I get the many proofs behind it and all of the mechanics of how to use it. What I don't get is why it works.. What was the though process of Brook Taylor when he devised his thing? I get that each new term is literally being added to previous ones along the y-axis to approximate the y value of the original function. But why is it that the coefficient that goes in front of x^n is the nth derivative of the function over n factorial? How does that makes sense? I know it works, but it seem like magic to me.. And I can't help but hate that.