  We give a relatively simple explanation of the light-cone supergraph
prediction for the UV properties of the maximally supersymmetric theories. It
is based on the existence of a dynamical supersymmetry which is not manifest in
the light-cone supergraphs. It suggests that N=4 supersymmetric Yang-Mills
theory is UV finite and N=8 supergravity is UV finite at least until 7 loops
whereas the $n$-point amplitudes have no UV divergences at least until $L=n+3$.
Here we show that this prediction can be deduced from the properties of
light-cone supergraphs analogous to the light-by-light scattering effect in
QED. A technical aspect of the argument relies on the observation that the
dynamical supersymmetry action is, in fact, a compensating field-dependent
gauge transformation required for the retaining the light-cone gauge condition
$A_+=0$.
