Intuition and visualization in mathematical problem solving

Topoi 29 (1):29-39 (2010)
Abstract
In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive resources. I will focus on two kinds of danger in recurring to visualization and I will show that they are not a good reason to conclude that visualization is not reliable, if we consider its use in mathematical practice. Then, I will give an example of mathematical reasoning with a figure, and show that both visualization and intuition are involved. I claim that mathematical intuition depends on background knowledge and expertise, and that it allows to see the generality of the conclusions obtained by means of visualization.
Keywords Mathematical intuition  Mathematical visualization  Diagrammatic reasoning  Problem-solving
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Kurt Gödel (1986). Collected Works. Oxford University Press.

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