Pythagoras, an emblematic seeker of knowledge, made significant contributions across philosophy, mathematics, astronomy, and music theory. His quest to understand universal order set a noteworthy precedent, embedding him in Western intellectual history. By exploring his life and accomplishments, we gain insights into his enduring influence and the legacy he left behind.

Beginnings

Born around 580 B.C.E. on the island of Samos in the Mediterranean, Pythagoras was the son of Mnesarchus. Little is known about his early years, primarily due to the fragmentary and often contradictory accounts from sources dating centuries after his death. His students evolved in diverse directions, partly leading to the inconsistencies in historic records.

Aristotle's Metaphysica references the "Pythagoreans" rather than Pythagoras himself, emphasizing the influence of his followers. Much of what is attributed to him was shaped through the lens of Platonism. Despite this, some teachings and life events can be traced back to Pythagoras, such as his belief in the transmigration of souls, possibly instilled by his teacher Pherecydes of Syros. Other influences reportedly included Thales of Miletus, whose teachings on rational integers likely spurred Pythagoras toward discovering irrational numbers.

Pythagoras's extensive travels through Egypt, Babylonia, and other Mediterranean regions exposed him to the rudimentary geometry of the time, which he later elevated to a science through his work on geometric proofs and axioms. A bust in Rome’s Capitoline Museum depicts him with a focused, contemplative demeanor, embodying his relentless pursuit of knowledge.

Philosophical Journey

Upon returning to Samos, Pythagoras found it under the rule of the tyrant Polycrates and faced a Greek mainland partly conquered by Persians. This political climate likely prompted his relocation in 529 B.C.E. to Croton in southern Italy, marking a transformative period in his life.

In Croton, Pythagoras established a philosophical school akin to a monastic order, advocating for a devout lifestyle and harmonious political existence. During a time when southern Italy was torn by political strife, he believed that philosophy and ethical living could guide society towards salvation. His belief in metempsychosis, the soul's journey through different lives, underscored his teachings.

He categorized his followers into akousmatikoi, listeners who practiced his teachings, and mathematikoi, those who delved into arithmetic, music theory, astronomy, and cosmology. The latter, after extensive study, were encouraged to question and develop their opinions, illustrating Pythagoras's approach to merging metaphysical and scientific teachings.

Scientific Endeavors

Pythagoras’s philosophical framework centered on numerical essence, drawing from observations of musical harmonies and geometric relationships. He discovered that musical intervals could be expressed through arithmetic ratios, such as a 2:1 ratio indicating an octave, which became foundational to his musical and numerical theories.

His understanding extended to music and mathematics, where he assigned numerical values to lyre strings and determined that these ratios could be universally applied to produce harmony. Fellow mathematician Hippasus later expanded these concepts, testing them with various instruments and materials.

The Pythagorean Theorem, his renowned contribution to geometry, states that the square of a right triangle's hypotenuse equals the sum of the squares of its other sides. Though variations of this theorem existed earlier, Pythagoras’s Greek perspective sought precise measurement of the square-to-diagonal ratio, although he found it was not a whole number. This led him to demonstrate the relationship using squares of the triangle's sides.

Pythagoras also ventured into astronomy, positing that the earth and universe are spherical. While he thought the earth was the central point around which celestial bodies orbited, later Pythagoreans proposed a "central fire," hinting at a heliocentric view that would influence future astronomers, including Copernicus.

Controversy and Legacy

Pythagoras and his followers were not without controversy. As democratic...