Hippasus of Metapontum was a philosopher and mathematician who lived in the 5th century BCE in southern Italy. He was a member of the Pythagorean school, a religious and intellectual community known for its studies in mathematics, music, and cosmology. The details of his life are obscure, but later ancient sources report that he was expelled from the Pythagorean community. According to these traditions, he was punished for revealing the group’s secret doctrines.

No writings by Hippasus survive today. Some ancient reports suggest he may have written a text called Mystic Discourse, but its existence is uncertain. His ideas are known only through later accounts.

Hippasus is historically significant for his association with a major mathematical discovery. He is most famously linked to the discovery of incommensurable magnitudes, which demonstrated that some geometric ratios, like the diagonal of a square, cannot be expressed as simple whole-number ratios. This finding challenged the core Pythagorean belief that all things could be explained by integers. Some sources also connect him to discoveries in musical harmony and the geometry of the dodecahedron. Modern scholars view his story—particularly his alleged expulsion—as emblematic of the tensions within early Pythagoreanism between secretive religious tradition and open scientific inquiry.