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The Role of Notations in Mathematics

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Abstract

The terms of a mathematical problem become precise and concise if they are expressed in an appropriate notation, therefore notations are useful to mathematics. But are notations only useful, or also essential? According to prevailing view, they are not essential. Contrary to this view, this paper argues that notations are essential to mathematics, because they may play a crucial role in mathematical discovery. Specifically, since notations may consist of symbolic notations, diagrammatic notations, or a mix of symbolic and diagrammatic notations, notations may play a crucial role in mathematical discovery in different ways. Some examples are given to illustrate these ways.

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Acknowledgments

I am grateful to Otávio Bueno, Catarina Dutilh Novaes, Danielle Macbeth, Dirk Schlimm, Nathalie Sinclair, Fabio Sterpetti, and Robert Thomas, for critical comments and helpful suggestions concerning earlier drafts of this paper.

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  1. Sapienza University of Rome, Piazzale Aldo Moro, 5, 00185, Rome, RM, Italy

    Carlo Cellucci

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Correspondence to Carlo Cellucci.

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Cellucci, C. The Role of Notations in Mathematics. Philosophia 48, 1397–1412 (2020). https://doi.org/10.1007/s11406-019-00162-9

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