What do we know about Pythagoras?

Image: abstract image representing the Pythagorean theorem AC²=AB²+BC² (Generated by an IA).

The Writings of Pythagoras!

A Total Absence of Original Writings

We have no texts written by Pythagoras himself (c. 570–495 BC).
All the writings we have about Pythagoras are of indirect origin. Most of the information about his work and ideas comes from later sources, primarily authors such as Euclid (c. 300 – c. 265 BC).
The Pythagorean theorem first appears in a mathematical context in Euclid's "Elements" (Book I, Proposition 47). "Elements" is dated approximately to the 3rd century BC, and it is possible that Euclid was not its sole author. This work is a compilation of thirteen books covering various aspects of mathematics and geometry. Although the original manuscripts have not survived to this day, handwritten copies were made during Antiquity and the Middle Ages.
Thus, Euclid's writings provide one of the earliest known formulations of this theorem in a formal mathematical framework. Proposition 47 reads as follows (modern translation):
"In a right-angled triangle, the square constructed on the hypotenuse is equal to the sum of the squares constructed on the other two sides."

Oral Transmission and Initiatic Secret

Members of the Pythagorean sect were known for maintaining the confidentiality of their teachings and transmitted their knowledge orally. It is likely that the theorem was taught and used in this context.
It is possible that Pythagoras' disciples later wrote down his teachings, but no writings have survived through time. Libraries and archives in Antiquity were often destroyed by fires, wars, or looting.

Secondary Greek Sources

The writings of historians and philosophers who came after Pythagoras are the main sources we have to understand his life and thought.
The most important accounts of Pythagoras come from later Greek historians and philosophers such as Diogenes Laërtius (180–240 AD) and Iamblichus (245–325 AD).

The Testimonies of Diogenes Laërtius and Iamblichus

Diogenes Laërtius wrote "Lives and Opinions of Eminent Philosophers," a biographical compilation of the lives of many ancient philosophers, including Pythagoras. The information about Pythagoras is based on various and sometimes legendary sources, and there is no guarantee that they are entirely accurate.
Iamblichus also wrote about Pythagoras in his work "Life of Pythagoras." However, like Diogenes Laërtius, it is essential to recognize that Iamblichus wrote several centuries after Pythagoras, and his work may reflect interpretations and theological elements of his time.

Pythagoras' Contributions Beyond the Theorem

Mathematics and Musical Harmony

Pythagoras is often associated with the discovery of musical ratios and the influence of numbers on music. He studied the relationships between the lengths of vibrating strings and the sound frequencies produced, thus establishing links between mathematics and music.

Number Theory and Arithmetic Perfection

Pythagoras developed fundamental ideas in number theory. His fascination with numerical properties led him to explore the relationships between integers, particularly the properties of prime numbers and the concepts of perfect numbers.

The Discovery of Irrational Numbers

Pythagoras discovered that the diagonal of a square with sides of length 1 cannot be expressed as a simple fraction. This led to the notion of irrational numbers, which cannot be represented as ratios of integers.

The Pythagorean Sect and Its Philosophy

Pythagoras founded the Pythagorean sect, a community where the study of mathematics was closely linked to philosophical, mystical, and religious aspects. Members of the sect believed in the importance of numbers in understanding the world.

The Transmission of Ancient Knowledge

From Greek to Medieval Latin Translations

In Western Europe during the Middle Ages, medieval scholars and clerics generally did not have access to the original Greek writings or direct Arabic translations.
The transmission of classical Greek knowledge was mainly done through translations from Greek to Latin, carried out by medieval scholars. Latin manuscripts containing these translations were often based on original Greek texts preserved in Byzantine libraries.
Although the original Greek texts have not survived, Greek copies and Latin translations were made in the Middle Ages, contributing to the preservation and transmission of their works in Western Europe.

The Central Role of the Arab World

However, some classical Greek texts were preserved in the Arab world, where they were translated into Arabic. Later, some of these Arabic translations were rediscovered in Western Europe, and scholars undertook to translate these Arabic texts into Latin. Thus, although access to the original Greek writings was limited, there was an indirect influence via Arabic translations.
Arab intellectuals merged Greek, Persian, Indian, and other traditions with their own cultural heritage.
The Arabs played an essential role in the preservation, transmission, and translation of ancient knowledge during the medieval Islamic era (7th to 13th century).