Pythagoras
The Life of Pythagoras
Pythagoras, the great mathematician and philosopher, is synonymous with the Pythagorean theorem. Even those who are far from mathematics still remember the theorem and its significance. The theorem is simple yet not obvious, and its contradiction of two principles gives it a special allure.
Pythagoras was born around 580 BCE on the island of Samos, Greece. His father, Mnesearchus, provided him with a good education and upbringing. At a young age, Pythagoras showed great aptitude for the sciences. Under the guidance of his first teacher, Hermotimus, he learned the basics of music and painting. Hermotimus instilled in him a love for nature and its mysteries.
Several years later, Pythagoras decided to continue his education in Egypt. With the help of his teacher, he managed to leave Samos and live with his relative Zoilus on the island of Lesbos. It was there that he met the philosopher Pherecydes, a friend of Thales of Miletus. From Pherecydes, Pythagoras learned about astrology, eclipse prediction, the secrets of numbers, medicine, and other sciences of the time.
After Lesbos, Pythagoras traveled to Miletus, where he attended lectures by Thales and his disciple Anaximander, a renowned geographer and astronomer. In Miletus, Pythagoras acquired significant knowledge during his time at the Miletus School. He then made a stop in Phoenicia, where he studied under the famous Sidonian priests.
His studies in Egypt further enhanced his knowledge, making him one of the most educated individuals of his time. In Egypt, Pythagoras found himself in Persian captivity. According to ancient legends, he encountered Persian magi during his captivity, delved into Eastern astrology and mysticism, and learned the teachings of Chaldean sages. The Chaldeans introduced Pythagoras to the accumulated knowledge of the Eastern peoples, including astronomy, astrology, medicine, and arithmetic.
Pythagoras spent twelve years in Babylonian captivity until he was freed by the Persian King Darius Hystaspes. At the age of sixty, Pythagoras decided to return to his homeland, which had undergone significant changes during his absence. Many Greek intellectuals had migrated to Southern Italy, known as Magna Graecia, to escape Persian rule. They founded colonies such as Syracuse, Agrigentum, and Croton. Pythagoras planned to establish his own philosophical school in Croton.
Pythagoras quickly gained popularity among the people. Utilizing the knowledge he acquired during his travels, he taught medicine, principles of political activity, astronomy, mathematics, music, ethics, and more in his own home. The students who graduated from his school went on to become prominent political figures, historians, mathematicians, and astronomers. Pythagoras was not only a teacher but also a researcher. His students, too, became researchers in their own right.
Pythagoras developed a theory of music and acoustics, creating the famous "Pythagorean scale" and conducting groundbreaking experiments on musical tones, expressing their relationships through mathematics. In the Pythagorean School, the idea of the earth's sphericity was first proposed. The concept that celestial bodies move according to specific mathematical relationships, known as the "harmony of the cosmos" and the "music of the spheres," ultimately revolutionized astronomy. Pythagoras also made significant contributions to geometry. Proclus, a Greek philosopher, praised Pythagoras's contributions to geometry, stating that he transformed the discipline into a free science, considering its principles in an abstract way and investigating theorems from an immaterial, intellectual perspective. Pythagoras also discovered the theory of irrational numbers and the construction of cosmic bodies.
Pythagoras introduced proof into mathematics, particularly in geometry. This systematic approach to proof transformed mathematics from a collection of ancient Egyptian and Babylonian practical recipes into a science. From the birth of mathematics, science as a whole emerged, as "no human investigation can be called true science unless it passes through mathematical proofs" (Leonardo da Vinci).
Pythagoras was the first to realize that geometry should consider abstract ideal objects, and the properties of these ideal objects should be established not through measurements of a finite number of objects but through reasoning applicable to an infinite number of objects. This chain of reasoning, which uses the laws of logic to reduce non-obvious statements to known or self-evident truths, is what constitutes mathematical proof.
It is widely accepted that Pythagoras did not discover the Pythagorean theorem, despite its association with his name. Its specific instances were known in China, Babylon, and Egypt before him. However, some argue that Pythagoras was the first to provide a comprehensive proof of the theorem, while others deny him this credit.
Pythagoras was surrounded by numerous legends, making it difficult to ascertain what is fact and what is fiction. He is remembered for his religious prophecies and as an embodiment of divine wisdom. There are tales of his golden thigh, of his ability to be in multiple places at once, and more. In some texts, he is depicted as a demigod, considering himself the son of Hermes. Pythagoras believed that there were three types of beings: gods, ordinary mortals, and those who resembled Pythagoras himself. In literature, Pythagoreans were often portrayed as superstitious and selective vegetarians, rather than mathematicians.
For his contemporaries, Pythagoras was primarily a religious prophet, an embodiment of divine wisdom. Herodotus referred to him as a "remarkable sophist," or a teacher of wisdom. He also noted that Pythagoreans did not bury their dead in woolen garments, suggesting a religious aspect to their beliefs.
The life of Pythagoras is shrouded in legends, making it difficult to discern what is true from what is fictional. Even the exact dates of his birth and death remain uncertain. Despite this, Pythagoras left an indelible mark on mathematics and philosophy. He was a pioneer in the systematic study of geometry, the introduction of proof, and the exploration of the relationships between numbers and musical harmony.
