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Metamath: Works & Standards

Metamath is a formal language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. Several databases of proved theorems have been developed using Metamath covering standard results in logic, set theory, number theory, algebra, topology and analysis, among others.

Language: English [EN]
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Metamath topic overview

The analysis highlights Works and Standards as prominent areas in the source structure around Metamath.

Related topics
39
Source areas
6
Connected nodes
45
Extracted relationships
69
Concept neighborhoods
26
Bridge connections
45

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Metamath databases · 15 topics
Overview · 9 topics
Metamath language · 7 topics
Other works connected to Metamath · 4 topics
Metamath proof checker · 3 topics
Natural deduction · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Developer
Norman Megill
License
GNU General Public License (Creative Commons Public Domain Dedication for databases)
Operating system
Linux, Windows, macOS
Release
0.07 in June 2005; 21 years ago (2005-06)
Repository
github.com/metamath/metamath-exe
Stable release
0.198 / 7 August 2021; 5 years ago (7 August 2021)

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Metamath language

Metamath proof checker

Metamath databases

Natural deduction

Other works connected to Metamath

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Metamath connects Entity context

The extracted context around Metamath shows recurring relationship patterns in the source. For example, Metamath → In, In Metamath, In Mmj2, Mel O'Cat, Mmide, Mmj2, Moreover Mmj2, Paul Chapman, The, There, This, William Hale, You Another extracted example is Metamath → Bach, Escher, Gödel, MIU, MU, Peano, Robert Solovay, The, The Metamath. Use these groups to spot repeated connection types before inspecting the individual relationships.

Metamath

Top relations

related to Editors · 13
Metamath → In, In Metamath, In Mmj2, Mel O'Cat, Mmide, Mmj2, Moreover Mmj2, Paul Chapman, The, There, This, William Hale, You
related to Databases without explorers · 9
Metamath → Bach, Escher, Gödel, MIU, MU, Peano, Robert Solovay, The, The Metamath
related to Metamath Proof Explorer · 8
Metamath → Hilbert, It, September, Tarski-Grothendieck, The, The Metamath Proof Explorer, Thus, ZFC
related to Metamath language · 5
Metamath → Instead, Proofs, The, The Metamath, ZFC
related to Natural deduction · 5
Metamath → As, Because Metamath, Hilbert-style, However, The Metamath Proof Explorer
related to Older explorers · 5
Metamath → Hilbert, Hilbert Space Explorer, Metamath Proof Explorer, Quantum Logic Explorer, The Metamath
related to Proof checkers · 5
Metamath → Ghilbert, Levien, Python, Raph Levien, Using
related to Metamath databases · 4
Metamath → Explorer, Hilbert, Most, The Metamath
related to Substitution · 3
Metamath → All Metamath, Proper, The
related to Metamath proof checker · 2
Metamath → It, The Metamath

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

proof set database proofs databases theorems logic mm use language using theory substitution system website rules explorer also user deduction

Metamath relationships Subject–Predicate–Object triples

TTTA extracted 69 structured relationships around Metamath. Examples in this analysis include Metamath → Developer → Norman Megill and Metamath → License → GNU General Public License (Creative Commons Public Domain Dedication for databases). The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
MetamathDeveloperNorman Megill1.00infobox
MetamathLicenseGNU General Public License (Creative Commons Public Domain Dedication for databases)1.00infobox
MetamathOperating systemLinux, Windows, macOS1.00infobox
MetamathRelease0.07 in June 2005; 21 years ago (2005-06)1.00infobox
MetamathRepositorygithub.com/metamath/metamath-exe1.00infobox
MetamathStable release0.198 / 7 August 2021; 5 years ago (7 August 2021)1.00infobox
MetamathTypeComputer-assisted proof checking1.00infobox
MetamathWebsiteus.metamath.org1.00infobox
MetamathWritten inANSI C1.00infobox
Metamathis aformal language and an associated computer program0.90text
Metamathrelated to Databases without explorersThe Metamath0.60section
Metamathrelated to Databases without explorersThe0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Metamath bring nearby vocabulary together. In this analysis, examples include Proof, Databases and Theorems. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Metamath
    • Proof
    • Databases
    • Theorems
    • Use
    • Also
    • Explorer
    • Website
    • Logic
    • Set
    • Mm
    • Checker
    • Substitution
  • metamath
    • Proof
    • Databases
    • Theorems
    • Use
    • Also
    • Explorer
    • Website
    • Logic
    • Set
    • Mm
    • Checker
    • Substitution
  • formal language
    • System
    • New
    • Written
    • Checker
    • Deduction
    • Also
    • Databases
    • Language
    • Metamath
    • Use
    • Substitution
    • Proofs
  • proof assistant
    • Explorer
    • Mm
    • Checker
    • Set
    • Use
    • Logic
    • Enter
    • Also
    • User
    • Website
    • Substitution
    • Databases
  • logic
    • Theory
    • Set
    • Explorer
    • Database
    • Theorems
    • Checker
    • Natural
    • Proof
    • Systems
    • Metamath
    • Axioms
    • Deduction
  • set theory
    • Theory
    • Database
    • Mm
    • Systems
    • Axioms
    • Explorer
    • Using
    • Checker
    • Example
    • Statements
    • Based
    • New
  • proof verifiers
    • Explorer
    • Mm
    • Checker
    • Set
    • Use
    • Logic
    • Enter
    • Also
    • User
    • Website
    • Substitution
    • Databases
  • formal systems
    • System
    • New
    • Checker
    • Deduction
    • Also
    • Website
    • Language
    • Theory
    • Databases
    • Use
    • Proofs
    • Based

Connections between topic areas Semantic bridges

For Metamath, one of the stronger structural bridges in this analysis connects Metamath with Metamath databases. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Metamath — Metamath databases · splits 30 ⟂ 16
Metamath — Overview · splits 36 ⟂ 10
Metamath — Metamath language · splits 38 ⟂ 8
Metamath — Other works connected to Metamath · splits 41 ⟂ 5
Metamath — Metamath proof checker · splits 42 ⟂ 4

Map overview Semantic statistics

Metamath

Nodes46
Edges45
Triples69
Avg. degree1.96
Density0.043478
Components1

Source & methodology

TTTA analyzes the structure around Metamath to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Works & Standards, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Metamath · EN edition · Analysis: TopicsToTalkAbout

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