# Visualization, Explanation and Reasoning Styles in Mathematics

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Part of the Synthese Library book series (SYLI, volume 327)

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Part of the Synthese Library book series (SYLI, volume 327)

This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams etc. have become the subject of intense interest. The historians and philosophers in this book agree that there is more to understanding mathematics than a study of its logical structure. How are mathematical objects and concepts generated? How does the process tie up with justification? What role do visual images and diagrams play in mathematical activity? What are the different epistemic virtues (explanatoriness, understanding, visualizability, etc.) which are pursued and cherished by mathematicians in their work? The reader will find here systematic philosophical analyses as well as a wealth of philosophically informed case studies ranging from Babylonian, Greek, and Chinese mathematics to nineteenth century real and complex analysis.

Algebra calculus geometry mathematics philosophy of mathematics proof

- DOI https://doi.org/10.1007/1-4020-3335-4
- Copyright Information Springer 2005
- Publisher Name Springer, Dordrecht
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-4020-3334-6
- Online ISBN 978-1-4020-3335-3
- Buy this book on publisher's site