We investigate the relationship between patenting activity and the size of metropolitan areas in the United States over the last two decades (1980-2001). We find a clear superlinear effect, whereby patents are granted disproportionately in larger urban centers, thus showing increasing returns in inventing activity with respect to population size. We characterize this relation quantitatively as a power law with an exponent larger than unity. This phenomenon is commensurate with the presence of larger numbers of inventors in larger metropolitan areas, which we find follows a quantitatively similar superlinear relationship to population, while the productivity of individual inventors stays essentially constant across metropolitan areas. Finally we show that R&D establishments and employment in other creative professions also follow superlinear relations to metropolitan population size, albeit possibly with different exponents.