Cartan's magic formula

Cartan's magic formula describes how the Lie derivative of a differential form combines two fundamental operations: the interior product and the exterior derivative. Specifically, it states that the Lie derivative of a form along a vector field equals the interior product of the form with the vector field, followed by the exterior derivative, minus the exterior derivative of the interior product. Conceptually, it helps us understand how a form changes as we move along a flow generated by a vector field, linking movement (Lie derivative), insertion (interior product), and differentiation (exterior derivative) into a unified framework.