Pythagoras

Pythagoras of Samos was an ancient Greek thinker who laid the foundations of a movement known as Pythagoreanism. He lived circa 570–495 BCE. Although celebrated for the Pythagorean theorem, his own contributions are surrounded by legend, and details of his life come largely from later biographies.

Life and movement: Born on the island of Samos, he traveled widely before settling in Croton (in southern Italy), where he established a community of followers. The group combined religious, ethical, and mathematical teachings, emphasizing communal living, strict rules, vegetarianism, and a shared body of doctrine. They maintained a degree of secrecy and ritual.

Beliefs and influence: Pythagoras and his followers believed that numbers and numerical relations underlie the structure of reality. They linked arithmetic, geometry, astronomy, and music through the idea of harmony of the spheres. Metaphysical beliefs included the transmigration of souls, or reincarnation.

Mathematical contributions: The association with the theorem a^2 + b^2 = c^2 in right triangles is a hallmark, but the theorem predates him. The Pythagoreans advanced number theory, including the study of prime numbers and perfect numbers, and they explored the concept of irrationality, a topic clarified by later figures such as Hippasus.

Legacy: Pythagoras' ideas influenced later Greek philosophy, notably Plato, and helped shape mathematics as a discipline. Attributions such as the Golden Verses reflect later tradition and the enduring cultural impact of his reputation.