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a religious and philosophical doctrine that flourished in ancient Greece during the sixth to fourth centuries B.C. Pythagoreanism takes as its point of departure the concept of number as the foundation of all being. At first, Pythagoreanism was passed on orally as a secret doctrine to members of a society organized by Pythagoras. The Pythagorean society was also a learned philosophical school, a political organization, and a religious and magic society of the “initiated.” Historically, it falls somewhere between primitive “male societies” and the spiritual “orders” of the Middle Ages.

The first written exposition of Pythagoreanism was provided by Philolaus. Only a few fragments of his works and those of John of Khios have survived. In the late fifth century, Pythagoreanism gradually drew closer to Socratic and Platonic philosophy. It assumed its final form toward the end of Plato’s life, at the time of his Academy. Archytas of Tarentus (first half of the fourth century) was the last major representative of Pythagoreanism. In the first century B.C. the ideas of Pythagoreanism became the foundation for the development of neo-Pythagoreanism, which existed until the third century. Among the most outstanding neo-Pythagoreans were Nigidius Figulus, Apollonius of Tyana, and Numenius of Apamea.

Unlike the Ionian school, which sought to reduce all being to a single material element, the Pythagoreans focused not on the elements but on their formation and arithmetic and geometric structure, combining these considerations with acoustics and astronomy. The foundation of Pythagoreanism is a doctrine of numbers in themselves, or of gods as numbers. This doctrine is developed into a theory of the universe as number, of things as numbers, of souls as numbers, and, finally, of art as number (for example, the concept of a numerical “canon” in sculpture, and the mathematization of music).

Pythagoreanism gave rise to a highly original arithmetic that attributed a plastic and animate meaning to every number. For example, the number “one” was treated as absolute and indivisible unity; the number “two” as a retreat into an indeterminate distance, or infinity; the number “three” as the first determinate shape in infinity; and the number “four” as the first physical embodiment of the triadic form.

According to tradition, the early Pythagoreans used observations of metal disks of various sizes or vessels filled to various levels to determine the numerical ratios that describe certain musical intervals: the fourth (4/3), the fifth (3/2), and the octave (1/2). These numerical ratios were associated with material elements or regular geometric bodies. Tones, semitones, and even smaller fractions of tones were understood by the Pythagoreans with an accuracy surpassing that of modern European acoustics. The Pythagoreans extended their physical arithmetic acoustic concept to the entire universe, which they believed to consist of ten celestial spheres. Each sphere emitted its own characteristic sound, consisted of a definite combination of regular geometric bodies, and incorporated a specific material element with a particular structure, proportionality, and consistency.

The Pythagorean theory that the soul is nonmaterial was originally included in the general theory of the cycle of matter, which gave rise to the famous Orphic and Pythagorean theory of the transmigration and eternal recycling of souls.

The Pythagorean theory of opposites represents a philosophical systematization of the very ancient mythological concept of binary opposites. There were ten basic pairs of opposites: limit (the finite) and the unlimited (infinite), odd and even, one and many, right and left, male and female, rest and motion, straight and curved, light and darkness, good and evil, square and oblong. The musical and ethical “agreement” (or fitting together) of opposites was called harmony by Philolaus.

The Pythagorean school advocated asceticism in the classical sense: the healthy soul requires a healthy body, and both require the continuous influence of music, as well as self-examination and elevation to the higher spheres of being. Thus, music, philosophical and mystical meditation, and medicine were virtually merged in Pythagoreanism.

The ideas of Pythagoreanism were widely known not only in antiquity but also during the Middle Ages and in modern times.


Diels, H. Fragmente der Vorsokratiker, 9th ed., vols. 1–2. Published by W. Kranz. Berlin, 1960. Chapters 14–20, pages 32–58.
In Russian translation:
Makovel’skii, A. Dosokratiki, part 3. Kazan, 1919.


Dynnik, M. A. Ocherk istorii filosofii klassicheskoi Gretsii. Moscow, 1936. Chapter 2.
Losev, A. F. Istoriia antichnoi estetiki. Moscow, 1963. Pages 263–315.
Méautis, G. Recherches sur le Pythagorisme. Neuchâtel, 1922.
Zeller, E. Die Philosophie der Griechen …, 7th ed., part 1, first half. Leipzig, 1963. Pages 445–617.
Frank, E. Plato und die sogenannten Pylhagoreer. Halle (Saale), 1923.
Haase, R. Geschichte des harmonikalen Pythagoreismus. Vienna, 1969.
Vogel, C. J. de. Pythagoras and Early Pythagoreanism. Assen, 1966.


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