Pythagorean School and Number Theory

Pythagoras established a school in Croton, southern Italy around 530 BCE, creating a secretive brotherhood that studied mathematics, philosophy, and mysticism. The Pythagoreans developed number theory as a philosophical discipline, maintaining that mathematical relationships underlie reality. They categorized numbers as perfect, abundant, or deficient, discovered irrational numbers through geometry, and established mathematical principles of musical harmonies. Their work included triangular numbers, perfect numbers, and the tetractys. Pythagorean contributions influenced later Greek mathematicians including Plato and Euclid, shaping subsequent Western mathematical development.