Source-linked AI summary
The zbMATH Open Knowledge Graph: Tracing Centuries of Mathematical Research
Yuni Susanti, Moritz Schubotz
TL;DR
Mathematical knowledge spanning centuries remains difficult to analyze computationally because existing platforms emphasize keywords, bibliographic metadata, and citations. The paper constructs the zbMATH Open KG by integrating expert-curated semantic content into a FAIR-aligned RDF graph, then demonstrates query-driven historically grounded scholarly exploration. The use cases show that it can surface patterns and candidate relationships that may be difficult to uncover in conventional citation networks.
Problem
The semantic structure and historical development of mathematical knowledge remain difficult to analyze computationally despite millions of digitized publications and existing keyword- and citation-based platforms.
Method
The paper constructs a FAIR-aligned RDF knowledge graph combining over 250 years of mathematical scholarship with expert-curated reviews, identities, keywords, classifications, software references, and Semantic Web vocabularies.
Results
The knowledge graph contains 34 million entities and 168 million RDF triples, and query-driven use cases demonstrate historically grounded scholarly exploration beyond conventional citation networks.
Takeaways & Limitations
The zbMATH Open KG provides an open semantic infrastructure for studying mathematical knowledge development and tracing intellectual relationships across centuries.
Takeaways & Limitations
The graph does not currently provide sufficient software-specific metadata to analyze trends in mathematical research infrastructure without external software knowledge graphs.
Abstract
from arXiv · showhide
We present the zbMATH Open Knowledge Graph, a large-scale RDF knowledge graph (KG) covering more than 250 years of mathematical scholarship. Unlike existing scholarly knowledge graphs that primarily capture bibliographic metadata and citation structures, the zbMATH Open KG integrates expert-curated semantic content, including reviews, keywords, subject classifications, software references, and disambiguated authorship. This combination of domain-specific representation of mathematical knowledge and extensive temporal coverage supports analyses that require fine-grained exploration of mathematical concepts, research fields, and scholarly relationships over time. The resulting graph comprises 34 million entities and 168 million RDF triples represented using established Semantic Web vocabularies, supporting interoperability and FAIR data principles. We further demonstrate its capabilities through query-driven historically grounded scholarly exploration use cases, illustrating how the knowledge graph can surface relationships and patterns that may be difficult to identify from bibliographic and citation information alone. The zbMATH Open KG provides an open semantic infrastructure for studying the development of mathematical knowledge and tracing scholarly connections across centuries of scholarship.
1 Introduction
The paper introduces zbMATH Open KG, a historically comprehensive RDF graph that combines centuries of mathematical scholarship with expert-curated semantic content. It follows FAIR and Semantic Web principles and supports validation and historically grounded scholarly exploration.
- Resource: 250 years of mathematical scholarship are represented in a large-scale RDF knowledge graph built from more than four million publications.The resource is constructed from the zbMATH Open platform and draws on over 150 years of curated scholarship.
- Semantic content: Expert-curated content includes reviews, disambiguated scholar identities, controlled keywords, MSC codes, and software references.These additions extend representation beyond bibliographic metadata and citation networks.
- Interoperability: 34 million entities and 168 million RDF triples are represented using established Semantic Web vocabularies and FAIR-aligned design.The graph uses established vocabularies and ontologies to support interoperability, while metadata is described with OWL, VoID, DCAT, and PROV-O.
- Access and reuse: Public RDF dumps, a triple-store deployment, a SPARQL endpoint, URI resolution, and construction source code support access and reuse.The source code is released for reproducibility, customization, and future extensions; the dump is updated approximately twice per year subject to upstream data availability.
- Evaluation and use: Validation covers serialization validity, structural consistency, and competency-question coverage, followed by query-driven historically grounded scholarly exploration use cases.The use cases demonstrate practical utility for exploring scholarly knowledge beyond conventional bibliographic and citation-based analysis.
2 Related Work
Existing scholarly knowledge graphs provide broad metadata and citation coverage, while mathematical knowledge initiatives address concepts, formalization, or domain-specific semantics in different ways. zbMATH Open KG complements these resources with an RDF-native representation of mathematically curated scholarly knowledge aligned with Semantic Web standards and FAIR principles.
- Broad scholarly graphs: Large scholarly graph initiatives primarily provide broad bibliographic metadata and citation networks across disciplines.Examples include MAG, MAKG, OpenAlex, and SemOpenAlex.
- Gap: Existing projects have limited representation and coverage of mathematical publication and knowledge.This limitation motivates domain-specific efforts focused on mathematical concepts, formal statements, and machine-readable knowledge.
- Positioning: zbMATH Open KG complements these efforts through RDF-native modeling of mathematically curated scholarly knowledge using established vocabularies and ontologies.Its explicit modeling of expert-curated semantic content supports fine-grained analysis of mathematical concepts, fields, and intellectual relationships.
3 The zbMATH Open Knowledge Graph
The zbMATH Open KG is constructed through a staged, standards-oriented process and models mathematical scholarship with explicit semantic structure. Its scale, historical coverage, curated entities, and validation results support broad scholarly retrieval while exposing specific coverage limitations.
- Construction Process: The construction process follows requirements specification, API-based acquisition, conceptualization, vocabulary integration, RDF implementation, and evaluation with planned versioned maintenance.Competency questions were checked by human experts, and the pipeline supports regeneration from updated zbMATH Open snapshots.
- Ontology and Schema Design: Established Semantic Web vocabularies model publications, citations, and concept organization, while zbMATH-specific classes and identifiers represent mathematical resources.The schema uses schema.org for scholarly entities, cito for citation relations, and SKOS for concept organization.
- Ontology and Schema Design: MSC codes and expert-curated controlled keywords are modeled with SKOS, preserving persistent identifiers and the hierarchical structure of mathematical subject classification.The hierarchy uses skos:broader and skos:narrower to retain the long-established organization of mathematics.
- Key Statistics: 34.5 million entities and nearly 170 million relationships across 39 predicate types make the graph a large, sparse, and well-linked mathematical resource.The graph density is 1.45 × 10^-7, and each entity connects to nearly ten others on average.
- Key Statistics: The graph centers on over four million articles, 1.1 million disambiguated persons, 3.10 million reviews, 3.01 million controlled keywords, and 6,734 MSC entities.These curated entities represent contributors, contextual publication assessments, and domain-specific semantic annotations.
- Evaluation and Validation: Structural validation found 61,380 missing-property violations caused by incomplete source records, while all other structural consistency checks reported zero violations.The violations comprised three missing titles and 61,377 missing authors, with correction expected through a future API update.
- Evaluation and Validation: CQ evaluation achieved 95.6% partial-or-better support and 86.7% full support, while unsupported cases included software programming-language information unavailable from the source.Some partially supported cases also depended on external links not exposed through the API.
4 Applications and Use Cases
The zbMATH Open KG supports historically grounded exploration beyond citation links by connecting mathematical publications through shared concepts, classifications, temporal patterns, and reviewer–author relationships. These queries surface candidate precursor connections, cross-field conceptual continuity, changing research activity, and potential intellectual continuities for further investigation.
- Scope of the use cases: The use cases are exploratory and are not intended to establish historical influence.They demonstrate how the KG surfaces candidate relationships and patterns for further scholarly and historical investigation.
- Precursor Discovery: Shared subject classifications and keywords can identify potential precursor connections between publications lacking explicit citation links.The 2020 paper “Modular d0-algebras” and a 1987 paper on BCK-semilattices share MSC codes and the keyword BCK-algebra despite being separated by 33 years.
- Cross-Field Conceptual Continuity: 463 early–later publication pairs linked the keyword spectral sequences across Algebraic Topology and Homological Algebra.The pairs combine the keyword with temporal information and MSC classifications to provide candidates for investigating cross-field conceptual development.
- Conceptual Resurgence: Temporal queries combining subject classifications and keywords can examine emergence, decline, and resurgence across mathematical fields.The illustrated comparison tracks publication activity in Probability and Logic by decade.
- Reviewer–Author Continuity: Reviewer–author relationships provide a way to explore potential intellectual continuity between scholars’ earlier reviewing activity and later research.For Hans L. Bodlaender, recurring topics such as treewidth, dynamic programming, and graph algorithms overlap between reviewed and authored publications.
- Further Applications: The KG provides a basis for historically aware retrieval, knowledge-development analytics, and semantic context for AI-assisted scholarly systems.Its controlled keywords, MSC codes, reviews, disambiguated scholars, relationships, and temporal coverage support analyses beyond bibliographic search and citation networks.
5 FAIR Compliance and Sustainability
The knowledge graph is distributed and maintained as a FAIR-oriented Semantic Web resource, with persistent identifiers, versioned releases, machine-readable descriptions, downloadable RDF, and public querying. Its reproducible pipeline and maintained ontology support continued evolution while preserving independently reproducible snapshots.
- Findable: Persistent URIs, versioned RDF dumps, and machine-readable VoID, DCAT, and PROV-O descriptions support findability and release-level metadata discovery.Core entities have URI resolution, and each release documents its scope, schema, and statistics.
- Accessible: Downloadable Zenodo RDF dumps, standard triple-store compatibility, and a public SPARQL endpoint support accessible use.The pipeline has been tested with Virtuoso and Apache Jena.
- Interoperable: W3C Semantic Web standards and reused vocabularies, together with retained external identifiers, support interoperability with external scholarly resources.The KG uses established vocabularies and preserves identifiers such as DOIs where available.
- Reusable: An OWL ontology, data descriptions, RDF dumps, documentation, source code, stable identifiers, and versioned snapshots support reuse and reproducibility.Licensing and attribution information accompany each distribution.
- Sustainability and Maintenance: A reproducible regeneration pipeline, periodic updates, persistent identifiers, and public repository hosting support sustainability while preserving reproducible releases.The ontology is maintained separately from individual data snapshots.
6 Conclusion
The paper presents an openly available, FAIR-aligned RDF knowledge graph integrating more than 250 years of expert-curated mathematical scholarship. Historically grounded use cases show that it can surface patterns and candidate relationships beyond conventional citation analysis, while future work includes external links and AI-assisted exploration.
- Conclusion: The zbMATH Open KG integrates more than 250 years of mathematical scholarship in an RDF graph grounded in expert-curated semantic information.It is openly available and designed to align with FAIR principles and Semantic Web standards.
- Conclusion: Historically grounded scholarly exploration can identify patterns and candidate relationships that may be difficult to uncover in conventional citation networks.These outputs provide starting points for further scholarly and historical investigation.
- Future Directions: Future work includes linking the KG to external knowledge graphs such as SemRepo to study mathematical software and infrastructure over time.Such linkage could enrich the current mathematical software references.
- Future Directions: Another future direction is investigating how KG-based context complements textual and embedding-based methods in AI-assisted retrieval and exploration.