 Even so, it was not until 1879, when Frege developed the necessary logical apparatus, that logicism could finally be said to have become technically plausible. After another five years’ work, Frege arrived at the definitions necessary for logicising arithmetic and during the 1890s he worked on many of the essential derivations. However, with the discovery of paradoxes such as  Russell’s paradox  at the turn of the century, it appeared that additional resources would need to be developed if logicism were to succeed.