Pythagoras

Pythagoras’ impact on mathematics, science, and philosophy is immeasurable. His theorem remains one of the most fundamental principles in geometry, his scientific insights paved the way for modern physics and astronomy, and his philosophical ideas shaped centuries of thought. Despite the mythical aura surrounding his life, his intellectual contributions continue to inspire scholars and researchers worldwide.

''Pythagoras did not teach, but healed souls''

His name means "he who speaks like Pythia''.
***Pythia was the High Priestess of God Apollo in the Oracle of Delphi who, being in ecstasy, conveyed the oracle of God to the person concerned in a usually laconic, obscure and enigmatic way.

1. Pythagoras’ Life and Background

Pythagoras (570 – 495 BCE), born on the island of Samos in ancient Greece, is one of the most influential figures in the history of mathematics, foundational concepts in science and profound philosophical insights, all of which continue to resonate in contemporary thought.

His teachers were Ermodamas and Aesopos who taught him, among many other, the union of science and philosophy, especially the deep meanings of Iliad and Odyssey, which he (according to Ploutarchos) added in his later teachings . Friends and teachers of Pythagoras were also Pittakos from Militos, Sapfo and Alkaeos.

He shaped the way we understand numbers and their relationships. His contributions extend beyond mathematics into the realms of science and metaphysics, making him one of the most significant figures in intellectual history. Although much of his life and work remains shrouded in mystery, his contributions continue to shape modern thought.

Pythagoras was the first person to define the term ''philosopher'': When he was asked whether he was wise (sophos) he replied ''no, I am not wise, I am friend (philos) of wisdom (sofia)/ Philosophos''.

He traveled extensively in his youth, studying with various teachers in Egypt, Mesopotamia, and possibly India, where he was exposed to various advanced mathematical, astronimical and philosophical teachings. Later, he settled in Croton (in modern-day Italy), where he founded the religious and philosophical Pythagorean Brotherhood - school «Ομακοείον» (''Omakoeion'').

This society was dedicated to the study of mathematics, music, and mysticism, emphasizing the belief that numbers govern the universe. The Pythagoreans followed strict ethical codes and viewed mathematical relationships as a key to understanding reality.

2. Contributions to Mathematics

Pythagoras' most famous contribution to mathematics is the Pythagorean Theorem, which states:
a2+b2=c2
This theorem describes the relationship between the sides of a right-angled triangle and remains fundamental in geometry, engineering, and physics. Although evidence suggests that Babylonian and Indian mathematicians knew about this principle earlier, Pythagoras and his followers provided the first known formal proof.

Other mathematical contributions attributed to Pythagoras include:

• The discovery of irrational numbers, challenging the belief that all numbers could be expressed as fractions.
• The concept of numerical harmony, linking numbers with musical intervals. 

• The classification of numbers into odd, even, perfect, and triangular numbers, laying the groundwork for number theory. 

  Pythagoras's contributions to arithmetic were fundamental in shaping the understanding of numbers, their relationships, and their deeper significance in the natural world. The Pythagoreans elevated arithmetic from a purely practical tool into a profound study that connected mathematics with philosophy, music, and even metaphysics.He viewed numbers as the fundamental essence of all things, believing that reality could be understood through numerical relationships. His idea of a mathematically ordered universe influenced the development of metaphysics.

  Pythagoras’s contributions to geometry not only advanced the discipline but also established a philosophical framework that linked mathematics, aesthetics, and the natural world. His influence persists in modern geometry, where the Pythagorean theorem remains a fundamental concept taught in schools worldwide. Although Pythagoras’s contributions to stereometry are not as directly documented as his work in arithmetic and geometry, his philosophical approach to numbers, shapes, and symmetry had a profound influence on the development of three-dimensional geometry. His focus on harmony, proportion, and the mathematical understanding of the natural world laid the groundwork for later thinkers, and his ideas about regular polyhedra, spherical geometry, and volume ratios helped inspire the formal study of three-dimensional shapes by subsequent generations of Greek mathematicians.

  3. Influence on Science

  Pythagoras made significant contributions to early scientific thought:

• Mathematical Harmony in Nature: He proposed that natural phenomena could be understood through mathematical principles, influencing later scientific disciplines.
• Acoustics and Music Theory: He discovered the relationship between the length of a vibrating string and the musical note it produces, leading to the foundation of modern acoustics. 

• Astronomy: He and his followers suggested that the Earth was a sphere and that celestial bodies followed numerical patterns. Some sources claim they believed in a heliocentric model, predating Copernicus.

   

  4. Contribution to Music

  Pythagoras's contributions to music and the harmonic motion of solids and spheres are foundational in both the philosophy and science of later developments in mathematics, astronomy, and physics. His discovery of the mathematical relationship between vibration, sound, and musical harmony shaped the development of acoustics. His belief in the mathematical order of the universe, expressed through the idea of the Harmony of the Spheres, influenced the study of celestial mechanics and the motion of bodies in space. These ideas continue to resonate in modern physics, where the study of motion - both harmonic and rotational - remains a crucial area of research.

  

   

  5. Contributions to Philosophy

  Pythagoras’ philosophical ideas were deeply intertwined with mathematics and mysticism. Key philosophical contributions include:

• Metempsychosis (Reincarnation): He believed in the transmigration of souls, suggesting that the soul is immortal and undergoes a cycle of rebirths.
• The Concept of Order and Harmony: He viewed the cosmos as a well-ordered system governed by numerical relationships, an idea that later influenced Plato and Western metaphysics.

• Ethical and Ascetic Teachings: Pythagoreanism emphasized a disciplined life, including dietary restrictions and moral purity, shaping later philosophical traditions.

  Pythagorean philosophy included concepts of harmony and balance in the cosmos, suggesting that everything is interconnected through mathematical relationships. This perspective set the stage for later philosophical inquiry, particularly in the works of Plato and Aristotelis.

  Pythagoras’s teachings also encompassed ethics and spirituality. He believed in the immortality of the soul and the transmigration of souls, promoting a way of life that emphasized moral conduct, self-discipline, and harmony with the universe.The Pythagorean school was as much a community as it was an intellectual organization, emphasizing collective learning, ethical living, and the pursuit of knowledge, which influenced later philosophical schools and traditions.

  6. Legacy and Influence

Pythagoras’ ideas laid the foundation for various fields of study:

• His mathematical theories influenced Euclid’s "Elements", a cornerstone of geometry.
• His scientific ideas inspired later thinkers like Aristotle, Copernicus, and Kepler. 

• His philosophical teachings shaped Platonism, influencing Western thought for centuries. While Pythagoras himself left no written works, his legacy was carried forward by his followers, ensuring his ideas endured through history.

  7. What others said about Pythagoras

  Herakleitos : "Pythagoras was wise and polymath"

  Herodotos : "Pythagoras was the best Greek philosophy teacher"

  Empedoklis from Akragantas: "Pythagoras had infinite wisdom and invaluable treasure of thought"