Beyond logic, the quote also carries psychological force. Hard problems often produce frustration, self-doubt, and the temptation to quit. Yet an easier related problem offers a reachable victory, and that small success can change the solver’s emotional state. Confidence grows not from abstract encouragement but from evidence that progress is possible.
Modern research on problem solving and motivation repeatedly shows that visible progress sustains effort. In this light, Pólya’s advice is humane as well as clever: it protects curiosity from discouragement. By finding a problem we can solve, we preserve the energy needed eventually to return to the larger one. [...]
