Magnets are the principal market for superconductors, but making attractive conductors out of the high-temperature cuprate superconductors (HTSs) has proved difficult because of the presence of high-angle grain boundaries that are generally believed to lower the critical current density, Jc. To minimize such grain boundary obstacles, HTS conductors such as REBa2Cu3O7-x and (Bi, Pb)2Sr2Ca2Cu3O10-x are both made as tapes with a high aspect ratio and a large superconducting anisotropy. Here we report that Bi2Sr2CaCu2O8-x (Bi-2212) can be made in the much more desirable isotropic, round-wire, multifilament form that can be wound or cabled into arbitrary geometries and will be especially valuable for high-field NMR magnets beyond the present 1 GHz proton resonance limit of Nb3Sn technology. An appealing attribute of this Bi-2212 conductor is that, being without macroscopic texture, it contains many high-angle grain boundaries but nevertheless attains a very high Jc of 2,500 A mm(-2) at 20 T and 4.2 K. The large potential of the conductor has been demonstrated by building a small coil that generated almost 2.6 T in a 31 T background field. This demonstration that grain boundary limits to high Jc can be practically overcome underlines the value of a renewed focus on grain boundary properties in non-ideal geometries.