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What did Pythagoras mean by the claim that all things are numbers?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — metaphysics Detail of a Roman copy (2nd century bce) of a Greek alabaster portrait bust of Aristotle (c. 325 bce); in the collection of the Museo Nazionale Romano, Rome.

The claim that "all things are numbers" is the foundational doctrine of Pythagoreanism, a philosophical movement established by Pythagoras in the 6th century BCE.12

In the context of metaphysics, this assertion means that the essence, structure, and order of the universe are fundamentally mathematical. Rather than identifying a physical substance (like water or air) as the primary element of reality, the Pythagoreans argued that the nature of all things can be determined by the numerical relations they express.234

This doctrine manifested in several ways:
* Proportionality: Pythagoreans observed that natural phenomena, such as musical harmony, are governed by simple whole-number ratios. They extended this to the cosmos, suggesting that the universe operates according to a hidden, measurable order.1243
* Symbolism: They invested numbers with mystical properties, associating specific values with concepts like justice, marriage, or unity.15
* Form as Reality: By emphasizing numerical proportions and harmony, the Pythagoreans shifted the focus of philosophy toward a view where form constitutes the basic reality of existence.43