Motif

Structural exploration of mathematics across fields and representations.

Status: Sketch ○

Initial scaffolding. No implementation yet.

Motif treats mathematics as a graph of structural relationships rather than a tree of fields. It extracts invariants from existing math, detects recurring structural patterns (motifs) across domains, and enables cross-field translation by normalizing to shared intermediate representations.

Key ideas

• Math as graph — Fields are clusters in a structure graph, not branches of a tree. Boundaries are historical artifacts, not structural necessities.
• Layered IRs — No single "true" representation. Multiple IR layers (surface DSL → structural IR → semantic core), like a compiler pipeline for mathematics.
• Cross-field translation — Remove artificial restrictions between disciplines. Tools transfer even when formulas don't.
• Structural motifs — Recurring patterns (symmetry, duality, optimization, composition) are the high-degree hubs in the math graph.
• Pruned search — The interesting manifold in idea-space is measure-zero. Discovery is navigation, not enumeration.

Architecture

human math DSLs (notation, conventions, field-specific idioms)
  → structural IR (invariants, transformations, relationships)
    → semantic core (interchangeable minimal foundations)

Each layer preserves meaning while exposing different structure. Translation happens above the core. The core ensures coherence.

Links

• GitHub