  We report a calculation in N = 4 Yang-Mills of the four-loop term g^4 in the
collinear anomalous dimension g(lambda) which governs the universal subleading
infrared structure of gluon scattering amplitudes. Using the method of
obstructions to extract this quantity from the 1/epsilon singularity in the
four-gluon iterative relation at four loops, we find g^4 = -1240.9 with an
estimated numerical uncertainty of 0.02%. We also analyze the implication of
our result for the strong coupling behavior of g(lambda), finding support for
the string theory prediction computed recently by Alday and Maldacena using
AdS/CFT.
