[cgdangelo]

> I could appreciate it a lot more when I understood what kind of problems were Newton and Leibniz trying to solve when they came up with the formalized notion of Calculus.

This always bothered me in many of my math classes. We'd go over a new formula or concept and just hammer it home until it stuck. Professors rarely gave real-world examples of the topics they were teaching or indicated to the students how these new theorem interacted with others. If I asked them explicitly I might get a more practical explanation, but it was rarely offered to me without inquiring first.

I used to have a lower opinion of people who'd complain about learning math because "it's so pointless, I'll never use any of this." It bothered me that they just didn't want to learn something new. In hindsight, even if that were partly true, I can't blame them for having that attitude because it may have been partially instilled in them by their professors.

I'll never forget the feelings I had after I connected the dots in my head and noticed the relationship between integrals. I knew that integration would give me the area underneath a curve, but now we were learning about double and triple integrals for surface area and volume. It dawned on me that I'm basically doing the same thing I was before, albeit in several planes with more curves. I remember a lot of different emotions: appreciation for the sensibility and beauty of mathematics; pride that I figured something out on my own; but also a tinge of frustration that this revelation was never encouraged by my professor.

[jasim]

Exactly! You were fortunate enough to realize this during your course itself. But a vast majority of students never stumble upon this revealation and treat Maths as another chore that needs to be done with.

The insight you described is what Math classes should be about, not practicing problem after problem without any knowing what or why.