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Mathematical Representations in Science: A Cognitive–Historical Case History
Author(s) -
Tweney Ryan D.
Publication year - 2009
Publication title -
topics in cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.191
H-Index - 56
eISSN - 1756-8765
pISSN - 1756-8757
DOI - 10.1111/j.1756-8765.2009.01043.x
Subject(s) - representation (politics) , cognition , cognitive science , faraday cage , epistemology , field (mathematics) , computer science , psychology , cognitive psychology , mathematics , philosophy , physics , politics , law , quantum mechanics , neuroscience , political science , magnetic field , pure mathematics
The important role of mathematical representations in scientific thinking has received little attention from cognitive scientists. This study argues that neglect of this issue is unwarranted, given existing cognitive theories and laws, together with promising results from the cognitive historical analysis of several important scientists. In particular, while the mathematical wizardry of James Clerk Maxwell differed dramatically from the experimental approaches favored by Michael Faraday, Maxwell himself recognized Faraday as “in reality a mathematician of a very high order,” and his own work as in some respects a re‐representation of Faraday’s field theory in analytic terms. The implications of the similarities and differences between the two figures open new perspectives on the cognitive role of mathematics as a learned mode of representation in science.