Pythagoreans

The Pythagoreans were a group of early Greek thinkers and a religious–philosophical school associated with Pythagoras of Samos (c. 570–495 BCE). Active in Magna Graecia, particularly in Croton (modern Crotona, Italy), they formed a community that combined mathematical inquiry with ethical and religious practices. The movement persisted beyond Pythagoras himself, with later leaders and students contributing to its teachings.

Central to the Pythagorean worldview was the belief that numbers and their relationships underlie the structure of reality. They pursued mathematical and musical harmony, geometric problems, and number theory, and they regarded numerical patterns as revealing hidden truths about nature, the cosmos, and the soul. Their daily life often included initiations, ritual meal practices, and a communal, ascetic lifestyle, with dietary rules such as vegetarianism in some versions of the tradition.

Among their notable ideas and contributions are the emphasis on mathematical proof and systematic investigation of numbers, as well as early work on ratios and proportions. They are traditionally associated with the Pythagorean theorem in geometry and with discoveries related to numerical properties, such as even–odd distinctions and perfect numbers. The group also explored the connection between mathematics, music, and astronomy, proposing that celestial and earthly order reflect mathematical harmony.

Legacy and historiography: the Pythagoreans influenced later Greek philosophy, including Plato, and left a lasting imprint on Western mathematics and science. Due to fragmentary sources, much of what is known about them arises from later writers, and no single authoritative account exists of their beliefs or practices.