The Mystery of the Black Knight’s Noetherian Ring - An investigation into the story-mathematics connection with a small detour through chess country
Apostolos Doxiadis Athens, GreeceAbstract: Apart from the obvious benefits of making mathematics more interesting, even more likeable to non-mathematicians, narrative can deepen our understanding of the practice and reality of mathematics. To see this, we have to widen our view of what mathematics is, or can be, beyond the strict limitations of the rigorous EAF (Esoteric Abstract Formalist) model bequeathed to us by Greek mathematics. Defining paramathematics as a field ‘on the side of’ mathematics, whose task is the narrative exploration of mathematical questions, I try to determine under what conditions a story can speak about mathematical reality in a non-trivial way. Exploring the matter through the medium of chess and then applying the transitive property (story to chess, chess to mathematics, therefore story to mathematics) I distinguish between roughly three different levels of mathematical discourse, and assign a different value to the relevance of storytelling – and thus the usefulness of paramathematical knowledge – in each one.