A method of making a poly(phenylene ether) comprises: in an exotherm period, continuous addition of oxygen and a monohydric phenol to a non-polar solvent and a polymerization catalyst comprising a metal salt, an amine, and a quaternary ammonium salt in a vessel, to form a polymerization mixture, wherein the oxygen and monohydric phenol are added in a mole ratio of 0.5:1 to 1.2:1; and cessation of the continuous addition of the monohydric phenol; and in a build period, continuation of oxygen addition until there is no further increase in viscosity of the polymerization mixture. A poly(phenylene ether) having an intrinsic viscosity of 0.5 to 2.0 deciliters per gram, measured in chloroform using an Ubbelohde capillary glass viscometer at 25° C., a polydispersity of 1 to 10, and a unimodal molecular weight distribution, is made by the method.