
Before the era of Sophists and Rhetoricians in ancient Athens, the education of children was undertaken by three different figures: the Paedotribis for physical exercise, the Kitharistis for music instruction, and the Grammatist for teaching language and arithmetic. In the 5th century BCE, a higher level of education beyond the basic one was introduced for the first time.
This new educational level consisted of two groups of subjects. One group contained four math-focused areas: Geometry, Arithmetic, Cosmology, and Music. ¹ The other group included three language-related fields: Grammar, Rhetoric, and Dialectic.
Together, they formed the equivalent of the secondary level of education, similar to today’s middle education, providing young people with the means to become responsible and active citizens in the Athenian Democracy.
This educational framework was implemented as it was throughout the entire territory and duration of the Hellenistic kingdoms. ² Graduates of this educational level usually filled positions as administrative officials, while a small percentage continued their studies at a higher level.
This educational system was fully adopted by the subsequent dominant Roman Empire (in the same countries and many more). The Roman, now Latin-speaking, tradition gave the names to the two training courses that became known as the Trivium (tre viae = three routes) and the Quatrivium (quator viae = four routes). As a whole, they are still recognized under the name Artes Liberales (Liberal Arts)³ and continue to be the main pathways for poetry and philosophy in the Western world.
- These four branches of mathematics were inherited as they were from the Pythagorean tradition.
- The Hellenistic kingdoms were the countries conquered by Alexander the Great after he had first subdued Athens.
- “Liberal” because they liberate people? Or maybe because they address to free spirits? Or perhaps because they were
made for free citizens (not slaves)?. Anyway, in ancient Greece used to call Brutal Arts those that serve
the production of material products…






