Intuition and information processing in mathematical activity

Abstract In the first part of the chapter, the basic characteristics of intuitive knowledge are outlined. Using examples from history and from experiments with children and adults, it is argued that at every level of mathematical reasoning, besides the formal and algorithmic aspects, the intuitive aspect must be considered. In the second part of the chapter, it is considered whether a formulation of information processing that encompasses intuitive cognition is possible. The conclusion is that if information processing is to cover the entire domain of human cognition, then it must span the intuitive as well as the logical aspects. Within such a formulation, the computer metaphor, which fails to capture the intuitive aspects of cognition, loses its central role, while still making an important contribution.