“Mathematics is a fascinating, yet mysterious, field. Some are drawn to it because of its rigour and because it yields absolute truths. Others are taken by mathematics’ capacity to describe our complex world in simple relations. When engaging with mathematics, however, questions arise. One might wonder how we were even able to develop and grasp all of the complex structures that constitute contemporary mathematics. A related question concerns the nature of the relations between elementary mathematical activities such as counting and measuring and the modern abstract theories of mathematics – if there are any such relations. Mathematics has a language of its own with technical terms, notations that are used to write expressions in a compact and convenient form, and a variety of visual representations such as figures and diagrams. This special language is also part of what makes mathematics difficult to understand. In this light, one may ask: What is the role of the notation and visual representations – are they essential components of contemporary mathematics or merely useful devices? Could it also be that they somehow aid our discovery of mathematical facts?”

( Carter 2024, p. 1)

In this passage, Jessica introduces central philosophical questions about mathematical practice, and she discusses several of them further in the Element. Divided into three sections, the Element begins with a general introduction to the philosophy of mathematical practice, continues with an exploration of structuralism from a practice perspective, and concludes with a discussion of the role of diagrams in mathematics.

If this has sparked your interest, you have free access to the full Element via this link until 26 December 2024:

https://www.cambridge.org/core/elements/introducing-the-philosophy-of-mathematical-practice/8FDBE76CB96FA8CFBD6AC960F2022023?fbclid=IwZXh0bgNhZW0CMTAAAR1kHHjHI5g7p9ir8GfVTWCPK5arFzVoWdpRX1eijnNghQPe8KRxlpijTYk_aem_tIc1w0gwSJ59ZSdHS9w3Sw