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What is "Applied Mathematics" Anyway? How the History of Fluid Mechanics Demonstrates the Role of Concepts in Applied Mathematics

Perry, Stephen (2021) What is "Applied Mathematics" Anyway? How the History of Fluid Mechanics Demonstrates the Role of Concepts in Applied Mathematics. [Preprint]

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Abstract

One of the more popular approaches to articulating the role of mathematics in
scientific modeling and explanation has been what is called the “mapping account.” The mapping account supposes that there is something like an isomorphism or homomorphism between a mathematical representation and the physical phenomenon it is representing. A notable recent formulation of the mapping account is given by Christopher Pincock. I use the case of representing viscosity in the Navier-Stokes Theorems and Prandtl’s Boundary Layer Theory to challenge this notion of direct correspondence between a piece of mathematics and the world.

I argue that physical concepts play a crucial role in mediating between mathematics and world, and I further argue that the way in which concepts play this role is complex, leading me to develop the notion of the "conceptual infrastructure" of a given physical concept, that is, how that concept may be used by a modeler. I draw on the work of Mark Wilson and Hasok Chang in generalizing the results about physical concepts I find in the case study, pointing the way to a different, more nuanced kind of account of not just applied mathematics, but mathematics in general.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Perry, Stephensperry381@gmail.com
Keywords: applied mathematics, mathematics, Navier-Stokes, fluid mechanics, mathematical representation, physical concepts, complex numbers, mapping accounts, applications of mathematics
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Practice
Specific Sciences > Physics > Condensed Matter
General Issues > History of Science Case Studies
Specific Sciences > Mathematics
General Issues > Models and Idealization
Depositing User: Stephen Perry
Date Deposited: 18 Jul 2021 21:06
Last Modified: 18 Jul 2021 21:06
Item ID: 19331
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Practice
Specific Sciences > Physics > Condensed Matter
General Issues > History of Science Case Studies
Specific Sciences > Mathematics
General Issues > Models and Idealization
Date: April 2021
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/19331

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