  An exact and general solution is presented for a previously open problem. We
show that the superconformal R-symmetry of any 4d SCFT is exactly and uniquely
determined by a maximization principle: it is the R-symmetry, among all
possibilities, which (locally) maximizes the combination of 't Hooft anomalies
a_{trial}(R) \equiv (9 Tr R^3-3 Tr R)/32. The maximal value of a_{trial} is
then, by a result of Anselmi et. al., the central charge \it{a} of the SCFT.
Our a_{trial} maximization principle almost immediately ensures that the
central charge \it{a} decreases upon any RG flow, since relevant deformations
force a_{trial} to be maximized over a subset of the previously possible
R-symmetries. Using a_{trial} maximization, we find the exact superconformal
R-symmetry (and thus the exact anomalous dimensions of all chiral operators) in
a variety of previously mysterious 4d N=1 SCFTs. As a check, we verify that our
exact results reproduce the perturbative anomalous dimensions in all
perturbatively accessible RG fixed points. Our result implies that N =1 SCFTs
are algebraic: the exact scaling dimensions of all chiral primary operators,
and the central charges \it{a} and \it{c}, are always algebraic numbers.
