M09 Mathematical Research Data in the Era of Artificial Intelligence

In Germany, the National Research Data Infrastructure (NFDI) mathematics plays an integral role. The Mathematical Research Data Initiative (MaRDI) steers the mathematics-related activities within the NFDI to make mathematical research data more Findable, Accessible, Interoperable, and Reproducible (FAIR). While this significantly advances research and innovation speed, and technological developments already have a significant impact on the publication landscape in general, manual effort for curation and interaction with information retrieval systems seems to still be a hindering factor for a wider uptake. While recent successes in mathematics were enabled by formalized computer proofs, most mathematical publications do not yet reveal MathRD, mathematics research data, including software, in a machine-processable form. In the proposed mini-symposium we discuss how recent advances in artificial intelligence can contribute to lower the barrier to reveal MathRD in a machine-processable form to speed up the process of making MathRD fair. We here bring together technology provider and working mathematicians to find a good balance between the needs of the community and the possibilities of the technology.

Accessing mathematical knowledge through formal queries often poses a barrier to researchers unfamiliar with controlled vocabularies or classification systems. In this talk, we present ongoing efforts to integrate natural language interfaces into zbMATH Open, a leading resource for mathematical research. We demonstrate how users can pose queries in everyday language -- such as "What are recent results on the Langlands program?" -- and retrieve relevant, structured mathematical content. We discuss the challenges of interpreting informal language in a highly formalized domain, outline the system architecture, and provide a live demonstration of the prototype. Our goal is to make mathematical knowledge more accessible, searchable, and ultimately more useful to a broader audience.

Wikimedia platforms, particularly Wikipedia and Wikidata, are widely used for sharing and structuring mathematical knowledge. This presentation explores how they facilitate such use. It outlines how structured data in Wikidata enhances the discoverability of mathematical concepts, enabling advanced semantic search and automated visualizations. We will showcase community-driven efforts to improve accessibility, featuring both technical and multilingual examples. We then demonstrate how Wikidata’s machine-readable framework interlinks mathematical entities with related concepts in physics, computer science, and beyond, thereby supporting interdisciplinary research. Finally, we highlight emerging trends where mathematical research both contributes to and benefits from Wikimedia, illustrating how these platforms strengthen open mathematical knowledge more generally.

The emergence of powerful AI systems in mathematics, from IMO successes to algorithmic discoveries, is tempered by the practical limitations of accessible tools. This presentation critically examines these limitations, including key failure modes like 'self-critique blindness' and the compounding of errors in research scenarios. We then introduce a durable framework for responsible AI integration, centered on the 'AI as Copilot' model. This is applied through seven practical research pathways, supported by a strategic guide to model selection that weighs the pros and cons of tools like the free Gemini 2.5 Pro, OpenAI's offerings, and Grok 4. The talk provides a clear methodology for using these technologies as a powerful augmentative force in mathematics.

15:30	Natural Language Interfaces for Mathematical Research Andreas Kühnemund, FIZ Karlsruhe - Leibniz-Institut für Informationsinfrastruktur Accessing mathematical knowledge through formal queries often poses a barrier to researchers unfamiliar with controlled vocabularies or classification systems. In this talk, we present ongoing efforts to integrate natural language interfaces into zbMATH Open, a leading resource for mathematical research. We demonstrate how users can pose queries in everyday language -- such as "What are recent results on the Langlands program?" -- and retrieve relevant, structured mathematical content. We discuss the challenges of interpreting informal language in a highly formalized domain, outline the system architecture, and provide a live demonstration of the prototype. Our goal is to make mathematical knowledge more accessible, searchable, and ultimately more useful to a broader audience.
16:00	Structuring, Discovering and Connecting Mathematical Knowledge through the Wikimedia Ecosystem Moritz Schubotz, FIZ Karlsruhe - Leibniz-Institut für Informationsinfrastruktur Wikimedia platforms, particularly Wikipedia and Wikidata, are widely used for sharing and structuring mathematical knowledge. This presentation explores how they facilitate such use. It outlines how structured data in Wikidata enhances the discoverability of mathematical concepts, enabling advanced semantic search and automated visualizations. We will showcase community-driven efforts to improve accessibility, featuring both technical and multilingual examples. We then demonstrate how Wikidata’s machine-readable framework interlinks mathematical entities with related concepts in physics, computer science, and beyond, thereby supporting interdisciplinary research. Finally, we highlight emerging trends where mathematical research both contributes to and benefits from Wikimedia, illustrating how these platforms strengthen open mathematical knowledge more generally.
16:30	Researching with Thinking Models: AI-Assisted Paths in Mathematics Jonas Henkel, Universität Marburg The emergence of powerful AI systems in mathematics, from IMO successes to algorithmic discoveries, is tempered by the practical limitations of accessible tools. This presentation critically examines these limitations, including key failure modes like 'self-critique blindness' and the compounding of errors in research scenarios. We then introduce a durable framework for responsible AI integration, centered on the 'AI as Copilot' model. This is applied through seven practical research pathways, supported by a strategic guide to model selection that weighs the pros and cons of tools like the free Gemini 2.5 Pro, OpenAI's offerings, and Grok 4. The talk provides a clear methodology for using these technologies as a powerful augmentative force in mathematics.
17:00	Open Exhibits for Communicating the Mathematics Behind AI Andreas Matt, IMAGINARY This talk presents interactive, openly licensed software exhibits designed to communicate key mathematical concepts of Machine Learning. Initially developed for the traveling exhibition I AM A.I., these tools offer a low-threshold introduction for broad audiences to topics such as neural networks, gradient descent, and reinforcement learning. Among others, a recognition tool for handwritten digits with a trainable neural network, an arcade-style game illustrating gradient descent, and a digital learning robot navigating a maze are shown. The talk concludes with a discussion on the potential of open data for science and mathematics communication.