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Mathematical Intuition vs. Mathematical Monsters

Geometrical and physical intuition, both untutored and cultivated, is ubiquitous in the research, teaching, and development of mathematics. A number of mathematical “monsters”, or pathological objects, have been produced which?according to some mathematicians?seriously challenge the reliability of intuition. We examine several famous geometrical, topological and set-theoretical examples of such monsters in order to see to what extent, if at all, intuition is undermined in its everyday roles.

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Mathematical Intuition vs. Mathematical Monsters