Pythagoras of Samos was an ancient Greek philosopher and mathematician who founded the Pythagorean brotherhood in Croton, Magna Graecia. His teachings connected mathematics, music, and cosmology, profoundly influencing Western philosophy and science.
Pythagoras is born on the Aegean island of Samos, to Mnesarchus, a gem engraver, and Pythais. His birth is traditionally dated to around 570 BCE. #history #mathematics
Pythagoras reportedly studies under Thales and Anaximander in Miletus, gaining early exposure to geometry and cosmology. These influences shape his later philosophical approach. #philosophy #history
Pythagoras travels to Egypt, where he studies with priests at temples, learning mathematics, geometry, and religious rituals. This stay deeply influences his views on the soul and numbers. #history #egypt
Pythagoras visits Babylon, likely during the reign of Cyrus the Great, and studies Babylonian astronomy, mathematics, and mysticism. He gains knowledge of advanced arithmetic and celestial cycles. #history #astronomy
Pythagoras returns to Samos during the tyranny of Polycrates. Displeased with the political climate, he decides to leave the island for Magna Graecia. #history #politics
Pythagoras introduces the concept of metempsychosis (reincarnation) to the brotherhood, claiming memory of past lives. This influences later Greek and Roman thought. #religion #philosophy
The Pythagorean community practices vegetarianism, believing in the kinship of all living beings. This ethical stance becomes a defining characteristic. #ethics #history
Pythagoras migrates to the Greek colony of Croton in southern Italy, where he gains influence among the aristocracy. He begins teaching his philosophical and mathematical doctrines. #history #philosophy
Pythagoras establishes a secretive religious and philosophical school known as the Pythagorean Brotherhood. Members live communally, study mathematics, and follow strict ethical rules. #philosophy #history
Pythagoras teaches that numbers are the ultimate reality and the basis of all things in the cosmos. This principle becomes the cornerstone of Pythagorean philosophy. #philosophy #mathematics
Pythagoras discovers that musical intervals correspond to simple numerical ratios: octave (2:1), fifth (3:2), and fourth (4:3). This links music and mathematics. #music #mathematics
Pythagoreans study perfect numbers (e.g., 6, 28) and figurate numbers (triangular, square, pentagonal). These investigations lay groundwork for number theory. #mathematics #history
The Pythagorean school develops a formal theory of musical harmony based on ratios, leading to the concept of the 'harmony of the spheres.' #music #science
Pythagoreans prove that the sum of interior angles in a triangle equals two right angles (180°), a key result in Euclidean geometry. #geometry #mathematics
The Pythagorean theorem (a² + b² = c²) becomes associated with Pythagoras, though known earlier. Proof is likely developed by his school. #geometry #mathematics
The brotherhood teaches that the soul is immortal and cycles through reincarnation until purified. This theology shapes Greek philosophy. #religion #philosophy
The Pythagorean pentagram (star polygon) is adopted as a symbol of the brotherhood, representing mathematical harmony and health. #symbol #mathematics
Pythagoras dies, likely around 495 BCE, possibly during an attack on the Pythagorean community in Croton. His death marks the end of his direct influence, but his school continues. #history #philosophy
According to legend, Pythagoras is killed while fleeing an attack by Cylon's followers, refusing to trample a bean field due to his superstitious beliefs. #history #legend
After Pythagoras's death, the Pythagorean brotherhood survives, led by followers like Aristaeus and later Philolaus. The school persists despite political conflicts. #history #philosophy
Pythagorean teachings begin to circulate in Athens, influencing philosophers such as Empedocles and later Plato. #philosophy #history
Pythagorean Hippasus discovers the incommensurability of the square root of 2, proving that not all numbers are rational. Legend says this revelation was suppressed. #mathematics #history
Legend claims Hippasus was drowned at sea for revealing the existence of irrational numbers, a punishment for violating Pythagorean secrecy. #mathematics #history
Pythagorean communities establish in cities like Tarentum, Sybaris, and Metapontum. They influence local politics and promote mathematical education. #history #politics
Philolaus of Croton writes a treatise on Pythagorean cosmology, proposing a central fire (Hestia) and a counter-earth. This is one of the first Pythagorean texts. #cosmology #philosophy
Pythagoreans study the five regular solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron), later associated with Plato. #geometry #mathematics
Cylon, a wealthy Crotonian, leads a revolt against the Pythagorean hegemony, resulting in the burning of the school and deaths of many members. #history #politics )
Archytas, a prominent Pythagorean, contributes to geometry, music theory, and engineering. He solves the doubling of the cube using a mechanical curve. #mathematics #music
Philolaus writes 'On Nature,' one of the first books on Pythagorean philosophy, describing a universe with a central fire. #philosophy #cosmology
Archytas uses a geometric construction to solve the Delian problem of doubling the cube, demonstrating advanced mathematical thinking. #mathematics #geometry
Pythagorean communities face attacks from democratic factions, leading to the destruction of many meeting places and the dispersal of members. #history #politics
The 'Golden Verses' of Pythagoras are compiled, summarizing Pythagorean ethical precepts and promoting a virtuous life. #ethics #philosophy
The Pythagorean school largely declines by 400 BCE, but its ideas persist through Plato and Aristotle, influencing later philosophy and science. #philosophy #history
Plato's Timaeus incorporates Pythagorean cosmology, mathematics, and the theory of the soul, cementing Pythagoreanism's impact on Western philosophy. #philosophy #history )