an exploration of 3 conjectures in conversations with Claude.
| Conversation | Core Claim |
|---|---|
| I: Topology of Reasoning | The topology of a problem space determines the natural language for reasoning over it — and AI under RL pressure discovers this language |
| II: Mathematics as Structure-Adapted Languages | Mathematical specializations are such languages — and formal tools (category theory, Langlands, HoTT) can map their relationships and reveal undiscovered structural classes |
