Proofs and Representations

The notion of representation plays a central role in mathematics: without particular representations the abstract objects of mathematics would be unthinkable. Reflections on the means of expression of abstract thoughts have a long tradition in philosophy, for example in the work of Leibniz and Frege. Notation systems, spatial and symbolic representations, and representation theorems are key notions across all mathematical subfields. In this vein, the aim of this workshop is to explore various ways in which proofs and representations advance mathematical knowledge and mathematical understanding. This workshop will address questions such as: Are representations mere instruments for conveying and illustrating mathematics, or do they play a more substantial role in the generation of mathematical knowledge and understanding, and if so, how? What is the relation between conceptual shifts in the history of mathematics and logic, and changes of representations? How do representations inform us about theoretical virtues of proofs and arguments, such as explanatoriness and purity? These are just some of the questions that we intend to get a better grasp of during this workshop, by looking at a wide range of representations––models, diagrams, notations, and more––as they have been used in historical cases, as well as through empirically based reflection and systematic analysis.