, including the well-known avoidance of beans and, for some, of meat.
Why did Pythagoreans not eat beans?
Ancient writers offered many explanations and none is certain. Suggestions included the bean's resemblance to the human body, a supposed link between beans and souls or the underworld, their effect on digestion and dreams, and their use in voting in city politics. The taboo was one of the akousmata, the traditional oral rules of the school.
Is numerology Pythagorean?
Modern numerology often calls itself Pythagorean, but the connection is loose. The ancient Pythagoreans gave numbers philosophical and religious significance, and later Neopythagoreans developed number symbolism. The letter-to-number systems used in modern numerology, however, were largely formulated in the nineteenth and twentieth centuries and have no demonstrated predictive power.
Sources and further reading
This entry replaces an article from the original Mystica encyclopedia (online since 2001). It was rewritten from the sources above by The Mystica Editorial Team under our editorial standards. Last reviewed: September 30, 2026.