MATH.23:9 - Consequences

A result becomes material for developing another mathematical problem. A failure can yield a condition, a construction or a new object of study. A success can reveal a family of operations and a way to transfer the result.

The method can stop with a well-formed conjecture and first attempt. Completing its proof, obtaining a computational procedure, learning the method and applying it to a physical subject have their own requirements. Keeping the connection to those uses makes partial progress useful without claiming their completion.