Practical lattice discretizations of supersymmetric gauge theories are
notoriously difficult to construct in four dimensions.  N=4
supersymmetric Yang–Mills (SYM) is the only known 4d theory for which
there exists a lattice formulation that exactly preserves a subset of
the supersymmetry algebra.  This exact supersymmetry has remarkable
consequences that are crucial to enabling practical non-perturbative
lattice calculations.  After reviewing some highlights of the N=4 SYM
lattice formulation, I will present a selection of results from our
ongoing numerical studies, including comparisons with analytic
predictions.