What is this? In this framework, both algorithms and axiomatic theories are represented as graphs, allowing procedural and logical structures to be studied within a unified formalism. Using Mermaid Markdown, we model computation (flowcharts) and logical dependency (axiom–definition–theorem) as the same type of object—enabling inspection, versioning, and machine-readable representation.
Two categories, one representation
Algorithms (Process Flow)
- Sieve of Eratosthenes
- Merge Sort, Quicksort
- Binary Search
- Dijkstra's Algorithm
- …
Axiomatic Systems (Logical Dependency)
- 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
🔀 Algorithms — Flowcharts
Step-by-step procedures: OR gates (branches), Loops (feedback), AND gates (sequential, parallel joins)
| Name ↕ | Subcategory ↕ | Complexity ↕ | Nodes ↕ | Edges ↕ | OR Gates ↕ | AND Gates ↕ | Loops ↕ |
|---|
📐 Axiomatic Theories — Dependency Graphs
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 |
|---|
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)
Red
Triggers & Inputs
Triggers & Inputs
Yellow
Structures & Objects
Structures & Objects
Green
Processing & Operations
Processing & Operations
Blue
Intermediates & States
Intermediates & States
Violet
Products & Outputs
Products & Outputs