Something that I think even fewer people appreciate is that all the same things apply to mathematics (except for "V. Physical Education"). Or at least should apply if mathematics is taught properly. Mathematics certainly develops insight and demands research. It sheds light on history. It is a foreign language. It's sometimes said that mathematics is the language of the universe. But mathematics is also art. Doing mathematics is less like chipping away at rock to reveal a hidden fossil than it's like a musician composing a symphony out of nothing.
Full disclosure. I majored in mathematics. I remember one light bulb moment in class when I realized that a theorem I was studying in a geometry class was, in fact, the same theorem I had earlier studied in an algebra class. The difference was all in the language used in geometry vs algebra, but the underlying theorem was the same in both cases. It was like studying two abstract paintings and suddenly realizing the two artists were each painting the same subject.
Another light bulb moment came when I was introduced to non-Euclidean geometry. The ancient Greeks felt that Euclid's postulates were a rigorous definition of how the real world is (e.g. that for any given line and a point not on that line, there is exactly one line in that plane that goes through the point and does not intersect the first line). Two millennia later, Einstein theorized that the real world isn't Euclidean at all (e.g., straight lines "curve"). That insight upset two thousand years of scientific history and has made all the difference in our modern world. But the mathematicians who invented non-Euclidean geometry (invented, not discovered) beat Einstein to the math, even though they didn't apply it to nature like Einstein did.
Let us teach music. Let us teach mathematics. Let us teach both, both for their practical benefits and for their beauty.
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