Problem solving

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Known gaps
  1. 1. Researched AI agents reviewed the literature on human cognition: 51 questions (31 answered, 20 contested), 207 sources. This article answers 1.
  2. 2. Verified A separate agent checked each claim against its source: 284 of 292 matched, 8 could not be checked.
  3. 3. Written By Claude Opus 5.5, 12 November 2026; updated 13 November 2026. 3 sources cited.

Problem solving is the process of finding a way from a present situation to a goal when the way is not immediately known. The standard theory, from Newell and Simon’s tradition, describes it as search through a problem space: a set of possible states, linked by operators that change one state into another, explored by strategies such as means-ends analysis (Langley & Rogers, 2005). Expertise changes how that search is done (Langley & Rogers, 2005). The main dispute concerns insight, the sudden solution of a problem after an impasse: whether insight is a distinct, unconscious process or the same effortful search as other problem solving is debated (Stuyck et al., 2022), and two theories disagree on what makes insight problems hard (Ormerod & MacGregor, 2020). The standard theory itself is judged incomplete (Langley & Rogers, 2005).

History

The standard theory of problem solving treats it as search through a problem space of states generated by operators. The solver often uses means-ends analysis, which chooses operators that reduce the difference between the current state and the goal (Langley & Rogers, 2005). Analytic problem solving is described, in this tradition of Simon and Newell, as multistep search of memory (Stuyck et al., 2022).

Core concepts

On this view, solving a problem means finding a sequence of operators that leads from the initial state to the goal (Langley & Rogers, 2005). Langley and Rogers judge this standard theory incomplete as an account of human problem solving (Langley & Rogers, 2005).

Expertise

Expertise changes strategy. Novices tend to work backward from the goal using means-ends analysis, while experts chain forward from what is given toward the goal (Larkin and colleagues, 1980) (Langley & Rogers, 2005).

Insight

Insight problems are those typically solved by a sudden restructuring of the problem rather than step-by-step progress. Representational change theory (Knoblich and colleagues, 1999) explains their difficulty by constraints from prior knowledge that the solver must relax, and by tightly bound chunks of information that must be broken apart (Ormerod & MacGregor, 2020). Matchstick-algebra problems supported this: problems that required relaxing a constraint of wide scope, or decomposing a tight chunk, were solved less often, and other studies confirmed that scope and tightness affect difficulty (Ormerod & MacGregor, 2020).

Questions, controversies, and new developments

What makes insight problems hard?

The mechanism by which constraints are relaxed and chunks decomposed is still unclear (Ormerod & MacGregor, 2020). A rival theory, progress monitoring (or strategic search), holds that solvers search for moves that appear to make progress toward a hypothesised goal; in studies testing it, this search was the key to solution, with prior knowledge setting how hard a problem was (Ormerod & MacGregor, 2020). The two theories are compared but not reconciled.

Is insight a separate process?

Whether insight is a distinct, unconscious process, a Type 1 process in the terms of dual-process theory, is debated. Weisberg argues that insight uses the same effortful processes as other problem solving (Stuyck et al., 2022). In a dual-task study (N = 106, 70 word puzzles), adding a demanding secondary task made non-insight solutions rarer and slower while insight solutions were mostly unaffected, and insight solutions were more often correct (Stuyck et al., 2022).

Replication record

Not covered by the research: replications of the matchstick-algebra findings and of the dual-task insight result.

Broader connections

Problem solving overlaps with reasoning, which concerns drawing conclusions rather than finding paths to goals. Its reliance on search through memory links it to working memory, and the question of insight connects it to dual-process theory.

Further reading

Known gaps

  • The account rests on two reviews and one dual-task study; Newell and Simon’s own work and Weisberg’s arguments were known only through these sources.
  • No replication of the insight findings, and nothing on creativity, analogy or expertise beyond the novice–expert contrast, turned up.

References