for the learning of mathematics

an international journal of mathematics education

Jan Zwicky - Vol. 30 Num. 1 (2010)
 Mathematical analogy and metaphorical insight


How are we to understand the power of certain literary metaphors? The author argues that the apprehension of good metaphors is importantly similar to the apprehension of fruitful mathematical analogies: both involve a structural realignment of vision. The author then explores consequences of this claim, drawing conceptually significant parallels between proofs and poems and suggesting that the shared epistemological structure of good metaphors and fruitful mathematical analogies raises an interesting ontological issue. Just as, and to the extent that, the fruitfulness of analogies may be taken to underwrite realism in mathematics, so the power of good metaphors may be regarded as evidence of a mind-independent universe.