Pythagoras was a religious figure, mathematician, and philosopher of ancient Greece. He believed that numbers possessed a mystical power, and he assigned unique meanings to each number.
“All things are unified through number and harmony.”
Based on this belief, Pythagoras sought to explain the laws of the universe and the order of nature entirely through numerical relationships.
Historical Context: What Was the Era of Pythagoras Like?
Pythagoras lived during the 6th century BCE, in what is known as the Archaic period of ancient Greece.
This was a time when culture, philosophy, and science were beginning to flourish throughout the Greek world.
His birthplace, the island of Samos, lies in the Aegean Sea and was already a prominent city known for its commerce and maritime trade.
In this vibrant and dynamic environment, Pythagoras developed his groundbreaking philosophy centered on number and harmony.
Geographical Background: The World Around Pythagoras
In the 6th century BCE, when Pythagoras was born, the Greek world was composed of several distinct but interconnected regions:
- Mainland Greece On the eastern side stood prominent city-states such as Athens (then known by its ancient name, Athēnai).
- The Aegean Sea Lying between the Greek mainland and Anatolia (Asia Minor), it was dotted with many islands, including Samos, Pythagoras’s birthplace.
- Crete A large island further south, located in the Mediterranean Sea.
- Anatolia (Asia Minor) Now the western coast of modern-day Turkey. Its western region was known as Ionia, home to flourishing Greek city-states.
- The Black Sea A large inland sea located to the north of Anatolia.
- The Levant South of Ionia, along the eastern Mediterranean coast (modern-day Syria, Lebanon, and Israel).
- Egypt Further to the south, reaching into the Nile Delta region, or Lower Egypt.
The eastern Mediterranean region was historically enriched by the surrounding Egyptian and Mesopotamian civilizations, and a vast network of trade connected the islands and coastal cities.
Samos, the birthplace of Pythagoras, was a key hub in this network, where diverse cultures and knowledge flowed freely—an environment that likely shaped his philosophical outlook.
The Pythagorean Theorem and Its Background
The relationship between the three sides of a right-angled triangle, known as the Pythagorean Theorem, or the theorem of the three squares, is one of the most famous theorems in geometry.
Sets of natural numbers that satisfy this theorem—such as (3, 4, 5) or (5, 12, 13)—are known as Pythagorean triples.
Interestingly, this rule predates Pythagoras (ca. 6th century BCE) and had already been used in various ancient civilizations:
- In ancient Babylonia (around 1800 BCE), clay tablets have been discovered that contain calculations involving the sides of right triangles.
- In ancient Egypt, a method known as rope-stretching was used in land surveying. Ropes tied with knots in the ratio 3:4:5 were used to form precise right angles.
These forms of practical knowledge were later systematized and came to be associated with the name of the Greek mathematician Pythagoras, carrying his legacy into the mathematical tradition we know today.
All Things Are Number — Pythagoras and His Faith in Numbers
Pythagoras believed that numbers possessed a mystical power.
He assigned unique meanings to each number and sought to explain all events in the universe through numerical relationships. In his view, each number had its own distinct personality or essence.
Pythagoras founded the Pythagorean brotherhood, a community of followers with whom he pursued studies in mathematics and philosophy. This group also emphasized religious and ethical teachings, and their practices blended intellectual pursuit with spiritual belief.
In Pythagoras’s time, science and mathematics had not yet been systematized as they are today. But the Pythagoreans’ emphasis on the significance of numbers laid the foundation for mathematics to become deeply intertwined with both philosophy and religion in ancient Greece.
Famous Quote by Pythagoras
“All things are number.”
Behind every phenomenon lies number, and the harmony of the world is expressed through proportion.
In other words:
“The universe is governed by ratio, and all things are number.”