Mathematics Database · Gary Welz · CUNY Graduate Center

Formal mathematical structure as visual graphs

Algorithms, axiomatic systems, and proofs expressed as labeled directed graphs using Mermaid Markdown — revealing structure that prose alone cannot show.

~30
Algorithms
~20
Axiomatic Systems
~15
Proofs

Approximate counts, and growing.

The Euclidean Algorithm — one of the oldest algorithms in recorded mathematics (~300 BC)

graph TD A["Input: two integers a, b"] --> B{Is b = 0?} B -->|Yes| C["Return a — this is the GCD"] B -->|No| D["Compute remainder: r = a mod b"] D --> E["Set a = b, b = r"] E --> B style A fill:#ddd8f5,stroke:#3d2d8e,color:#000 style B fill:#e1bee7,stroke:#4a148c,color:#000 style C fill:#c8e6c9,stroke:#1b5e20,color:#000 style D fill:#ddd8f5,stroke:#3d2d8e,color:#000 style E fill:#ddd8f5,stroke:#3d2d8e,color:#000
Indigo = computation step Purple = decision Green = terminal result

What this is

The Mathematics Database represents algorithms, axiomatic systems, and proofs as labeled directed graphs using Mermaid Markdown. This unified representation reveals structural properties — such as the regularity of algorithm capsules across mathematically distant domains — that conventional prose and static diagrams obscure. The corpus spans classical geometry, number theory, algebra, set theory, mathematical logic, and theoretical computer science.

Browse and explore

Algorithms

Flowcharts of computational procedures — sorting, searching, number theory, graph algorithms.

Axiomatic Systems

Dependency graphs of logical structures — Euclid's Elements, Peano arithmetic, ZFC set theory, group theory, category theory.

Proofs

Proof graphs encoding justification structure — diagonalization family, incompleteness, independence results.

Research

Proof Graphs and Algorithm Capsules: A Corpus Study of Diagonalization Proofs from Cantor to Gödel to Goodstein

Gary Welz · CUNY Graduate Center / New Media Lab

Preprint available on Zenodo

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