we prove global well-posedness of the $(d+1)$-dimensional $(d\geq 4)$ massless maxwell-dirac equation in coulomb gauge for data with small scale-critical sobolev norm. a key step is to exploit (and justify) a deep analogy between maxwell-dirac and maxwell-klein-gordon (for which an analogous result was proved earlier by krieger-sterbenz-tataru), which says that the most difficult part of maxwell-dirac takes essentially the same form as maxwell-klein-gordon. this is a joint work with c. gavrus.