Virtue Epistemology of Mathematical Practice

Twenty-first century philosophy of mathematics has exhibited a turn towards issues of mathematical practice. This represents a shift from the field's traditional focus on metaphysical questions to a focus on epistemology, in particular social epistemology. One of the most productive programmes in twenty-first century epistemology has been virtue epistemology. These parallel developments suggest that the time is ripe for a virtue epistemology of mathematics. The aretaic turn has provided fruitful results in various philosophical disciplines. These fruits have not yet been harvested in the philosophy of mathematics. Our conference seeks to rectify this situation. The benefits to undertaking such research are the following:

First of all, paying attention to mathematical virtues highlights the social side of mathematics. Social processes are central to mathematical breakthroughs, the development of new concepts, peer-review and collaboration between mathematicians. A lack of reflection on what features and virtues of our practices are important leads to these only being brought about in the mathematical community in an ad hoc fashion. The careful and rigorous study of mathematical virtues can reveal the guiding principles of mathematical communities, inform us how to develop new technologies and tools for mathematicians, and help to design the real and virtual spaces for mathematical interactions.

Secondly, mathematical virtue theory has impacts in the mathematics itself. By studying which features we value in mathematics, we shape the way that theorems, concepts and techniques are developed. For instance, interestingness, simplicity, rigour and beauty all play vastly different roles in mathematics, but all of them are directly relevant to the mathematics that is produced. In this conference we will make concrete the ways in which such virtues influence mathematical results.

Finally, mathematics education is not merely about teaching students a list of theorems, but is about teaching them how to do mathematics and how to be a mathematician. But these aims involve the cultivation of certain mathematical virtues, like inventiveness, perseverance and open-mindedness. The study of mathematical virtues will thus provide valuable guidance for mathematical educators, and the wider process of inducting students into mathematical practices as valuable contributors.