AUFF NOVA Grant for Jessica Carter
Creating a multidisciplinary framework to analyse mathematical inventions
Abstract
To many, mathematics is a mysterious field. One might wonder how we were able to develop the complex structures of contemporary mathematics. Furthermore, mathematics has its own specialized language with technical terms, notations that are used to write expressions in a compact form, and various visual representations such as diagrams. This language is part of what makes mathematics difficult to understand. In this light, we ask: What role do these visual representations and notations play? Could it be that they aid in the discovery of mathematical facts?
Currently, there is no framework capable of addressing the complexity of how mathematical inventions are made. The aim of the project is thus twofold. First, together with international and local collaborators, Carter seeks to develop a multidisciplinary philosophical framework that draws on insights from relevant fields such as mathematics, the history of mathematics, semiotics, information theory and cognitive science. Second, the goal is to explore to what extent the components can explain how (visual) representations contribute to mathematical discoveries.