# On the Unreasonable Reasonableness of Mathematical Physics

# On the Unreasonable Reasonableness of Mathematical Physics

A Cognitive View

Mathematics plays an essential role in physics, yet little attention has been given to the cognitive structures and processes that underlie this role. The computational and derivational advantages of mathematical approaches in physics are central, but there is also an important representational role. First, mathematical representations can aid and extend visual representations, adding, for example, a dynamic aspect to static images. Second, even nonvisual imagery can be accommodated mathematically (as in “Maxwell’s Equations,” the partial differential equations which can be taken as representing stresses and strains within an invisible field). Such mathematical representations depend upon a set of well-learned expert skills that function as sophisticated retrieval devices. These representations are *metaphors*, in contrast with the *analogies* that are more commonly discussed by cognitive scientists. A cognitive-historical case study of Maxwell’s development of his mathematical representations and their relation to Faraday’s theoretical ideas about fields is used to illustrate these claims.

*Keywords:*
mathematics, physics, mathematical representations, expert skills, metaphors, analogies, Maxwell, Faraday

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