Tobias Grøsfjeld: The art of bad art: Diagrammatics in mathematical physics

Abstract.

The purpose of a proof is to reduce statements to a series of trivialities, ideally letting as many readers as possible agree that there is no way the final statement could be false. Unfortunately, the nature of research inevitably requires the introduction of specialized notation, some of which may obfuscate the underlying meaning to unfamiliar readers, including experts in closely related fields.
However, by adopting visual diagrammatics that emphasize structures over implementation details, one can more easily recognize similarities between fields. This is particularly effective in mathematical physics, as it greatly benefits from collaborations between mathematicians and physicists while also often being subjected to topological constraints. This gives us a toolset for how to visually manipulate many forms of diagrammatics regardless of our background, allowing collaborators to more quickly reach equivalent conclusions which can subsequently be translated into their preferred language of choice.

This thesis focuses on demonstrating the usage of various diagrammatics and their advantages over traditional symbolic syntax in order to prove novel statements in knot theory and mathematical physics in approachable ways.

Thesis on DiVA