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.