What I find interesting about Euclid is that he makes no additional effort to communicate what is interesting an important about mathematics. His proofs have an

What I find interesting about Euclid is that he makes no additional effort to communicate what is interesting an important about mathematics. His proofs have an inherent beauty that is self-evident. Indeed, this self-evident quality is a big part of what makes them so beautiful. Each one is like a perfectly constructed plot. I was introduced to this my Freshman year in college. I remember thinking "this is absolutely amazing - why didn't anybody tell me about this before?" That sense was shared by every one my classmates, who - universally - felt robbed by their 9-12 education. To this day I remain angry about the utter mediocrity of math education that strips the work of any sense of historical context, the sequence by which one branch emerged from another, the causes of these developments, and the sense of aesthetic delight that comes from discovering what amounts to new and increasingly powerful uses of human reasoning. At the same time, I felt deeply fortunate that I got the education I did, realizing how far from the norm it is. I also realize that if you DO have to explain why something is important, it's probably because your audience has lost the story's thread. They've stopped seeing the subject from the inside out, and are just going through the motions to pass the test, get the grade, and move on a.s.a.p. The highly fragmented nature of contemporary curriculum design not only increases the chances of this happening, it virtually guarantees disengagement. The OP is right to observe that people who truly learn do so in spite of the system, not because of it.