The trivium consists of the following three subjects:
The quadrivium of the following four:
Grammar should be understand as the study of language. Well developed verbal skills are essential for effective communication. So we can reason check this one as a necessary part of a general curriculum.
Logic and rhetoric are about arguing and persuading others in favor or against a specific course of action. These skills are of great importance when it comes of preparing young people to become citizens of a democratic republic. We believe that puzzle solving is a good method to stimulate logical reasoning in children.
Arithmetic and geometry are the foundation of what is usually called mathematics (remember that algebra did not exist in antiquity). Few people will doubt the importance and usefulness of math (including algebra) in modern society.
The relevance of astronomy in a space based society should be a no brainer. Scientific studies show that both listening and making music has a positive effect on cognitive development:
Learning with music can change brain structure (ScienceDaily)
Music students do better in school than non-musical peers (ScienceDaily)
We can establish that the classic curriculum of the trivium and quadrivium still provides a solid and relevant foundation for education in a modern society.