Abstract
In this short Introduction to the present section, I will first briefly point out the reasons why the chapters collected here present original research in the context of the philosophy of the practice of mathematics, and open even newer perspectives. It is important to note that one crucial issue for future research will be to explore the connections within these chapters and with other chapters included in other sections – in particular, but not exclusively, the sections on Proof, on “Experimental” mathematics, and on the Semiology of Mathematical Practice. Second, I will present a short – and not exhaustive – summary of the themes that are tackled in the chapters. There will be overlaps and common threads: These chapters are indeed the final product of several discussions and exchanges within the community of the philosophers of the mathematical practice, which is extending toward other regions of philosophy thus blurring standard boundaries.
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Notes
- 1.
For more information about the Association, see http://www.philmathpractice.org
- 2.
See Starikova’s article in this volume and Giardino (2022), where I distinguish between thought experiments, real experiments, and quasi-experiments in mathematics.
- 3.
On this point, she draws on previous work. See De Toffoli (2021).
References
De Toffoli S (2021) Groundwork for a fallibilist account of mathematics. Philos Q 71(4):823–844
Ferreirós J (2016) Mathematical knowledge and the interplay of practices. Princeton: Princeton University Press
Giardino V (2022) Experimenting with triangles. Axiomathes 32(Suppl 1):55–77
Hamami, Morris (2021) Plans and planning in mathematical proofs. Rev Symb Log 14(4):1030–1065
Tanswell F (forthcoming) Go forth and multiply: on actions, instructions and imperatives in mathematical proofs. In: Bueno O, Brown J (eds) Essays on the work of Jody Azzouni. Cham: Springer
Acknowledgements
I wholeheartedly thank Bharath Siraman for his work and patience in the course of these long years. My thanks also go to the authors, who have taken the time and the energy to respond to the challenge of the theme of this section and present new perspectives in the philosophy of the mathematical practice. I am sure that their chapters will be a reference for future research.
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Giardino, V. (2023). New Perspectives: An Introduction. In: Sriraman, B. (eds) Handbook of the History and Philosophy of Mathematical Practice. Springer, Cham. https://doi.org/10.1007/978-3-030-19071-2_126-1
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