Pythagoras migrated to southern Italy about 532 BC, apparently to escape Samos's tyrannical rule, and established his ethico-political academy at Croton (now Crotone).

It is difficult to distinguish Pythagoras's teachings from those of his disciples. None of his writings have survived, and Pythagoreans invariably supported their doctrines by indiscriminately citing their master's authority. Pythagoras, however, is generally credited with the theory of the functional significance of numbers in the objective world and in music. Other discoveries often attributed to him (e.g., the incommensurability of the side and diagonal of a square, and the Pythagorean theorem for right triangles) were probably developed only later by the Pythagorean school. More probably the bulk of the intellectual tradition originating with Pythagoras himself belongs to mystical wisdom rather than to scientific scholarship.

Pythagoras migrated in his youth to Rhegium. He made a statue of Philoctetes, noted for the physical expression of pain; an Apollo shooting the Python at Delphi; and a man singing to the lyre. His technical improvements went far in ending Archaic stiffness in Greek sculpture. No existing work can be certainly attributed to him, and, although his influence must have been widespread, attempts to identify copies of his works remain conjectural.