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It would be easy to laugh at the constant breathlessness with which contemporary technical endeavors are reported. But we ought not laugh, because we have a serious problem. What do we teach when it's all changing?
In every age, people apprehend order in the world and learn to speak of it with each other. When they do so they make a lasting contribution to human culture. It would be foolish to cast such contributions aside in exchange for nothing more than novelty.
People can mistakenly present the development of human knowledge as if it were endless rupture, a series of breaks retaining nothing from the past. Some do this because they find such talk expedient. Others are naïve, chronologically quarantined.
The mathematics of the quadrivium has enduring value. This value does not change, even when scientists make new advances. The Pythagorean Theorem is a theorem of Euclidean geometry whether or not you choose to study non-Euclidean geometry. We won't find a largest prime number. Dividing a string in two produces a sound that is harmonious with the one produced by the whole. The full moon follows the first quarter by about a week, and eclipses sometimes come six months apart, but never three.
Astronomy is the tricky part, so let me give you a warning about what is the most provocative aspect of A Brief Quadrivium. The book includes Ptolemaic astronomy.
This might appear crazy or anachronistic. It isn't.
Mathematical models of phenomena are that. They are mathematical models. Sometimes, within the professional practice of science, certain models are replaced by other models. That doesn't mean that the old models weren't decent models. It means that certain people, with specific goals, have chosen a new approach.
Ptolemy's astronomy is in fact marvelous, clear, and precise. It is well-suited to the ordinary student.
A hammer doesn't help me turn a screw, but I still find a hammer useful. So too with ancient astronomy. There are some phenomena that it does not describe well. There are many, though, that it does describe well. Those phenomena are a great place to start.
Note:
Ptolemy is someone who wrote, among other things, a book called The Almagest. It is an astronomy textbook. Ptolemy lived from about 100 to 175 AD. One way you can pronounce his name is "tall" + "ehh" + "me."
You can read more about Ptolemy in the article on sources.