Problem

A problem is a condition or question that people recognize as a gap between what currently exists and what is desired, with an unclear path to reaching the goal. The term is used in daily life, mathematics, engineering, philosophy, and government administration. Regardless of context, problems share a common structure: an initial state, a goal, and constraints (what is permissible to do).

A problem is not something that exists objectively in the world alone; it depends on how people define it. The same condition—such as water scarcity—one person may see as a technological problem (wells and pumps), while another may see as a distribution problem (who gets access to water). This is why defining the problem itself is considered a contested step.

Parts of every problem

Standard analysis divides a problem into three parts: the current state (what exists), the goal (what is needed), and the path between the two. When both endpoints are clear but the path is unclear, the problem is called well-structured; mathematics and games like chess are of this kind. When the goal itself is unclear, the problem is called ill-defined or unstructured, such as urban planning.

So-called wicked problems

Planning science has identified a type of problem that has no single definition, no provably correct solution, and in which each step creates new problems. Examples cited include poverty, climate change, and peace. In such cases, those solving them work through incremental improvements, not complete solutions.

Ways of solving problems

Common approaches to solving a problem include: breaking the problem into smaller parts, redefining (restating the question differently), comparing with past cases, and trial and error. In mathematics and computer science, there is a strict definition: a problem is a question with inputs and desired outputs, where problems are measured by how much computation and time they require. There are also recognized unsolvable problems demonstrated through mathematical proof.