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Moritz Schubotz

Publications and source records attributed to Moritz Schubotz.

At least 19 recordsLinked to original sources
arXiv2026

The zbMATH Open Knowledge Graph: Tracing Centuries of Mathematical Research

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.

cs.DL↗
arXiv2026

Graph-Based Discovery of Mathematical Software Communities and Publication-to-Community Prediction

Research software forms distinct co-usage communities that span traditional disciplinary boundaries, yet the structure of these communities remains largely unexplored. We present a graph-based framework for discovering mathematical software communities and predicting their association with research publications. We construct a software co-usage network from publication-software relationships using a curated swMATH dataset and subsequently apply community detection method, revealing a heterogeneous landscape of mathematical software communities. We formulate publication-to-community mapping as a multi-label classification task and further investigate whether community membership can be predicted from lightweight scholarly metadata. Specifically, we compare two feature representations of scientific publications: Mathematics Subject Classification (MSC) and title-based embeddings. Across a range of models, structured MSC representation consistently provides a stronger precision-recall trade-off, demonstrating that structured domain metadata captures software-community structure more effectively than compressed title-only semantics in this setting. This work highlights the continuing value of structured scholarly metadata for large-scale research software discovery, classification and recommendation.

cs.IR↗
arXiv2026

Syntax Meets Semantics: Understanding Scientific Formulae

Scientific formulae are a fundamental component of scholarly communication, yet their dual nature -- as structured syntax and carriers of semantics -- remains underexplored in scholarly information retrieval. Although prior studies show that jointly modeling syntactic and semantic modalities improves retrieval performance, the relationship between their underlying representations has not been systematically investigated. In this work, we empirically study cross-modal correspondence between formula syntax and semantics. We find that their native representation spaces exhibit extremely weak observable correspondence despite strong latent correlation, indicating a substantial representation mismatch between the two modalities. We further evaluate whether this mismatch can be reduced using standard representation learning and alignment techniques. We represent syntactic structure using graph-based encoders and semantic information using text-based encoders, then apply contrastive learning to induce a shared representation space. Results show that the learned alignment substantially improves cross-modal retrieval, suggesting that explicit representation learning can recover correspondence absent from the original representation spaces.

cs.IR↗
arXiv2026

Aspect-Aware Content-Based Recommendations for Mathematical Research Papers

Content-based research paper recommendation (CbRPR) has seen advances in computer science and biomedicine, but remains unexplored for mathematics, where paper relatedness is more conceptual than explicit textual or citation-based similarity. Mathematics papers may be connected through shared proof techniques, logical implications, or natural generalizations, yet exhibit minimal textual or citation overlap, rendering existing CbRPR ineffective. To address this gap, we first conduct an expert-driven study characterizing mathematical recommendations, revealing that relevance is inherently \textit{aspect}-driven. Grounded in this insight, we introduce GoldRiM (small, expert-annotated) and SilverRiM (large, automatically derived), the first datasets for \textit{aspect}-aware CbRPR in mathematics. Recognizing that LLM embeddings of mathematical content alone yield suboptimal representation, we propose AchGNN, an \textit{aspect}-conditioned heterogeneous GNN that jointly models textual semantics, citation structure, and author lineage. Across GoldRiM and SilverRiM, AchGNN consistently outperforms prior \textit{aspect}-based CbRPR methods, achieving substantial gains across all evaluated \textit{aspects}. We conduct ablation studies to analyze the contributions of individual \textit{aspect} supervision, authorship lineage, and graph-structural signals to AchGNN's performance. To assess domain generality, we further evaluate AchGNN on the \textit{Papers with Code} dataset of machine learning publications, demonstrating that our \textit{aspect}-aware approach effectively transfers beyond mathematics. We deploy our system on the MaRDI platform to help mathematicians with recommendations and release datasets and code publicly for reproducibility.

cs.IR↗
arXiv2026

Large-Scale Measurement of NAT Traversal for the Decentralized Web: A Case Study of DCUtR in IPFS

The promise of decentralized peer-to-peer (P2P) systems is fundamentally gated by the challenge of Network Address Translation (NAT) traversal, with existing solutions often reintroducing the very centralization they seek to avoid. This paper presents the first large-scale measurement study of a fully decentralized NAT traversal protocol, Direct Connection Upgrade through Relay (DCUtR), within the production libp2p-based InterPlanetary File System (IPFS) network. Drawing on over 4.4 million traversal attempts from 85,000+ distinct networks across 167 countries, we provide an empirical analysis of modern P2P connectivity. We establish a conditional success rate of $70\% \pm 7.1\%$ for the hole-punching stage, given that prerequisite relay reservation and public address discovery succeed, providing a crucial new benchmark for the field. Critically, we empirically challenge the long-held belief of UDP's superiority for NAT traversal, demonstrating that DCUtR's high-precision, RTT-based synchronization yields statistically indistinguishable success rates for both TCP and QUIC ($\sim70\%$). Our analysis further validates the protocol's design for permissionless environments by showing that success is independent of relay characteristics and that the mechanism is highly efficient, with $97.6\%$ of successful connections established on the first attempt. Building on this analysis, we propose a concrete roadmap of protocol enhancements aimed at achieving universal connectivity and contribute our complete dataset to foster further research in this domain.

cs.NI↗
arXiv2026

LLM-supported document separation for printed reviews from zbMATH Open

This paper presents a specialized methodology for digitizing and segmenting mathematical documents from zbMATH Open, a comprehensive database of mathematical literature, to enhance machine processing capabilities. Currently, approximately 831,000 documents exist only in scanned volumes, which makes them not machine-processable. Furthermore, these scans often span multiple pages or share pages with other documents and incorporate diverse typesetting techniques, posing challenges for automated processing. To address these issues, we evaluate various Optical Character Recognition (OCR) tools and document separation techniques, proposing an optimized pipeline that outperforms existing approaches. Our study identifies Mathpix as the most effective OCR tool for LaTeX conversion, demonstrating superior performance based on BLEU and Edit Distance metrics. For document separation, we fine-tune generative Large Language Models (LLMs) and integrate them into a Majority Voting framework, achieving 97.5% accuracy when providing the text of the document. Additionally, our method identifies the start and end indexes for 90.6% of the test dataset, with an accuracy of 98.4% on applicable cases, resulting in an overall accuracy of 89.1% on the entire dataset. This approach surpasses traditional baselines, including regular expressions, ChatGPT-4o, and computer vision-based techniques. As a practical outcome, we process 810,977 mathematical documents into machine-readable text and extract precise document boundaries for 721,288 documents in LaTeX format. These contributions significantly improve accessibility for mathematical information retrieval systems, machine learning models, and related applications.

cs.DL↗
arXiv2025

Challenging Tribal Knowledge -- Large Scale Measurement Campaign on Decentralized NAT Traversal

The promise of decentralized peer-to-peer (P2P) systems is fundamentally gated by the challenge of Network Address Translation (NAT) traversal, with existing solutions often reintroducing the very centralization they seek to avoid. This paper presents the first large-scale, longitudinal measurement study of a fully decentralized NAT traversal protocol, Direct Connection Upgrade through Relay (DCUtR), within the production libp2p-based IPFS network. Drawing on over 4.4 million traversal attempts from 85,000+ distinct networks across 167 countries, we provide a definitive empirical analysis of modern P2P connectivity. We establish a contemporary baseline success rate of $70\% \pm 7.1\%$ for the hole-punching stage, providing a crucial new benchmark for the field. Critically, we empirically refute the long-held 'tribal knowledge' of UDP's superiority for NAT traversal, demonstrating that DCUtR's high-precision, RTT-based synchronization yields statistically indistinguishable success rates for both TCP and QUIC ($\sim70\%$). Our analysis further validates the protocol's design for permissionless environments by showing that success is independent of relay characteristics and that the mechanism is highly efficient, with $97.6\%$ of successful connections established on the first attempt. Building on this analysis, we propose a concrete roadmap of protocol enhancements aimed at achieving universal connectivity and contribute our complete dataset to foster further research in this domain.

cs.NI↗
arXiv2025

Fraudulent Publishing in Mathematics: A European Call to Action and How Information Infrastructure Can Help

The IMU-ICIAM working group's new report on Fraudulent Publishing in the Mathematical Sciences documents how gaming of bibliometrics, predatory outlets and paper-mill activity are eroding trust in research, mathematics included. This short EMS note brings that analysis home to Europe. We urge readers to recognise the warning signs of fraudulent publishing, to report serious irregularities so that they can be investigated and sanctioned, and to reflect critically on their own editorial and reviewing practices. We then sketch why Europe is well placed to lead a structural response: a decade of policy development on open science; mature infrastructures for data, software and scholarly communication; and new capacity for community-led diamond open access. Finally, we outline developments towards non-print contributions across member countries including the growth of formal proofs (e.g. with Lean and Isabelle) and we highlight the role of zbMATH Open as a European quality signal that can help editors, reviewers and authors steer clear of problematic venues.

cs.DL↗
arXiv2025

Fraudulent Publishing in the Mathematical Sciences

This report is the first of two publications of a joint Working Group of the International Mathematical Union (IMU) and the International Council of Industrial and Applied Mathematics (ICIAM). In it, we shall analyze the current state of publishing in the mathematical sciences and explain the resulting problems. Our second publication will offer concrete recommendations, guidelines, and best practices for researchers, policymakers, and evaluators of mathematical research. It will explain how to detect and counteract attempts to game bibliometric measures, empowering the community to reclaim control over research evaluation and drive necessary change.

math.HO↗
arXiv2025

Author Intent: Eliminating Ambiguity in MathML

MathML has been successful in improving the accessibility of mathematical notation on the web. All major screen readers support MathML to generate speech, allow navigation of the math, and generate braille. A troublesome area remains: handling ambiguous notations such as \( \vert x\vert\). While it is possible to speak this syntactically, anecdotal evidence indicates most people prefer semantic speech such as ``absolute value of x'' or ``determinant of x'' instead of ``vertical bar x vertical bar'' when first hearing an expression. Several heuristics to infer semantics have improved speech, but ultimately, the author is the one who definitively knows how an expression is meant to be spoken. The W3C Math Working Group is in the process of allowing authors to convey their intent in MathML markup via an intent attribute. This paper describes that work.

cs.DL↗
arXiv2024

An Overview of zbMATH Open Digital Library

Mathematical research thrives on the effective dissemination and discovery of knowledge. zbMATH Open has emerged as a pivotal platform in this landscape, offering a comprehensive repository of mathematical literature. Beyond indexing and abstracting, it serves as a unified quality-assured infrastructure for finding, evaluating, and connecting mathematical information that advances mathematical research as well as interdisciplinary exploration. zbMATH Open enables scientific quality control by post-publication reviews and promotes connections between researchers, institutions, and research outputs. This paper represents the functionalities of the most significant features of this open-access service, highlighting its role in shaping the future of mathematical information retrieval.

cs.DL↗
arXiv2024

Reducing the climate impact of data portals: a case study

The carbon footprint share of the information and communication technology (ICT) sector has steadily increased in the past decade and is predicted to make up as much as 23 \% of global emissions in 2030. This shows a pressing need for developers, including the information retrieval community, to make their code more energy-efficient. In this project proposal, we discuss techniques to reduce the energy footprint of the MaRDI (Mathematical Research Data Initiative) Portal, a MediaWiki-based knowledge base. In future work, we plan to implement these changes and provide concrete measurements on the gain in energy efficiency. Researchers developing similar knowledge bases can adapt our measures to reduce their environmental footprint. In this way, we are working on mitigating the climate impact of Information Retrieval research.

cs.IR↗
arXiv2024

Taxonomy of Mathematical Plagiarism

Plagiarism is a pressing concern, even more so with the availability of large language models. Existing plagiarism detection systems reliably find copied and moderately reworded text but fail for idea plagiarism, especially in mathematical science, which heavily uses formal mathematical notation. We make two contributions. First, we establish a taxonomy of mathematical content reuse by annotating potentially plagiarised 122 scientific document pairs. Second, we analyze the best-performing approaches to detect plagiarism and mathematical content similarity on the newly established taxonomy. We found that the best-performing methods for plagiarism and math content similarity achieve an overall detection score (PlagDet) of 0.06 and 0.16, respectively. The best-performing methods failed to detect most cases from all seven newly established math similarity types. Outlined contributions will benefit research in plagiarism detection systems, recommender systems, question-answering systems, and search engines. We make our experiment's code and annotated dataset available to the community: https://github.com/gipplab/Taxonomy-of-Mathematical-Plagiarism

cs.IR↗
arXiv2024

Can LLMs Master Math? Investigating Large Language Models on Math Stack Exchange

Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a distinctive challenge, primarily due to its specialized structure and the precision it demands. In this study, we adopted a two-step approach for investigating the proficiency of LLMs in answering mathematical questions. First, we employ the most effective LLMs, as identified by their performance on math question-answer benchmarks, to generate answers to 78 questions from the Math Stack Exchange (MSE). Second, a case analysis is conducted on the LLM that showed the highest performance, focusing on the quality and accuracy of its answers through manual evaluation. We found that GPT-4 performs best (nDCG of 0.48 and P@10 of 0.37) amongst existing LLMs fine-tuned for answering mathematics questions and outperforms the current best approach on ArqMATH3 Task1, considering P@10. Our Case analysis indicates that while the GPT-4 can generate relevant responses in certain instances, it does not consistently answer all questions accurately. This paper explores the current limitations of LLMs in navigating complex mathematical problem-solving. Through case analysis, we shed light on the gaps in LLM capabilities within mathematics, thereby setting the stage for future research and advancements in AI-driven mathematical reasoning. We make our code and findings publicly available for research: \url{https://github.com/gipplab/LLM-Investig-MathStackExchange}

cs.CL↗
arXiv2024

WikiTexVC: MediaWiki's native LaTeX to MathML converter for Wikipedia

MediaWiki and Wikipedia authors usually use LaTeX to define mathematical formulas in the wiki text markup. In the Wikimedia ecosystem, these formulas were processed by a long cascade of web services and finally delivered to users' browsers in rendered form for visually readable representation as SVG. With the latest developments of supporting MathML Core in Chromium-based browsers, MathML continues its path to be a de facto standard markup language for mathematical notation in the web. Conveying formulas in MathML enables semantic annotation and machine readability for extended interpretation of mathematical content, in example for accessibility technologies. With this work, we present WikiTexVC, a novel method for validating LaTeX formulas from wiki texts and converting them to MathML, which is directly integrated into MediaWiki. This mitigates the shortcomings of previously used rendering methods in MediaWiki in terms of robustness, maintainability and performance. In addition, there is no need for a multitude of web services running in the background, but processing takes place directly within MediaWiki instances. We validated this method with an extended dataset of over 300k formulas which have been incorporated as automated tests to the MediaWiki continuous integration instances. Furthermore, we conducted an evaluation with 423 formulas, comparing the tree edit distance for produced parse trees to other MathML renderers. Our method has been made available Open Source and can be used on German Wikipedia and is delivered with recent MediaWiki versions. As a practical example of enabling semantic annotations within our method, we present a new macro that adds content to formula disambiguation to facilitate accessibility for visually impaired people.

cs.DL↗
arXiv2023

Making Mathematical Research Data FAIR: A Technology Overview

The sharing and citation of research data is becoming increasingly recognized as an essential building block in scientific research across various fields and disciplines. Sharing research data allows other researchers to reproduce results, replicate findings, and build on them. Ultimately, this will foster faster cycles in knowledge generation. Some disciplines, such as astronomy or bioinformatics, already have a long history of sharing data; many others do not. The current landscape of so-called research data repositories is diverse. This review aims to perform a technology review on existing data repositories/portals with a focus on mathematical research data.

cs.DL↗
arXiv2023

Bravo MaRDI: A Wikibase Powered Knowledge Graph on Mathematics

Mathematical world knowledge is a fundamental component of Wikidata. However, to date, no expertly curated knowledge graph has focused specifically on contemporary mathematics. Addressing this gap, the Mathematical Research Data Initiative (MaRDI) has developed a comprehensive knowledge graph that links multimodal research data in mathematics. This encompasses traditional research data items like datasets, software, and publications and includes semantically advanced objects such as mathematical formulas and hypotheses. This paper details the abilities of the MaRDI knowledge graph, which is based on Wikibase, leading up to its inaugural public release, codenamed Bravo, available on https://portal.mardi4nfdi.de.

cs.DL↗