Pythagoras

Quick Facts

• Who: Pythagoras of Samos, a Greek religious teacher and early philosopher.
• Lived: c. 570-c. 495 BCE.
• Where: Born on Samos; taught mainly at Croton in southern Italy.
• Tradition: Pre-Socratic philosophy and the Pythagorean way of life.
• Known for: The soul's rebirth, disciplined communal living, number as a clue to reality, musical harmony, and the later Pythagorean school.
• Source caution: Pythagoras left no secure writings. Many famous doctrines were developed by later Pythagoreans and then attached to him.

The Big Question

Can a human life become ordered by the same pattern that orders the cosmos?

Pythagoras answered with a way of life. The world is not just noise and chance. It has order, proportion, and rhythm. A person should learn that order through music, mathematics, discipline, and purification of the soul.

In One Minute

Pythagoras is famous today for the Pythagorean theorem, but the historical Pythagoras was probably better known as the founder of a strict religious-philosophical community. His followers treated philosophy as training for the whole person.

The teaching most securely connected with him is the transmigration of souls. This means that the soul survives death and can be reborn in another body. Because of this, Pythagorean life stressed purity, self-control, respect for living things, and careful habits.

The larger Pythagorean tradition joined this religious life to mathematics. It saw number and proportion as signs of deep order. Musical intervals gave the clearest example: pleasant notes can be described by simple ratios. From there, Pythagoreans pictured the soul and the cosmos as things that could be harmonious or disordered.

What They Taught

Pythagoras taught that philosophy should change how a person lives. The goal was to make the soul orderly, pure, and fit for a better life after death.

The first major doctrine is transmigration, also called metempsychosis. This is the view that the soul is immortal and moves from one living body to another. A human soul might be reborn in another human body, and some reports say it could pass into animals. That belief made ordinary conduct serious: diet, speech, desire, and treatment of living things all affected the soul.

The second major doctrine is purification. Purification means training the soul away from confusion, violence, appetite, and disorder. It involved rules, ritual, diet, silence, memory exercises, music, and loyalty to the community. Some rules now sound strange, such as rules about beans or ritual purity. Their point was to make philosophy a daily practice.

The third doctrine is the famous Pythagorean love of number. Here we have to be careful. Early evidence makes Pythagoras himself look more like a religious founder than a professional mathematician. Later Pythagoreans, especially in the fifth century BCE, made number central to philosophy. Still, the tradition attached to Pythagoras taught that number is not merely a tool for counting sheep or measuring land. Number shows structure. It reveals how things fit together.

Music made this idea vivid. An octave can be expressed by the ratio 2:1. A fifth can be expressed by 3:2. A fourth can be expressed by 4:3. A ratio is a relation between quantities. For Pythagoreans, this was a clue that beauty can have a hidden pattern.

The fourth doctrine is harmony. Harmony means an ordered relation among parts. In music, it is the fitting relation between notes. In a person, it is the fitting relation between desire, habit, and reason. In the cosmos, it is the ordered arrangement of the heavens. The Greek word kosmos means an ordered whole, not just "outer space."

Key Ideas With Examples

• Transmigration: The soul survives death and is reborn. If souls can pass through different bodies, humans and animals are kin in a deeper sense.
• Purification: The soul can be made cleaner and more orderly through practice. Silence trains speech and attention. Music can calm the emotions. Diet can train appetite.
• Number: Number reveals form and structure. A triangle is understood by its relations, not by touching one drawn example.
• Ratio: A ratio is a comparison between quantities, such as 2:1 or 3:2. Musical intervals showed Pythagoreans that a felt quality, like consonant sound, can have a mathematical pattern.
• Harmony: Harmony is order among parts. A tuned lyre has well-related strings. A disciplined person has desire and thought working together.
• Tetractys: The tetractys is the triangular arrangement of 1 + 2 + 3 + 4 = 10. Later Pythagoreans treated it as a symbol of completeness because those numbers generate the basic musical ratios.
• Pythagorean theorem: In a right triangle, the square on the longest side equals the sum of the squares on the other two sides. The rule is older than Pythagoras in some form, and we do not have proof that he discovered it.

Major Works

Pythagoras has no secure surviving work. Ancient writers often say little about what he himself wrote or taught, and later followers freely used his name. The safest "works" to know are surrounding texts and traditions.

• Pythagorean sayings, or acusmata: Short oral teachings, rules, and question-and-answer formulas. They cover ritual conduct, purity, cosmic symbols, and practical discipline. They show Pythagorean philosophy as a lived path.
• Fragments of Philolaus: Philolaus was a later Pythagorean, not Pythagoras himself. His fragments are important because they give early evidence for a more explicit theory of limit, unlimitedness, number, and cosmic order.
• The Golden Verses: This later poem was attributed to Pythagoras in antiquity. It is not reliable as a book by him, but it gives a useful picture of the moral Pythagoras: examine your actions, control desire, honor the divine, and train the soul.

Why It Matters

Pythagoras matters because he made philosophy look like a whole way of life. He joined belief, discipline, community, music, mathematics, and moral training. Later Greek philosophy often kept that ambition: wisdom should change the soul, not just win debates.

He also helped give mathematics a new dignity. Mathematics was not only useful for builders, merchants, or surveyors. It could reveal deep structure. This idea shaped Greek geometry, music theory, astronomy, and metaphysics.

Proponents, Critics, and Opponents

The main proponents were the Pythagorean communities that traced their life to Pythagoras. Ancient sources sometimes distinguish acusmatics, who emphasized sayings and rules, from mathematics-focused Pythagoreans, who emphasized study and explanation. The division is hard to reconstruct, but it captures a real tension: Is Pythagoreanism mainly a sacred discipline, or mainly a mathematical philosophy?

Plato was deeply receptive to Pythagorean themes. His interest in mathematics, purification, the soul, and cosmic order has obvious Pythagorean echoes. Later Platonism and Neoplatonism strengthened the link even more.

Aristotle is one of the most important critical witnesses. He discusses "the Pythagoreans" as thinkers who made number and opposites basic, but he is much less clear that Pythagoras himself taught the later mathematical system. That makes Aristotle useful for both influence and caution.

Parmenides is a helpful contrast: Pythagoreanism seeks intelligible order through number and harmony, while Parmenides asks what can be thought or said without contradiction. Empedocles shares some religious atmosphere with Pythagoreanism, especially purification and the soul's exile. The Upanishadic Sages offer a broader comparison because they also speak about rebirth and liberation, though their framework is different.

The sharpest criticism is historical. Ancient and modern readers have often credited Pythagoras with too much: the theorem, rigorous geometry, detailed cosmology, and elaborate number symbolism. Some of that belongs to later Pythagoreans. Some may be legend.

Related Pages

• Pre-Socratics
• Plato
• Aristotle
• Parmenides
• Empedocles
• Upanishadic Sages
• Platonism
• Neoplatonism