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How do problem-solving programs work? How much has been accomplished with them so far? What kinds of developments may be anticipated over the next few years? Two research programs under development are discussed as illustrations of the evolution of heuristic programming systems. Applications of these techniques in studies of problem solving in mathematics and symbolic logic, in industrial and business problems, in laboratory tasks, chess playing and the understanding of language also are considered. The emphasis throughout is on exposition of methods and goals. The paper concludes with a discussion of longer range problems, aspirations, and research strategies in work on artificial intelligence.