  We present an explicit analytic calculation of the differential of the planar
n-particle, two-loop MHV scattering amplitude in N=4 super Yang-Mills theory.
The result is expressed only in terms of the polylogarithm functions Li_k(-x),
for k=1,2,3, with arguments x belonging to the special class of dual conformal
cross-ratios known as cluster X-coordinates. The surprising fact that these
amplitudes may be expressed in this way provides a striking example of the
manner in which the cluster structure on the kinematic configuration space
underlies the structure of amplitudes in SYM theory.
