Philosophy of mathematical practice is a branch of philosophy of mathematics starting with the assumption that mathematics is not only a body of eternal truths, but also a human activity with its specific dynamics of change and history. By observing a wide range of mathematical practices, including advanced practices, questions beyond foundations and access to abstract objects arise. Examples of such questions are: Why do mathematicians reprove a theorem which already has an accepted proof? When is a proof explanatory? What is mathematical understanding? What are the epistemic roles of diagrams and visualization in mathematics? How did certain mathematical concepts evolve over time? These questions tend to admit localized answers, specific to certain contexts, rather than applying for all mathematics. In recent years, researchers have been accumulating detailed case studies to answer them. Moreover, interdisciplinary endeavours have been pursued, bringing together not only philosophers and historians, but also cognitive scientists, sociologist, anthropologists, mathematics education researchers, and computer scientists.
The collection Mancosu 2008 contains an important sample of articles on the philosophy of mathematical practice. For a more interdisciplinary collection, in which issues in sociology of mathematics and mathematical education are also included, see Van Bendegem & van Kerkhove 2007. Book length studies are Corfield 2003, Ferreiros 2016, and Wagner 2017.
The introduction of Mancosu 2008 is very informative and clarifies the position of philosophy of mathematical practice in the landscape of philosophy of mathematics. For general descriptions of different approaches on mathematical practice, see Van Bendegem 2014. A recent survey article is Carter 2019.
- Explanation in Mathematics (73)
- The Infinite (292)
- The Application of Mathematics (235)
- History of Mathematics (195)
- Philosophy of Mathematics, General Works (447)
- Mathematical Explanation (123)
- Philosophy of Mathematics, Misc (617)
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