Stokes's Theorem and Divergence Question Just a theory question. Does a surface necessary have to be closed for Stokes's theorem to apply? I know for it is true for Green's theorem and it is supposed to be a baby version of Stokes's theorem. Also I know that it is necessary true for the Divergence theorem as well (from physics on Gauss's law)

It seems to me that you are confusing two different uses of the word "closed".

A "closed surface", as in the formulation of Divergence Theorem, means a surface without boundary. In other words, a surface which has no "edge", like a sphere or a torus, and as opposed to a hemisphere (which has a circle as boundary). In this sense, the surface in the statement of Stokes' theorem need certainly not be closed. In fact, integrating the curl of a smooth vector field over a closed surface yields $0$, so it's not exactly the most interesting case. (Can you say why it's $0$? It follows from Stokes' theorem.)

On the other hand I think you might be thinking of a surface as "closed" as a topological subspace of $\mathbb{R}^3$, which is not at all the same thing.