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Sheldon R. Smith, The Mystery of Applied Mathematics?: A Case Study in Mathematical Development Involving the Fractional Derivative, Philosophia Mathematica, Volume 22, Issue 1, February 2014, Pages 35–69, https://doi.org/10.1093/philmat/nkt026
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Abstract
I discuss the applicability of mathematics via a detailed case study involving a family of mathematical concepts known as ‘fractional derivatives.’ Certain formulations of the mystery of applied mathematics would lead one to believe that there ought to be a mystery about the applicability of fractional derivatives. I argue, however, that there is no clear mystery about their applicability. Thus, via this case study, I think that one can come to see more clearly why certain formulations of the mystery of applied mathematics are not convincing.