Curl of Gradient is Zero/Physical Interpretation

Physical Interpretation of Curl of Gradient is Zero
From Vector Field is Expressible as Gradient of Scalar Field iff Conservative, the vector field given rise to by $\grad F$ is conservative.

The characteristic of a conservative field is that the line integral around every simple closed contour is zero.

Since the curl is defined as a particular closed contour line integral, it follows that $\map \curl {\grad F}$ equals zero.