Last fall I read “A diagrammatic view of differential equations in physics” by Evan Patterson, Andrew Baas, Timothy Hosgood and James Fairbanks. They show that you can use diagrams to write down the sorts of equations on manifolds that physicists care about. In this post I’ll try to convey the main ideas of the paper to you so that: (1) I can get you excited about it and (2) I can refer back to these notes in the future.
This is a companion discussion topic for the original entry at https://bmbumpus.com/2023/04/13/diagrammatic-equations/