TITLE: Motivation of Splines
QUESTION [12 upvotes]: What is the motivation of splines, in particular cubic splines. For example, why does it matter that they have any type of smoothness at the knots.

REPLY [2 votes]: Splines are useful for representing data and physical phenomena, especially if you have a prior notion of smoothness. They strictly enforce this notion and the level that you choose can be thought of as a form of regularization if you were to employ the splines to facilitate an inference (solution to an inverse problem).