How to Deal with Mathematical Practice? -- How and Why Mathematics is Unique as a Social Practice -- Mathematics As Objective Knowledge And As Human Practice -- The Comparison Of Mathematics With Narrative -- Theory of Mind, Social Science, and Mathematical Practice -- Taking Mathematical Practice Seriously -- Incommensurability In Mathematics -- Mathematical Progress As Increased Scope -- Proof in C17 Algebra -- The Informal Logic Of Mathematical Proof -- The Special Case of Mathematical Education -- Mathematicians’ Narratives About Mathematics -- Philosophy of Mathematics and Mathematics Education -- Mathematical Practices In And Across School Contexts -- The Importance of a Journal for Mathematics Teachers -- On The Interdisciplinary Study of Mathematical Practice, with a Real Live Case Study.

Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt the urge, first of all, to bring together the widest variety of authors from these different domains and, secondly, to show that this diversity does not exclude a sufficient number of common elements to be present. In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.