Pythagoras 570 BC – 495 BC

Pythagoras was a Greek philosopher and mathematician born on the island of Samos around 570 BC. He founded a religious and philosophical brotherhood at Croton in southern Italy, where his followers pursued a communal life of study, asceticism, and ritual purification. The Pythagoreans held that number is the principle of all things and that the cosmos is structured by mathematical ratios, an idea that profoundly influenced Plato. Pythagoras left no writings, and the doctrines transmitted under his name combine his own teachings with those of his school. His influence on Western mathematics, music theory, and metaphysics is foundational.

Pythagoras of Samos (c. 570–c. 495 BC) was an early Greek philosopher and the founding figure of the philosophical-religious community whose work shaped Greek mathematics, astronomy, and philosophy. He emigrated from Samos to Croton in southern Italy around 530 BC and established the religious-philosophical community for which he is remembered. The historical Pythagoras is poorly attested — none of his own writing survives, and reliable accounts of his teaching are late — but the philosophical-religious movement he founded was substantial and influential.

The Pythagorean tradition treated number as the principle of reality. The harmonic ratios discovered in musical intervals — the octave, the fifth, the fourth — were taken as evidence that the cosmos is mathematically structured and that disciplined inquiry into numerical relationships could disclose its underlying order. The doctrine of the harmony of the spheres extends this to astronomy: the heavenly bodies move in mathematically determined orbits whose proportions produce a music human beings cannot directly hear.

The Pythagorean community lived under strict communal rules, observed unusual dietary prohibitions (famously of beans), and held the doctrine of the transmigration of souls. Pythagoras's influence on Plato is enormous — the mathematical structure of the Timaeus's cosmology, the doctrine of the immortality of the soul, the political organization of the Republic — and through Plato on the broader Western philosophical tradition. He is the source through which mathematics entered Western philosophy as a foundational discipline.