Carter J. Introducing the Philosophy of Mathematical Practice

Cambridge: Cambridge University Press, 2024. — 80 p.This Element introduces a young field, the 'philosophy of mathematical practice'. We first offer a general characterisation of the approach to the philosophy of mathematics that takes mathematical practice seriously and contrast it with 'mathematical philosophy'. The latter is traced back to Bertrand Russell and the orientation referred to as 'scientific philosophy' that was active between 1850 and 1930. To give a better sense of the field, the Element further contains two examples of topics studied, that of mathematical structuralism and visual thinking in mathematics. These are in part presented from a methodological point of view, focussing on mathematics as an activity and questions related to how mathematics develops. In addition, the Element contains several examples from mathematics, both historical and contemporary , to illustrate and support the philosophical points.Introduction
Different Approaches to Philosophy of Mathematics
Scientific and Mathematical Philosophy
Philosophy of Mathematical Practice
Structure in Mathematics
Structuralism in Philosophy
Emergence of Structures
The Role of Interrelations in Mathematics
Visual Thinking in Mathematics
Diagrams in Euclid’s Elements
Diagrams in Contemporary Mathematics and Logic
Diagrams as Effective Representations
Conclusion
References
Acknowledgements