Intuition and visualization in mathematical problem solving

Topoi 29 (1):29-39 (2010)
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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.

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Valeria Giardino
Centre National de la Recherche Scientifique

References found in this work

The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.
Collected works.Kurt Gödel - 1986 - New York: Oxford University Press. Edited by Solomon Feferman.
Logical reasoning with diagrams.Gerard Allwein & Jon Barwise (eds.) - 1996 - New York: Oxford University Press.

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