Vincent Coumans, HAN University of Applied Sciences, Netherlands
Title of the talk:
Studies on Definitions in Mathematical Practice
In this talk, I will give an overview of the research that led to my PhD dissertation Studies on Definitions in Mathematical Practice (https://repository.ubn.ru.nl/handle/2066/291649). The overall question of this dissertation is how mathematicians think about and interact with definitions in practice. The fact that we are interested in definitions in practices, means that we look at definitions in contemporary mathematical research practice as opposed to, for instance, idealized accounts of definitions in logic.
The dissertation consists of five parts:
- A literature review of existing research on definitions in practice,
- An interview study with research mathematicians,
- A philosophical account of explanatory definitions,
- A corpus analysis of arXiv publications,
- General observations based on the research.
During the talk, I will give a brief overview of the dissertation’s results and hope to have a fruitful dialogue with the participants on the possible implications of this research for mathematics education.