The algorithmic side of Riemann’s mathematics
“My efforts in number theory have been directed toward basing the work not on arbitrary representations [Darstellungsformen] or expressions but on simple foundational concepts and thereby—although the comparison may sound a bit grandiose—to achieve in number theory something analogous to what Riemann achieved in function theory, in which connection I cannot suppress the passing remark that in my opinion Riemann’s principles are not being adhered to in a significant way by most writers—for example, even in the newest works on elliptic functions; almost always they disfigure the theory by unnecessarily bringing in forms of representation [Darstellungsformen again] which should be results, not tools, of the theory.”