The so-called Philosophy of Mathematical Practice involves attempts to understand what mathematical practices and mathematical research practices look like. These include looking at the way in which mathematicians prove theorems and how they use diagrams. This PhD thesis contributes to the analysis of how mathematicians deal with definitions. In an effort to achieve this, several methods were used, such as interviews and a so-called ‘corpus analysis’, which involved the examination of more than 30,000 mathematical publications. This PhD thesis shows that, although definitions are primarily mathematical abbreviations, they also have a variety of social functions in terms of communication and understanding. The corpus analysis also shows that in different areas of mathematics, definitions emerge with varying degrees of prominence. In addition to providing new insights about definitions in mathematical practice, this PhD thesis also lays the foundation for further research on this topic. This PhD thesis analyses the existing research on definitions in mathematics and develops conceptual tools for studying this topic.
Vincent Coumans (1993) studied Mathematics at Radboud University and graduated with cum laude distinction. In 2018, he began his PhD within the Philosophy of Mathematical Practice at the Institute for Science in Society. During this time, he was also heavily involved in teaching and designed the Philosophy of Mathematical Practice course for the Master’s students at the Faculty of Science. He currently teaches within the Master’s programme in Mathematics Teacher Education at HAN University of Applied Sciences.