  The light-like cusp anomalous dimension is a universal function that controls
infrared divergences in quite general quantum field theories. In the maximally
supersymmetric Yang-Mills theory this function is fixed fully by integrability
to the three-loop order. At four loops a non-planar correction appears which we
obtain for the first time from a numerical computation of the Sudakov form
factor. Key ingredients are widely applicable methods to control the
number-theoretic aspects of the appearing integrals. Our result shows
explicitly that quadratic Casimir scaling breaks down at four loops.
