## Mathematics and Scientific RepresentationMathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics. |

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### Contents

1 Introduction | 3 |

Epistemic Contributions | 23 |

Other Contributions | 167 |

Method of Characteristics | 301 |

BlackScholesModel | 303 |

Speed of Sound | 305 |

Two Proofs of Eulers Formula | 307 |

309 | |

317 | |

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abstract objects abstract varying acausal representation accurate agent application approach argue assumptions Batterman Bénard cells best explanation boundary layer catastrophe theory causal representation chapter Colyvan complex numbers complex potential confirmation consider constitutive representations density deployed derivative representations discussion domain ematical epistemic equations Euler equations example existence explanatory power failure fictionalist fluid framework Frigg given heat equation indispensability argument interpretation involve kind Laplace’s mathe mathematical beliefs mathematical claims mathematical concepts mathematical entities mathematical structure mathematicians mathematics contributes metaphysical multiple realizability natural numbers Navier-Stokes equations objects ofthe parameter perturbation theory physical system position prior problem proposal pure mathematics question Quine’s rainbow ray representation ray theory real numbers realist reason relevant represent representational content result Riemann surface role saddle points scale scientist semantic solution sort square root function Steiner success of science target system theorem tions understand velocity wave Wilson