e is about the Coolest Number there is.
Pie get's all the Headlines, and it is a Vastly Important Fundamental Number, but e is the Unsung Player in my Book.
The concept that d/dx e^x = e^x is one of those things that when you First see it you say, hummmm, that's kinda Neat. That the Rate of Change of the Function
Is the Function for all points in It's Domain. But the more you see it, the more you Understand that it Explains Many things.
Couple that with the Relations with it's Inverse Function Ln(x), ie y = Ln(x) <=> e^y = x and you have a Very Powerful tool for Integration.
And d/dx ln(x) = 1/x which you seein All Kinds of things like Harmonics, Wave Theory, Decay, etc.
Like I said, e is just a Damn Cool Number.