The AdS/CFT correspondence implies a deep relation between Wilson loops, a fundamental observable in gauge theories, and minimal area surfaces in hyperbolic space. The problem of finding minimal area surfaces ending on a given contour is a traditional problem in mathematics. In the case of hyperbolic space the equations that determine such surface are integrable implying the existence of an infinite number of conserved charges. In this talk I will show that the defining property of the surfaces is that all conserved charges vanish and how to use that information to find the minimal area. In particular I will discuss a formula for the area in terms of the Schwarzian derivative of the contour. \\ \\ Based on http://arxiv.org/pdf/1406.4945.pdf