PYTHAGORAS

Pythagoras was born on Samos around 570 BCE, son of an engraver or merchant. The island was ruled by the tyrant Polycrates, whose court attracted artists and thinkers — but also whose tyranny eventually drove Pythagoras away.

He travelled extensively — to Egypt, where he reportedly spent years with priests learning geometry and religion; to Babylon, where he absorbed astronomical knowledge; possibly to India, though this is disputed. By the time he settled in Croton, a Greek colony in southern Italy, around 530 BCE, he had assembled a synthesis of mathematical, musical, astronomical, and mystical knowledge.

At Croton, he founded the Pythagorean brotherhood — part philosophical school, part religious cult, part political faction. Members lived communally, shared property, followed strict dietary and behavioural rules, and maintained secrecy about inner teachings. They believed in the transmigration of souls and practiced elaborate purification rituals. Yet they also developed rigorous mathematics: the theorem that bears Pythagoras’ name, the theory of proportions, the mathematical basis of musical harmony.

The brotherhood became politically powerful in Croton, which generated resentment. Around 509 BCE, anti-Pythagorean riots broke out. Their meeting house was burned; many members died. Pythagoras fled to Metapontum, where he died around 495 BCE. The school survived, splitting into “mathematici” (who focused on numbers) and “acousmatici” (who focused on rules and sayings).

He wrote nothing, or nothing survived. We know him only through later reports, some admiring, some hostile, all uncertain. The man himself remains hidden behind legend.

The Pythagorean insight is radical: the universe is not made of water, air, or any physical stuff — it is made of number. Mathematical relationships are not just useful descriptions; they are the ultimate reality underlying appearances.

The evidence came from music. When Pythagoreans discovered that harmonious intervals correspond to simple numerical ratios, they concluded that beauty itself is mathematical. If music is number made audible, perhaps the cosmos is number made visible. The “music of the spheres” — the idea that planetary motions embody mathematical harmonies — followed naturally.

This led to a distinctive metaphysics. Numbers were not abstractions but realities more fundamental than physical objects. The number one represented unity, two represented diversity, three harmony, four justice (2×2, the first square). Odd numbers were male, even numbers female. Ten (1+2+3+4) was sacred, the tetractys, containing all musical ratios.

Behind this numerical mysticism lay genuine mathematics. The Pythagoreans proved geometric theorems, developed the theory of proportions, and discovered that some ratios (like the diagonal of a square to its side) cannot be expressed as ratios of whole numbers — irrational numbers, which threatened their entire worldview.

They also taught the transmigration of souls — that the soul is immortal and passes through multiple lives, human and animal. This connected to their vegetarianism and their ethics: if your soul might inhabit an animal, you shouldn’t eat animals. Philosophy was preparation for death, purifying the soul for its next journey.

The combination of rigorous mathematics and mystical religion seems strange to modern minds. But for Pythagoras, they were one: mathematics reveals the divine order of the cosmos, and understanding that order purifies the soul.