Foundational typology & GLMP working paper (2026)
The essay Primitive Relations and Computational Complexity uses this database as its primary mathematical diagram corpus (algorithms + axiomatic dependency graphs). For regulatory “algorithms” (gene-circuit flowcharts), see the companion GLMP database table — not merged into the table below, but conceptually parallel. Interactive viewers: Programming Framework.
Quick entry points (axiomatic roots discussed there):
Two categories, one representation
- Sieve of Eratosthenes
- Merge Sort, Quicksort
- Binary Search
- Dijkstra's Algorithm
- …
- Euclid's Elements
- Group Theory
- Peano Arithmetic
- Ring Theory, Field Theory
- …
Start Here
Search the collection or explore the interactive Whole of Mathematics visualization.
📊 Database Table
💡 Click any name to view its interactive flowchart or dependency graph
Step-by-step procedures: OR gates (branches), Loops (feedback), AND gates (sequential, parallel joins)
| Name ↕ | Subcategory ↕ | Complexity ↕ | Nodes ↕ | Edges ↕ | OR Gates ↕ | AND Gates ↕ | Loops ↕ |
|---|
Axiom–definition–theorem dependency graphs (arrows = depends on)
| Name ↕ | Subcategory ↕ | Complexity ↕ | Nodes ↕ | Edges ↕ | Axioms ↕ common notions, postulates |
Definitions ↕ defs |
Lemmas ↕ auxiliary results |
Theorems ↕ propositions |
Corollaries ↕ direct consequences |
|---|
Justificatory graphs with source, assumption, construction, assertion, inference, algorithm capsule, contradiction, and conclusion roles. Pages live under proof-graphs/.
| Name ↕ | Subcategory ↕ | Complexity ↕ | Nodes ↕ | Edges ↕ | Capsules ↕ | Temp asms ↕ | Frontier ↕ |
|---|
What This Enables
- Compare mathematical systems by graph structure
- Measure complexity of proofs or algorithms
- Identify reusable substructures across domains
- Provide machine-readable representations for AI-assisted mathematics
Why This Approach Matters
- Makes mathematical structure inspectable—procedures and logical dependencies visible as graphs
- Bridges computation and proof—algorithms and axiomatic systems share the same diagrammatic representation
- Enables machine-readable math representations (Mermaid is text-based, versionable, composable)
- Potential use in education, formal verification, and AI reasoning systems
Diagrams are generated from natural language descriptions using LLMs.
📈 Collection Overview
🎨 Color Scheme (5-Color System)
Triggers & Inputs
Structures & Objects
Processing & Operations
Intermediates & States
Products & Outputs