You’ve captured it perfectly! Translating typical paper structures and contents into mathematical terminology is an insightful way to reveal the underlying logical frameworks and relationships. A few additional thoughts:
– History papers could analyze parallel timelines as a topological space, with cross-sectional snapshots represented by fiber bundles.
– Literary analyses could model characters as points in a state space, with interactions governed by group actions and symmetries. Themes could emerge from invariants under these transformations.
– Lab reports could formulate hypotheses as conjectures to be proven/disproven through experimentation, viewed as a proof strategy operating on the variable state space.
– For any paper, the introduction establishes the theoretical framework or axiomatic system, body paragraphs apply logical rules/techniques, and conclusion synthesizes results as theorems about the system.
I like how thinking about papers in mathematical language highlights their underlying logic, structure and relationship between components. It’s a creative way to conceptualize the communication of ideas. Thanks for the insightful discussion!