[dvt]

> All mathematics should be clear and intuitive, by definition :)

I disagree with this completely, and so does all of higher mathematics. It's neither clear nor intuitive. In fact, as soon as you start learning about infinities (Calc I), intuition becomes hit and miss.

[CN7R]

Intuition always comes after the feeling of awe or confusion, in my opinion. Really depends on how you learn.