Abstract

The philosophy of mathematical practice (PMP) is a branch of the philosophy of mathematics that is motivated by, and closely engaged with, mathematical practice. Studies in this area take as their starting point questions that arise in the practice of mathematics, such as how to examine problematic concepts like infinity, what counts as a proof, and how mathematical understanding should be characterized. Moreover, philosophical discussions of such issues should be grounded in relevant mathematical content.

Different interpretations of practice shape work in PMP. One interpretation understands practice as referring to the activities of human beings. According to this view, mathematical knowledge is shaped through various forms of mathematical activity. Another interpretation emphasizes that philosophical inquiry must engage with mathematical content, such as its concepts, results, and methods. Finally, a historical approach regards mathematics, its theories, and its concepts as shaped by human agents in diverse cultures and social settings. This latter perspective opens a range of topics that intersect with work in the philosophy and history of mathematics.

In addition to being informed by studies of mathematics more generally, PMP draws on and is informed by a range of other fields, including cognitive science, social science, and mathematics education.

This article introduces the central motivations, methods, and themes of PMP and explores three major areas in which it has proved fruitful: mathematical reasoning and proof, mathematical explanation, and visual thinking in mathematics.

https://iep.utm.edu/math-practice/