We argue that divergence of black hole entropy at the horizon, first shown by t'Hooft, is due to the uncertainty principle. The region near the horizon is in a thermal state, so entropy is linear to energy. We first show that a similar divergence due to an infinitely sharp boundary occurs for the energy and entanglement entropy of relativistic and non-relativistic field theories, extending previous results in quantum mechanics. We argue that the origin of the divergence is the position/momentum uncertainty relations and show that when the boundary is smoothed the divergence is tamed.  Then we apply our ideas to black hole entropy. We show that the ``brick wall'' which renders the entropy finite can be interpreted as smoothing of the sharp boundary at the horizon and that any other smoothing of the boundary will result in the same finite answer for the entropy.