Pythagoras: Number as the Key to the Cosmos

Pythagoras of Samos, born around 570 BCE, moved to Croton in southern Italy, where he founded a community that combined philosophy, mathematics and a strict way of life. The Pythagoreans taught that number is the underlying structure of reality. A key piece of evidence was music: they found that harmonious intervals correspond to simple ratios, such as 2:1 for the octave, suggesting that mathematics governs the physical world. They also believed in the transmigration of souls, which led to rules such as avoiding certain foods.

Because the community was secretive and later followers credited discoveries to the founder, historians find it hard to know what Pythagoras himself did, including whether he proved the famous theorem named after him, which Babylonian mathematicians had used earlier. His lasting influence is the conviction that nature can be described mathematically, an idea that shaped Plato and, much later, modern science.