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## Abstract

The nature of mathematical reasoning has been the scope of many discussions in philosophy of mathematics. This chapter addresses how mathematicians engage in specific modelling practices. We show, by making only minor alterations to accounts of scientific modelling, that these are also suitable for analyzing mathematical reasoning.

In order to defend such a claim, we take a closer look at three specific cases from diverse mathematical sub-disciplines, namely Euclidean geometry, approximation theory, and category theory. These examples also display various levels of abstraction, which makes it possible to show that the use of models occurs at different points in mathematical reasoning. Next, we reflect on how certain steps in our model-based approach could be achieved, connecting it with other philosophical reflections on the nature of mathematical reasoning. In the final part, we discuss a number of specific purposes for which mathematical models can be used in this context.

The goal of this chapter is, accordingly, to show that embracing modelling processes as an important part of mathematical practice, enables us to gain new insights in the nature of mathematical reasoning.

In order to defend such a claim, we take a closer look at three specific cases from diverse mathematical sub-disciplines, namely Euclidean geometry, approximation theory, and category theory. These examples also display various levels of abstraction, which makes it possible to show that the use of models occurs at different points in mathematical reasoning. Next, we reflect on how certain steps in our model-based approach could be achieved, connecting it with other philosophical reflections on the nature of mathematical reasoning. In the final part, we discuss a number of specific purposes for which mathematical models can be used in this context.

The goal of this chapter is, accordingly, to show that embracing modelling processes as an important part of mathematical practice, enables us to gain new insights in the nature of mathematical reasoning.

Original language | English |
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Title of host publication | Springer Handbook of Model-Based Science |

Subtitle of host publication | Section E: Mathematical Models and Models in Mathematics |

Editors | Lorenzo Magnani, Tommaso Bertolotti |

Publisher | Springer |

Pages | 537-549 |

Number of pages | 23 |

ISBN (Electronic) | 978-3-319-30526-4 |

ISBN (Print) | 978-3-319-30525-7 |

Publication status | Published - 2017 |

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