Pythagoras of Samos (c. 570–495 BCE) is one of the most enigmatic and influential figures in the history of philosophy, mathematics, and science. Best known today for the Pythagorean Theorem, his legacy extends far beyond geometry. He was a mystic, mathematician, philosopher, religious leader, and founder of a movement that shaped Western thought for centuries.
This essay explores the life, teachings, and legacy of Pythagoras, placing his contributions in the broader context of ancient Greek philosophy and science.
1. Early Life and Travels
Pythagoras was born on the Greek island of Samos, located in the eastern Aegean Sea. While historical accounts of his life are shrouded in legend and written long after his death, some details are widely accepted. He likely traveled extensively in his youth, including time spent in Egypt, Babylon, and possibly India. These travels exposed him to diverse philosophical, mathematical, and religious ideas, which he would later synthesize into his own teachings.
In Egypt, he is believed to have studied geometry and ritual practices; in Babylon, he may have encountered mathematical astronomy. These influences would profoundly shape his later philosophy, particularly his belief in the harmonious structure of the cosmos and the mathematical nature of reality.
2. The Pythagorean Brotherhood
Upon returning to the Greek world, Pythagoras settled in Croton, a city in Magna Graecia (southern Italy), where he founded a philosophical and religious community known as the Pythagorean Brotherhood. This group was part philosophical school, part religious cult, and part political force. Members lived a communal life, adhered to strict rules of conduct, and followed teachings that blended mathematics, music, cosmology, and spirituality.
Central to the Brotherhood was the belief that numbers were the essence of all things. They held that the universe could be understood through numerical relationships and proportions, an idea that prefigured much of modern science. For the Pythagoreans, numbers were not just tools for calculation but living principles that structured reality itself.
3. Mathematical Contributions
The most famous mathematical idea associated with Pythagoras is the Pythagorean Theorem:
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
(a² + b² = c²)
While this theorem was known to the Babylonians centuries earlier, Pythagoras or his followers are credited with the first formal proof of the theorem. This synthesis of logical reasoning and spatial understanding helped lay the foundation for Greek mathematics and geometry as a deductive science.
Pythagoras also made significant contributions to number theory. The Pythagoreans classified numbers as odd and even, prime and composite, and explored properties of perfect numbers (numbers equal to the sum of their proper divisors) and amicable numbers (pairs of numbers where each is the sum of the other’s divisors). They were also fascinated by triangular numbers and square numbers, which could be arranged into geometric shapes.
4. Music and Harmony
One of Pythagoras’ most original insights was the connection between mathematics and music. According to tradition, he discovered that harmonious musical intervals corresponded to simple numerical ratios. For example, the octave corresponds to a 2:1 ratio, the fifth to 3:2, and the fourth to 4:3.
These observations led to the theory of the “music of the spheres”—the idea that celestial bodies move in accordance with mathematical ratios and thus produce a kind of cosmic music inaudible to the human ear. While this idea is metaphorical, it had a profound impact on later cosmology, inspiring thinkers from Plato to Kepler.
5. Philosophy and Metaphysics
Pythagoras was not just a mathematician but also a deeply spiritual philosopher. He believed in the immortality and transmigration of the soul (metempsychosis), a concept he may have adopted from Eastern religions or Orphic tradition. According to this belief, the soul passes through cycles of rebirth in various forms, both human and animal, until it is purified and reunited with the divine.
The Pythagoreans advocated for a way of life that emphasized self-discipline, moral purity, vegetarianism, and philosophical contemplation. They believed that understanding mathematical truth was a form of spiritual purification and a path toward unity with the cosmos.
For Pythagoras, harmony was the ultimate principle—whether in music, numbers, the soul, or the heavens. This notion of cosmic harmony would go on to influence major philosophical traditions, including Platonism and Neoplatonism.
6. Legacy and Influence
Although no writings by Pythagoras survive, his ideas were transmitted through his followers and later philosophers. The distinction between what Pythagoras himself taught and what the Pythagorean school developed is blurred, but the influence of the movement is undeniable.
Plato was heavily influenced by Pythagorean thought, particularly the idea that abstract forms (like numbers and geometrical shapes) are more real than the physical world. In Plato’s Timaeus, the cosmos is described as a living being ordered according to mathematical principles—a view very much in line with Pythagorean cosmology.
Euclid, the great mathematician of Alexandria, built upon Pythagorean mathematics in his seminal work Elements, which remained the definitive textbook on geometry for over two millennia.
In later centuries, Pythagoras was revered as a mystical sage. During the Renaissance, thinkers such as Kepler, Galileo, and Descartes echoed Pythagorean ideas in their belief that the universe was governed by mathematical laws. Kepler explicitly referred to Pythagoras in his theory of planetary motion, which attempted to uncover the harmonies of the solar system.
The Pythagorean influence extends even into modern physics. The belief that nature follows elegant mathematical rules underpins the work of Einstein, Schrödinger, and countless other scientists. In this sense, Pythagoras can be seen as the grandfather of the scientific worldview.
7. Criticisms and Mysticism
Despite his profound impact, Pythagoras and his followers were not without controversy. The secrecy of the Pythagorean Brotherhood and its cult-like practices invited suspicion. In Croton, their growing influence led to political unrest, and the school was eventually suppressed.
There is also criticism of their mystical approach to numbers. While they achieved remarkable insights, they also assigned symbolic meanings to numbers and sometimes indulged in numerology—an approach not aligned with empirical science. For example, the discovery of irrational numbers, such as the square root of 2, deeply disturbed the Pythagoreans because it contradicted their belief that all quantities could be expressed as ratios of whole numbers.
Nevertheless, even their “failures” helped spur intellectual development, forcing future mathematicians and philosophers to grapple with the complexities of number and magnitude.
Conclusion
Pythagoras was more than the namesake of a theorem. He was a pioneer whose fusion of mathematics, music, cosmology, and philosophy laid the foundation for Western science and metaphysics. His belief in the rational structure of the universe, the moral importance of self-discipline, and the transcendent power of numbers inspired generations of thinkers.
Though much about his life remains shrouded in mystery, Pythagoras’s influence is clear and enduring. From the music of the spheres to the equations of modern physics, the idea that the universe is built on number and proportion continues to resonate. In the words of the philosopher Bertrand Russell, “Pythagoras was intellectually one of the most important men that ever lived.”
