MATH.19:2 - Problem

Forward calculation can produce true statements without approaching the wanted conclusion. Working backward can produce a useful-looking requirement that is stronger than the available assumptions. Combining the two requires discovering a statement that is both obtainable and sufficient for the next inference.

The difficulty can be hidden in a parameter or an order of composition. A proof for one selected object may be used as if it covered all objects; an auxiliary claim may quietly assume the theorem being proved. A recursive step can demand a result for a changed parameter even though the induction hypothesis fixes it.

The needed result is an argument with its assumptions and connections recoverable. If it cannot yet be completed, identify the remaining mathematical claim and what proving or refuting it would enable.