 Now Frege, himself, ironically, had revolutionised mathematics by introducing hitherto unprecedented standards of rigour in the formalisation of mathematical theories. He recognised (§90: 185–6) that one could improve vastly on Heine and Thomae by treating mathematical theories, their language, axioms and rules, as formal, mathematical objects in their own right. This is exactly what the Hilbert programme set out successfully to achieve, creating the new disciple of metamathematics.