A developmental process, independent of morphogenetic (shape) change, that is required for the pronephros to attain its fully functional state. In mammals, the pronephros is the first of the three embryonic kidneys to be established and exists only transiently. In lower vertebrates such as fish and amphibia, the pronephros is the fully functional embryonic kidney and is indispensable for larval life. [ GOC:mtg_kidney_jan10 ]