Pythagoras of Samos (c. 570–495 BCE) was an ancient Greek philosopher and mathematician, best known for the Pythagorean theorem, a fundamental principle in geometry. His life is shrouded in mystery, as very little reliable historical documentation exists. Much of what we know about him is a mix of history and legend.

Early Life

Pythagoras was born on the island of Samos in ancient Greece, around 570 BCE. He was reportedly well-traveled, spending time in Egypt, Babylonia, and possibly India, where he may have learned various mathematical and philosophical concepts. He was influenced by both Greek and Eastern thought.

Pythagorean School

Around 530 BCE, Pythagoras moved to Croton in southern Italy, where he founded a religious and philosophical school. His followers, known as Pythagoreans, believed in the immortality of the soul, the transmigration of souls (reincarnation), and that the universe was fundamentally mathematical in nature. Pythagoras himself taught that numbers were the essence of all things.

Mathematics and Contributions

Pythagoras’ most famous contribution is the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Although this theorem was likely known to the Babylonians, Pythagoras and his school were the first to provide a formal proof.

The Pythagoreans also contributed to number theory, developing ideas about even and odd numbers, triangular numbers, and ratios, particularly in relation to music theory. Pythagoras discovered that the intervals between harmonious musical notes could be expressed as ratios of small whole numbers, linking music and mathematics.

Philosophical Beliefs

Pythagoras’ teachings extended beyond mathematics. His school adhered to a strict code of conduct that blended religious ritual with a quest for knowledge. Pythagoreans believed in living a life of purity, harmony, and self-discipline. They practiced vegetarianism, as they believed in the transmigration of souls, which made them averse to killing animals.

Pythagoras also explored cosmology, proposing that the Earth was spherical and that the planets and stars moved in a harmonic pattern—an idea known as the "Music of the Spheres."

Later Life and Death

Pythagoras’ school eventually became embroiled in political conflicts in Croton, which led to its dissolution. Some accounts suggest that Pythagoras fled to nearby cities, and others claim he was killed during political upheaval around 495 BCE. His followers continued to spread his ideas, though the school split into factions after his death.

Legacy

Pythagoras had a profound influence on later philosophers, especially Plato, who incorporated Pythagorean ideas into his own work. While Pythagoras himself may not have written anything, his ideas laid the groundwork for developments in mathematics, philosophy, and science. His influence continued into the Renaissance and beyond, shaping the trajectory of Western thought.

Pythagoras remains a legendary figure in the history of mathematics and philosophy, embodying the blend of mysticism and rational inquiry that characterized early Greek thought.