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The zbMATH Open Knowledge Graph: Tracing Centuries of Mathematical Research
Yuni Susanti, Moritz Schubotz
Intelligence
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Summary
The paper introduces the zbMATH Open Knowledge Graph, a large-scale RDF knowledge graph covering over 250 years of mathematical scholarship. It integrates expert-curated semantic content, including reviews, keywords, subject classifications, software references, and disambiguated authorship, into a graph comprising 34 million entities and 168 million triples. The resource is designed for interoperability using Semantic Web vocabularies and supports fine-grained exploration of mathematical concepts and scholarly relationships over time.
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zbMATH Open Knowledge Graph → createdby → Yuni Susanti
confidence 95% · Yuni Susantiand Moritz Schubotz... We present zbMATH Open Knowledge Graph
zbMATH Open Knowledge Graph → createdby → Moritz Schubotz
confidence 95% · Yuni Susantiand Moritz Schubotz... We present zbMATH Open Knowledge Graph
zbMATH Open Knowledge Graph → derivedfrom → zbMATH Open
confidence 95% · Constructed from the zbMATH Open platform [34]
zbMATH Open Knowledge Graph → hasentitycount → 34 million
confidence 95% · The resulting graph comprises 34 million entities
zbMATH Open Knowledge Graph → hastriplecount → 168 million
confidence 95% · and 168 million RDF triples
zbMATH Open Knowledge Graph → affiliatedwith → FIZ Karlsruhe
confidence 90% · Yuni Susantiand Moritz Schubotz FIZ Karlsruhe... We present zbMATH Open Knowledge Graph
zbMATH Open Knowledge Graph → coverstemporalrange → 1763-2026
confidence 90% · covering more than 250 years... publications dating back to 1763... 1763–2026
zbMATH Open Knowledge Graph → hostedon → Zenodo
confidence 90% · We provide the full RDF data dumps via Zenodo
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Abstract
Abstract: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.
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- Source: https://arxiv.org/abs/2609.00969v1
- Canonical: https://arxiv.org/abs/2609.00969v1
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The zbMATH Open Knowledge Graph: Tracing Centuries of Mathematical Research Yuni Susantiand Moritz Schubotz FIZ Karlsruhe, Berlin, Germany yuni.susanti, moritz.schubotz@fiz-karlsruhe.de Abstract. We present zbMATH Open Knowledge Graph, a large-scale RDF knowledge graph (KG) covering more than 250 years of mathemat- ical scholarship. Unlike existing scholarly knowledge graphs that primar- ily 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 math- ematical 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 com- prises 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, illus- trating how the knowledge graph can surface relationships and patterns that may be difficult to identify from bibliographic and citation infor- mation alone. The zbMATH Open KG provides an open semantic infras- tructure for studying the development of mathematical knowledge and tracing scholarly connections across centuries of scholarship. Resource type: Dataset/Knowledge Graph License:C-BY-SA 4.0 DOI:https://doi.org/10.5281/zenodo.21497975 URL:https://github.com/zbMATHOpen/zbmath-open-kg Keywords: knowledge graphs· scholarly data· mathematics 1 Introduction Mathematics is one of the oldest continuously evolving scientific disciplines, with a documented scholarly record spanning over many centuries. Beyond formal results, its literature captures the long-term conceptual, methodological, and in- tellectual development of mathematical knowledge. Despite the availability of millions of digitized publications, the semantic structure and historical devel- opment of mathematical knowledge remain difficult to analyze computationally. Existing platforms primarily support keyword-based search and citation-based discovery, offering limited support for investigating how mathematical concepts arXiv:2609.00969v1 [cs.DL] 1 Sep 2026 2Y. Susanti et al. emerge, how ideas migrate across subfields, and how intellectual lineages are formed across generations. [9,10,13]. In this work, we present zbMATH Open Knowledge Graph (zbMATH Open KG), a large-scale and historically comprehensive RDF-based knowledge graph of mathematical publications and scholarly knowledge. Constructed from the zb- MATH Open platform [34], the longest-running abstracting and reviewing ser- vice in mathematics, the resource builds upon more than 150 years of curated mathematical scholarship, covering over four million publications spanning 250 years [34]. Unlike existing scholarly knowledge graphs that primarily represent bibliographic metadata and citation networks [28,17,1,2,4], zbMATH Open KG integrates expert-curated semantic knowledge, including: – expert-written reviews providing contextual interpretations of publications, – disambiguated identities of scholars, including authors and reviewers, – expert-curated controlled mathematical keywords, – expert-assigned Mathematics Subject Classification (MSC) [3] codes, a domain- specific taxonomy that has provided a stable conceptual organization of mathematics across decades, – software references associated with mathematical publications. To support interoperability within Semantic Web ecosystem, we construct the knowledge graph using established vocabularies and ontologies. The result- ing graph comprises more than 34 million entities and 168 million RDF triples and is designed to align with FAIR [33] principles. Beyond data publication, the zbMATH Open KG supports distinct use cases of scholarly knowledge discovery we collectively term historically grounded scholarly exploration: the analysis of long-term intellectual relationships and scholarly development beyond citation networks and bibliographic metadata. By combining expert-curated semantics with centuries of scholarly records, the zbMATH Open KG establishes a foun- dation for studying the development of mathematical knowledge and tracing intellectual relationships across centuries of scholarly development. Contribution. Our main contributions can be summarized as follows: 1. We construct zbMATH Open KG, a large-scale RDF knowledge graph span- ning over 250 years of mathematical scholarship grounded in expert-curated semantic contents. The resource is publicly released and made accessible 1 through the following: (a) We provide the full RDF data dumps via Zenodo for long-term accessibil- ity and preservation. The dump is updated periodically, approximately twice per year, subject to the availability of upstream data sources. (b) We deploy the knowledge graph in a triple store and provide a public SPARQL endpoint for direct querying. (c) We enable URI resolution for the core entities (e.g., publications, schol- ars, software references), supporting linked data access. 1 See Page 1 for the DOI and URL; SPARQL endpoint is available on GitHub. The zbMATH Open Knowledge Graph3 (d) We release the full source code for the knowledge graph construction to support reproducibility, customization and future extensions. 2. We design the resource according to FAIR principles and Semantic Web standards. The OWL ontology is published with VoID, DCAT and PROV-O metadata description to support machine-readable discovery and reuse. 3. We evaluate the resource at three complementary levels: serialization valid- ity, structural consistency, and competency-question coverage. Beyond these validations, we demonstrate the practical utility of the resource through query-driven historically grounded scholarly exploration use cases. 2 Related Work Knowledge graphs have become an important paradigm for representing and interlinking scholarly information. Large-scale initiatives such as the Microsoft Academic Graph (MAG) [31], its Linked Data transformation Microsoft Aca- demic Knowledge Graph (MAKG) [16], and its successor OpenAlex [28] provide extensive coverage of scholarly metadata and citation networks. Semantic rep- resentations such as SemOpenAlex [17] further improve interoperability with Semantic Web technologies, while domain-specific resources such as LPWC [19] focuses on machine learning publications, and SemRepo [29] extend the LPWC scholarly knowledge graphs by linking publications with software and research ar- tifacts. Similarly, established scholarly databases including arXiv [1], DBLP [2], and Semantic Scholar [4] provide broad bibliographic coverage. However, these resources primarily represent publication-level metadata and citation relation- ships, with limited expert-curated, high-quality semantic knowledge and long- term conceptual development within a scientific domain. These projects cover a wide spectrum of scholarly disciplines; however their representation and coverage of mathematical publication and knowledge remains limited. Several initiatives have been undertaken to capture the structure and semantics of mathematical knowledge. For instance, the OntoMath ontology [14] models mathematical concepts and relations for semantic search, while projects such as Formal Abstracts [8], Lean [5], and Coq [20] focus on formalizing mathe- matical statements and machine-verifiable knowledge. MMLKG provides a the- saurus for describing mathematical definitions, statements, and proofs based on the Mizar Mathematical Library [32]. These efforts provide deep representations of mathematical content but primarily target formal reasoning. More recently, AutoMathKG [6] integrates paper with theorems and proofs; however, its con- struction relies heavily on semi-automatic extraction and LLM-assisted process- ing and focused to enhance LLM mathematical reasoning. MaRDI knowledge graph [30], based on Wikidata data modeling, integrates mathematical research data from multiple sources, offering broad coverage of mathematical research ar- tifacts. However, their structure is tightly coupled to Wikidata’s internal model, relying on Wikibase identifiers and property models rather than standard Se- mantic Web vocabularies [30]. 4Y. Susanti et al. The zbMATH Open KG complements these efforts by providing an RDF-native representation of mathematically curated scholarly knowledge. Unlike Wikidata- based approaches such as MaRDI, the zbMATH Open KG is built on established Semantic Web vocabularies and ontologies and designed to align to its stan- dards and FAIR principles. Additionally, the explicit modeling of expert-curated semantic contents enables analyses requiring fine-grained understanding of math- ematical concepts, fields, and intellectual relationships. 3 The zbMATH Open Knowledge Graph In this section, we describe the construction process of the zbMATH Open KG (§3.1), followed by ontology and schema design (§3.2) and key statistics (§3.3). Finally, we evaluate the graph to assess its validity and coverage (§3.4). 3.1 Knowledge Graph Construction The development of the zbMATH Open KG follows a knowledge engineering methodology largely guided by METHONTOLOGY [23], complemented by on- tology engineering practices from SAMOD [25] and LOT [27]. The construction process consists of the following stages: 1. Requirements Specification. We first defined the scope of the knowledge graph by identifying the core entities, relationships, and intended usage sce- narios. Competency Questions (CQs) were formulated and checked by hu- man experts to capture representative scholarly information needs, including historical semantic exploration. We share the full CQs in our repository. 2. Knowledge Acquisition. The raw dataset was acquired from the zbMATH Open platform via its official API 2 . The acquired metadata served as the primary source for ontology development and instance generation. 3. Conceptualization. Based on the acquired data, we iteratively developed the conceptual model and structural requirement of the knowledge graph. Core classes such as publications, authors, and reviews were identified to- gether with their semantic relationships, including the required properties and datatypes. The conceptual model was repeatedly refined as additional metadata characteristics and competency questions were analyzed. 4. Vocabulary Integration. We maximized interoperability through the reuse of established Semantic Web vocabularies. For instance, scholarly entities are primarily modeled using schema.org [21], citation relations using cito [26], and concept organization using skos [24]. Domain-specific concepts (e.g., mathematical subject classification and keywords) are introduced within the zbMATH namespace. See the detail of ontology and schema design in 3.2. 5. Implementation. The pipeline automatically converts the raw data into RDF triples. To facilitate customization (e.g., custom KG subsets genera- tion), we share the full source code in our repository. 2 https://oai.zbmath.org/ December 2025 snapshot (Accessed: 15/12/2025) The zbMATH Open Knowledge Graph5 6. Evaluation and Maintenance. The generated RDF knowledge graph is evaluated at three levels to assess its validity and coverage: serialization validity, structural consistency, and competency-question coverage. See the detailed evaluation in 3.4. Maintenance is planned through periodic updates with versioned release, supported by the pipeline that enables regeneration from the zbMATH Open snapshots as new releases become available. 3.2 Ontology and Schema Design Figure 1 illustrates the schema design of the zbMATH Open KG, including an overview of the entity types, the object properties, and the data type properties. To support interoperability with the Linked Data ecosystem, the model follows the best practice of semantic reuse strategy by adopting established Semantic Web vocabularies wherever possible and extending them with zbMATH Open - specific classes and persistent identifiers for mathematical resources. dcterms:title rdfs:label :url :identifier :sameAs :propertyID :isPartOf :reviewer :item Reviewed :Scholarly Article zb:keyword- concept :keywords :cito:cites skos:broader skos:narrower xsd:gYear dcterms:issued skos:Concept Scheme xsd:string xsd:string :Periodical :isPartOf xsd:string rdfs:label xsd:string :name rdfs:subClassOf zb:msc- concept xsd:string rdfs:label skos:prefLabel skos:notation rdfs:seeAlso skos:notation skos:prefLabel rdfs:label :Person skos:inScheme :authorOf :author dcterms:creator dcterms:creator :Review :review xsd:date xsd:string dcterms:created :inLanguage xsd:string xsd:string :name xsd:string :reviewAspect xsd:string :reviewBody xsd:string xsd:string :name :Software Application :software xsd:string xsd:string xsd:string xsd:string :pagination xsd:string dcterms:language xsd:gYear :datePublished xsd:string :name :title :Property Value :identifier xsd:string :value xsd:string Prefixes : zb: skos: dcterms: cito: xsd: rdfs: https://schema.org/ https://zbmath.org/ http://w.w3.org/2004/02/skos/core# http://purl.org/dc/terms/ http://purl.org/spar/cito/ http://w.w3.org/2001/XMLSchema# http://w.w3.org/2000/01/rdf-schema# dcterms:identifier rdfs:label dcterms:subject rdfs:label skos:inScheme rdfs:label xsd:stringxsd:string :Organisation dcterms:publisher xsd:string rdfs:label xsd:string :name zb:journal- article zb:book-series zb:collection- article zb:preprints dcterms:type xsd:string rdfs:label :identifier xsd:string xsd:string :name DOI External URI xsd:string xsd:string xsd:string rdfs:label xsd:string xsd:string Fig. 1: Schema overview of the zbMATH Open Knowledge Graph. 3 Scholarly Entity Representation. The core of the model represents mathematical scholarly publications and their contextual relationships. Publication entities are 3 For readability, only the core classes and relationships are shown; the figure is not intended as an exhaustive representation of all object and properties. 6Y. Susanti et al. modeled using schema.org terms (schema:) [21]. This representation captures not only the main bibliographic records (schema:ScholarlyArticle, schema:Person for representing scholars i.e., authors and reviewers) but also the broader scholarly ecosystem surrounding a scholarly article, including reviews, periodicals, pub- lishers, and associated mathematical software. Bibliographic and Citation Modeling. Bibliographic metadata including article ti- tles, publication dates, languages, identifiers (e.g., DOI), url, publishers, and doc- ument types are additionally represented using Dublin Core Terms (dcterms:) [11], following established practices in digital library data modeling. Citation relation- ships are represented using the Citation Typing Ontology (cito:) [26] for explicit modeling of publication-level citation networks. Mathematical Semantic Representation. One of the key features of the zbMATH Open KG is the explicit representation of mathematical semantics. The organi- zation of the Mathematics Subject Classification (MSC) codes [3] and expert- curated controlled keywords are modelled using SKOS (skos:) [24], while re- taining persistent zbMATH Open -specific identifiers. The hierarchical structure of the MSC taxonomy is modeled using skos:broader and skos:narrower, pre- serving the long-established disciplinary organization of mathematics. Interoperability and Extensibility. Additionally, RDF Schema (rdfs:) is used to define classes, hierarchies, and labels; XML Schema datatypes (xsd:) provide standardized datatypes for literal values. The ontology defines zbMATH Open- specific classes and persistent IRIs for mathematical resources while maintain- ing interoperability with the Linked Data ecosystem via established Semantic Web vocabularies. The model is intentionally lightweight and extensible, allow- ing future integration of additional mathematical resources, such as datasets, formalized results, or mathematical objects (e.g., formulae). The complete on- tology specification is publicly available alongside the released data and machine- readable metadata descriptions. 3.3 Key Statistics Table 1 illustrates the scale, coverage, and structural properties of the con- structed zbMATH Open KG. With over 34.5 million entities and nearly 170 million relationships spanning 39 distinct predicate types, it represents one of the most comprehensive structured resources in mathematics. On average, each entity is connected to nearly ten others, reflecting a well-linked but non-redundant struc- ture. The graph density of 1.45× 10 −7 reflects the expected sparsity typical of heterogeneous scholarly RDF graphs, where the number of observed relationships remains small compared to all possible pairwise connections. Importantly, 15.4 million RDF entity resources (over 80%) are explicitly typed, providing semantic annotations that improve interpretability and sup- port more precise queries over bibliographic records. Although zbMATH, the original platform, was established in 1931 [34], the knowledge graph captures a The zbMATH Open Knowledge Graph7 Table 1: Quantitative metrics of the zbMATH Open Knowledge Graph MetricDescriptionValue Number of EntitiesAll distinct nodes (subjects/objects in triples) 34,099,406 Number of RDF Resources All distinct nodes (subjects/objects in triples) 18,995,799 Number of Typed Resources Resources with :type declaration15,392,393 Type Coverage (%)% of resources with a defined type81.03% Number of EdgesTotal number of triples168,670,821 Number of Relation Types Unique predicate types used in edges39 Average DegreeMean number of edges per entity9.89 Graph DensityRatio of actual to possible edges 1.45× 10 −7 Temporal CoverageTime span covered by temporal data1763–2026 temporal span of more than 250 years through the inclusion of publications dat- ing back to 1763. This extensive temporal coverage supports analyses of scholarly production and the development of entities and relationships over time. Table 2 summarizes the distribution of core entities within zbMATH Open KG. The entity distribution reflects the scholarly focus and expert-curated nature of the KG. At its center are more than 4 million articles, which form the backbone of the graph. These publications are connected to a curated network of over 1.1 mil- lion disambiguated person entities [12], including more than 1.12 million authors and nearly 14 thousand reviewers, providing a curated representation of schol- arly contributors and supporting reliable attribution of research contributions. Table 2: Core entities in zbMATH Open Knowledge Graph Entity# Instances Scholarly articles4,070,393 Person1,125,474 —Authors1,125,238 —Reviewers13,942 Subjects (MSC)6,734 Keywords3,008,881 Organization3,524 Periodical7,350 Reviews3,098,767 Software30,857 Identifiers10,522,258 —DOI2,446,976 The scholarly articles are complemented by 3.10 million expert-written reviews, which provide contextual interpretations and as- sessments of mathematical publications be- yond bibliographic metadata. Furthermore, the presence of 3.01 million controlled key- words and 6,734 mathematics subject clas- sification entities demonstrates the integra- tion of domain-specific semantic annota- tions that support fine-grained organiza- tion and retrieval of mathematical knowl- edge. The ecosystem is further represented through thousands of organizations i.e., pub- lishers (3,524) and periodicals (e.g., journals) (7,350), as well as over 30,000 references to mathematical software linked to publication, capturing important contextual elements of mathematical research. The resource contains more than 10.5 million identifiers, including nearly 2.5 million DOI references, which facilitate interoperability with external scholarly resources and persistent identification of research outputs. 8Y. Susanti et al. Table 3: Summary of the structural consistency check results. CheckValidation criterionViolations Required properties Scholarly articles contain required properties:61,380 Title (dcterms:title)3 Author (dcterms:creator, schema:author)61,377 Publication date (schema:datePublished )0 Document type (dcterms:type)0 Datatype consistency Date values use the expected RDF datatypes0 Author references Article authors are represented as schema:Person0 Document typeArticle types belong to the defined document-type vocabulary 0 MSC referencesArticle subjects resolve to defined MSC concepts0 Keyword references Article keywords resolve to defined keyword con- cepts 0 Review references Reviewed articles and reviewers resolve to resources of the expected classes 0 SKOS hierarchy skos:broader and skos:narrower relations are mutually consistent 0 3.4 Evaluation and Validation The generated knowledge graph was validated at three complementary levels 4 : (i) syntactic validity of the RDF serialization, (i) structural consistency, and (i) CQ-based evaluation, described in detail in the following. First, the syntactic validity of the generated RDF serialization was verified using both Apache Jena and RDFLib Pyton library [7], and was subsequently loaded into the OpenLink Virtuoso and Apache Jena Fuseki triple stores [15] to verify successful ingestion and to support the SPARQL-based validation. All RDF files were successfully parsed and loaded without syntax or ingestion errors, confirming that the generated resource was syntactically valid. Second, the consistency check was performed to assess compliance with the structural requirements defined during the knowledge graph construction. These checks targeted various aspects of structural consistency, such as missing required properties, invalid or unexpected datatypes, and inconsistent class assignments, among others. For each requirement, a SPARQL query was executed over the complete graph to retrieve resources violating the corresponding constraint; the number of returned resources was used as the violation count. Representative results from the checks performed are summarized in Table 3. The structural check identified 61,380 missing-property violations (3 missing titles, 61,377 missing authors). Manual inspection confirmed that these violations originate from the incomplete records in the source API, where the title or author information is not provided (“None”). The issue is reported to zbMATH platform and is expected to be addressed through a future correction of the API. All other structural consistency checks resulted in zero violations. 4 All CQs, SPARQL queries, and codes for evaluation are available in GitHub (Page 1). The zbMATH Open Knowledge Graph9 Table 4: Summary of the CQ-based evaluation results. CQ category#CQsFullPartialNot Coverage Core Bibliographic and Retrieval24 23 (95.8%) 0 (0%) 1 (4.2%) 95.8% Scholarly History and Relationships 21 16 (76.2%) 4 (19.0%) 1 (4.8%) 95.2% Third, the validity and coverage of the knowledge graph were assessed using CQs, which were defined during development to formalize the information re- quirements the resource is intended to support. A total of 45 CQs were specified, covering the principal retrieval and relational capabilities of the KG, including bibliographic retrieval, scholarly relationships, and temporal and historical in- formation. We organized the CQs into (i) Core Bibliographic and Retrieval and (i) Mathematical Scholarly History and Relationships. For each CQ, a SPARQL query was executed against the graph, and the result was manually compared with the expected answer. Table 4 summarizes the evaluation results. The CQ-based evaluation demonstrates broad competency coverage, with 95.6% of evaluated cases being at least partially-supported and 86.7% fully- supported. The partially-supported CQs primarily concern information available through external resources, e.g., Wikidata links that can potentially be used to obtain institutional or country information of the scholar identities. Although such links are available on the platform, they are not currently exposed via the API and thus cannot be incorporated into zbMATH Open KG. This limitation can be addressed by exposing these links, which would enable analyses of scholarly relationships across institutions and other biographical information. The not-supported CQs concern information not available in the source, e.g., programming language of mathematical software. While zbMATH Open KG links software to publications, it does not currently provide sufficient software-specific metadata to analyze trends in mathematical research infrastructure. Such in- formation would require explicit linkage to external software knowledge graphs (e.g., SemRepo [29]). Overall, the evaluation provides an assessment of the cur- rent coverage of the resource and to identify areas for future extension. 4 Applications and Use Cases To demonstrate the utility of the knowledge graph, we present several use case examples we collectively term historically grounded scholarly exploration. These use cases illustrate how the distinctive content of the knowledge graph, particu- larly its extensive temporal coverage, subject classifications based on the MSC taxonomy, expert-curated keywords, and reviewer-author relationships, supports the exploration of mathematical knowledge across generations of scholarship. Importantly, these use cases are not intended to establish historical influence; rather, they demonstrate how the KG can surface relationships and patterns for further scholarly and historical investigation. Each use case is operationalized through SPARQL queries, available in our repository. 10Y. Susanti et al. 4.1 Precursor Discovery: Potential Connections Beyond Citation One potential capability of the zbMATH Open KG is to surface historically ear- lier contributions that may be foundational and semantically relevant to later developments but are not connected through explicit citation. Identifying such potential “precursor” connections can help reconstruct a more faithful scholarly lineage and provide a richer view of mathematical knowledge development. Corrections to some results for BCK logics and algebras (1988) MSC:03G25 Algebraic Logic MSC:06F35 Ordered Structures BCK-algebra On ideal and congruence lattices of BCK-semilattices (1987) MSC:06A12 Lattices and Orders Blocks and compatibility in d0-algebras (2017) Modular d0-algebras (2020) 1987 1988 2017 2020 Fig. 2: Potential connections identified through shared concepts and subject clas- sifications. As an illustrative example of this use case, we queried zbMATH Open KG for the 2020 paper “Modular d 0 -algebras” and identified the 1987 paper “On ideal and congruence lattices of BCK-semilattices” as potential precursor connection. Although separated by 33 years, both works share subject classification codes (MSC:03G25, MSC:06A12) and the keyword BCK-algebra. The earlier work investi- gates structural properties of BCK-semilattices, while the later work investigates d 0 -algebras in a related mathematical setting. Although the two publications are not explicitly connected by citation, their shared subject classifications and keywords, which were expert-curated, reveal a conceptual connection that may otherwise be difficult to identify through citation-based analysis. The knowledge graph surfaces the 1987 publication as a candidate for further scholarly and historical investigation. Other examples of such cases are illustrated in Figure 2. 4.2 Cross-Field Conceptual Continuity via MSC-Prefixes Bridging The zbMATH Open KG enables exploration of how mathematical concepts recur across research fields through the hierarchical structure of the subject classifi- cation i.e., the MSC code. MSC codes provide a relatively stable taxonomy of mathematical subjects [3] and, in the zbMATH Open KG, are assigned to the publication by mathematical experts. Such cross-field conceptual continuity can be difficult to identify from citation networks, as emerging fields may reinter- pret established concepts within new frameworks without directly citing relevant earlier work. The zbMATH Open KG supports the systematic identification of re- The zbMATH Open Knowledge Graph11 curring concepts across different mathematical fields and periods by leveraging MSC code hierarchies with controlled keywords and temporal information. Algebraic Topology 55-x < 1990 > 2020 55Nxx Homology /Cohomology 18Gxx Homological Algebra cohomology 55Rxx Fiber Spaces spectral_sequences Homology and cohomology theories of general spaces (1989) On incidence algebras and their representations (2022) cohomology Topology (1986) Homology theories for complexes based on flats (2021) cohomology Rational homotopy theory and differential forms (1981) Gabriel-Zisman cohomology and spectral sequences (2021) spectral_sequences Fig. 3: Conceptual Continuity: Algebraic Topology → Homological Algebra. An illustrative example derived from zbMATH Open KG examines the distribu- tion of the concept spectral sequences across two MSC areas: Algebraic Topology (MSC:55) and Homological Algebra (MSC:18), as illustrated in Figure 3. Within Algebraic Topology, publications associated with the keyword occur in subfields such as homology and cohomology theories (55Nxx) and fiber spaces (55Rxx), where spectral sequences constitute an important methodological theme. The same keyword also occurs in later publications classified under Homological Al- gebra (18Gxx), illustrating its recurrence in a different disciplinary context. For example, the 2021 work “Gabriel-Zisman cohomology and spectral sequences” is associated with the keyword and classified within Homological Algebra. Using the keyword spectral sequences together with temporal information and MSC classification codes, we identified a total of 463 early–later publication pairs spanning these two MSC areas. These pairs reveal recurring semantic as- sociations across mathematical fields and time periods and provide candidates for further scholarly investigation of cross-field conceptual development. 4.3 Conceptual Resurgence: Tracking the Re-emergence of Ideas Scientific concepts and ideas do not always develop along continuous trajectories. Some may receive sustained attention, decline in prominence, and later reappear in new theoretical or applied contexts. Identifying such patterns can provide his- torians with candidates for investigating intellectual cycles and help scientists discover areas experiencing renewed activity. The extensive temporal coverage of the zbMATH Open KG supports this exploration by combining temporal infor- mation with curated subject classifications and keywords, allowing patterns of emergence, decline, and resurgence to be examined systematically. 12Y. Susanti et al. Fig. 4: Temporal dynamics of mathematical subject areas: publication activity in Probability (MSC 60*) and Logic (MSC 03*) by decade. We queried zbMATH Open KG to illustrate this use case by examining publi- cation activity in Probability (MSC:60) and Logic (MSC:03). Figure 4 presents the results aggregated by decade. Probability shows a sustained increase in publica- tion activity throughout the twentieth century, with more pronounced growth after the 1950s. Representative works associated with this area include Kol- mogorov’s 1933 Grundbegriffe der Wahrscheinlichkeitsrechnung”. Logic exhibits a marked increase during the 1930s (representative publication: Gödel’s incom- pleteness theorems), followed by a period of comparatively lower activity and renewed growth from the 1970s onward. Publications in this later period include works associated with fuzzy logic, such as Zadeh’s 1965 Fuzzy Sets”, as well as developments connecting logic with computer science and formal methods. These patterns illustrate how the knowledge graph can make non-linear research dynamics visible at the subject-field level, identifying periods of changing re- search activity that can serve as starting points for further investigation of the concepts, methods, and publications associated with these transitions. 4.4 Potential Intellectual Connections via Scholarly Engagement The zbMATH Open KG incorporates mathematicians-curated reviews of publica- tions, linking such reviewers to the publications they assessed and their authors through reviewer–author relationships. These connections provide an additional perspective for exploring potential intellectual continuities between a scholar’s earlier scholarly engagement as a reviewer and their subsequent research. As an example, we queried the zbMATH Open KG for a specific scholar, Hans L. Bodlaender. We identified a potential intellectual connection between his early reviews (2000 or earlier) of graph-theoretic publications (MSC 05C*) and his later The zbMATH Open Knowledge Graph13 Reviewed Papers (Graph Theory, 05C*) Authored Papers (Computer Science, 68Q*/68W*) (1998) Hypergraph traversal revisited complexity algorithms (1999) Treewidth & minimum fill-in (weakly triangulated) treewidth minimum_fillin (2000) Minimum fill-in for distance-hereditary graphs (2003) Algorithmic aspects of treewidth dynamic_programming graph_algorithms (2002) Computing treewidth with modular decomposition (2007) Quadratic kernelization for convex recoloring (2017) Cut and count on branch decompositions Fig. 5: Potential intellectual continuity identified through author–reviewer rela- tionships: the case of Hans L. Bodlaender. authored work (2000–2025) in the field of computer science (MSC 68*). Keywords such as treewidth, dynamic programming, and graph algorithm recur across the reviewed and authored publications, indicating topical overlap between research he encountered through reviewing in early years and topics appearing in his later authored publications. These overlaps identify candidate connections that can be further investigated using bibliographic and historical evidence. This example illustrates how zbMATH Open KG can complement publication- and citation-based analysis by incorporating human scholarly engagement into the exploration of potential research continuities and possible pathways of scholarly knowledge transmission. 4.5 Other Potential Applications The zbMATH Open KG provides an open semantic infrastructure for mathemat- ical scholarship that can support applications beyond bibliographic search and citation network-based analysis. Other potential applications include: Historically Aware Scholarly Information Retrieval. The zbMATH Open KG sup- ports scholarly retrieval that accounts for the historical development of math- ematical knowledge over periods of time, supported by its extensive temporal coverage combined with expert-curated semantic information. It can potentially identify semantically related works despite changes in terminology, disciplinary boundaries, or the absence of direct citation links. This provides a basis for his- torically informed literature discovery that complements conventional keyword- and citation-based scholarly search. Knowledge Development Analytics. The explicit representation of concepts through controlled keywords, subject domains through MSC codes, and expert-curated 14Y. Susanti et al. reviews, software references, disambiguated scholars, and their relationships, combined with extensive temporal coverage, provides a basis for quantitative analyses of mathematical knowledge over extended periods. Researchers can in- vestigate patterns of emergence, specialization, cross-field continuity, resurgence, and changing research activity, as well as long-term trends in the development of mathematical disciplines over more than 250 years. Semantic Infrastructure for AI System. The zbMATH Open KG can serve as a semantic backbone for AI-assisted scholarly applications, such as graph-based scientific question answering and recommendation systems [18,22], retrieval- augmented generation, and agentic literature exploration. Particularly, explicit semantic relationships via the hierarchical MSC codes and controlled keywords provide structured sources of context that complement bibliographic metadata and unstructured text, while expert-curated reviews add broader contextual interpretations of publications beyond its original text. This supports more grounded and explainable AI-assisted exploration of mathematical literature. 5 FAIR Compliance and Sustainability Findable Persistent URIs are assigned to all entities, with URI resolution enabled for the core entities (e.g., publications, scholars, software references). RDF dump releases are versioned and accompanied by machine-readable metadata describ- ing the scope, schema, and statistics of the corresponding release. Dataset-level descriptions (VoID, DCAT, PROV-O) support machine-readable discovery and indexing within the Linked Data ecosystem. Accessible The complete RDF data are distributed as downloadable dumps through Zenodo, providing a persistent distribution channel and long-term preser- vation of released snapshots. The RDF representation can be loaded into stan- dard RDF triple stores; the pipeline has been tested with Virtuoso and Apache Jena. A public SPARQL endpoint is provided to support direct querying of the published knowledge graph in addition to bulk access through RDF dumps. Interoperable The KG uses W3C Semantic Web standards and systematically reuses established vocabularies. Where available, external identifiers such as DOIs and other external links and identifiers are retained, facilitating linking with external scholarly resources and knowledge graphs. Reusable The resource is accompanied by its OWL ontology and data-level de- scription, RDF dumps, documentation, and source code. Stable namespaces and identifiers support the reuse of entities across releases; versioned RDF snap- shots enable reproducible experiments against a fixed resource state. Licensing and attribution information for the released data and accompanying artifacts is provided with each distribution. The released knowledge graph and all accom- panying artifacts and source code are distributed under C-BY-SA 4.0. The zbMATH Open Knowledge Graph15 Sustainability and Maintenance The knowledge graph construction process is designed as a reproducible pipeline over the continuously maintained zbMATH Open platform. Periodic regeneration from updated source data, versioned re- leases, persistent entity identifiers, and public repository hosting support the continued evolution of the knowledge graph while allowing individual releases to remain independently reproducible. The ontology is maintained separately from individual data snapshots, enabling future extensions without requiring changes to the underlying identifier scheme. RDF dump releases are updated periodi- cally, approximately twice per year subject to the availability of the underlying data and resource and infrastructure constraint. 6 Conclusion We presented zbMATH Open Knowledge Graph, a large scale RDF knowledge graph that integrates more than 250 years of mathematical scholarship grounded in expert-curated semantic information. Its extensive temporal coverage and domain-specific semantic structure provide a reusable foundation for computa- tional exploration of mathematical knowledge beyond conventional bibliographic and citation-based analysis. The zbMATH Open KG is openly available and de- signed to align with FAIR principles and Semantic Web standards. We demonstrated the utility of the knowledge graph through historically grounded scholarly exploration use cases, illustrating how it can identify patterns and candidate relationships that may be difficult to uncover in conventional citation networks and provide starting points for further scholarly and historical investigation. Future directions including, but not limited to: (i) Extending the zbMATH Open KG through links to external knowledge graphs and related resources e.g., linkage to SemRepo[29] could enrich the current mathematical software references, enabling the study of the development and adoption of mathematical software and infrastructure over time. (i) Investigating how KG-based context from zbMATH Open KG complements textual and embedding-based methods in AI-assisted retrieval and explo- ration of the mathematical literature. Supplementary Material: See Page 1. Acknowledgment This work was supported by the LUMEN project, funded by the European Union’s Horizon Europe Research and Innovation Programme (Grant: 101187940, and by the DFG‘s MaRDI project (Grant: 460135501). The views and opin- ions expressed are those of the authors only and do not necessarily reflect those of the funding organizations or the granting authorities. Disclosure of Interests. 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