Research data in mathematics includes theoretical text publications as well as code and data from computation-intensive as well as computer-assisted research. The spectrum ranges from formulas and lists of mathematical objects to models, algorithms, software, databases, visualisations and mathematical documents. This diversity, the claim to truth in mathematics and the general goal of being able to apply the results in non-mathematical research requires special knowledge and relevant tools for handling mathematical research data.

The MaRDI community offers a low-threshold entry point and an initial overview of the professional handling of mathematical research data, as well as a presentation of fundamental topics in research data management (RDM) such as the FAIR principles. MaRDI (Mathematical Research Data Initiative) is the only mathematics-related consortium of the German national research data infrastructure (Nationale Forschungsdateninfrastruktur, NFDI). It has strong interdisciplinary links to engineering and chemistry, among other fields.

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The quarterly MaRDI newsletter Math & Data Quarterly provides information on new developments in the handling of mathematical research data. The MaRDI portal is the central entry point for all RDM services provided by MaRDI, and the MaRDI HelpDesk is the central point of contact for all enquiries, including those from researchers.

Recommendations for handling research data in mathematics are provided by the DFG in its Code of Conduct for Good Scientific Practice, the mathematics review board (Fachkollegium Mathematik) in its guidelines (German only), the German Mathematical Society (German only) and the MaRDI white paper Research Data Management Planning in Mathematics.

The status quo regarding the use of data management plans in mathematics-related research is described in an article published by EMS Magazine. MaRDI provides templates and exemplary wordings, while the math-specific RDMO plugin MaRDMO facilitates planning and compliance with the FAIR principles in mathematical research.

The MediaWiki Math Search Extension facilitates the findability of digital mathematical research data. In addition, various MaRDI knowledge graphs not only facilitate the findability of mathematical research data, but also its accessibility: This applies in particular to the complete knowledge graph with its query service and the subgraphs for numerical algorithms and mathematical models.

MaRDMO facilitates the documentation of workflows and tools used in mathematical modelling. Initial community projects, developed with the MaRDI Helpdesk on best practices, provide inspiration and best practices for the sustainable preparation of your own projects.

MaRDIflow enables FAIR workflows in the field of scientific computing; interoperability can additionally be ensured through open interfaces.

The MaRDI Packaging System (MaPS) facilitates the storage of mathematical software setups, providing a streamlined and efficient alternative to dockers or VMs, as MaPS also allows software environments to be easily shared. The JSON-based .mrdi data format enables individual mathematical research data to be stored without any loss of information.

Since mathematical results and methods are also used in other disciplines, providing comprehensible documentation is particularly important when publishing mathematical research data. More information on this topic can be found under Describing and Documenting research data.

An overview of math-specific repositories and databases is provided by a publication from the MaRDI portal team, as well as re3data and the MathBases website. Mathematical software can be discussed, for example, in publications such as the Journal of Statistical Software, the Journal of Software for Algebra and Geometry, or the Journal of Open Research Software.

There are also generic data journals to publish mathematical research data, such as Scientific Data or Data.

Preprints of mathematical papers can usually be found on arXiv, zbMATH offers comprehensive, interlinked bibliographic data for publications in mathematics, and swMATH is a database for information on mathematical software.

The MaRDI portal provides an overview of MaRDI services and links mathematical research data from various sources.

MaRDI maintains a Zenodo community with curated datasets from the field of graphical modelling and causality research. The consortium is also involved in the mlr3 interoperability project for machine learning in R. The open platforms OpenML and CauseMe are used to exchange datasets, algorithms and experiments from machine learning.

The German Mathematical Society runs an online course on good scientific practice.

In mathematics, sensitive personal data is only used in exceptional cases.

A prototype of a mathematics-related Train-the-Math-Trainer programme (German only) is available; more in-depth training materials are currently being designed. The Infrastructure for Mathematics lecture at the University of Leipzig is the first event of its kind on mathematics-related research data management; scripts and slides are available. An interdisciplinary course (German only) is already available as an open educational resource.

Paper: Handreichung zum Umgang mit Forschungsdaten in der Mathematik
Authors: Fachkollegium Mathematik
Year of publication: 2023
Link to the DFG website

Paper: Research data management planning in the German mathematical community
Authors: Tobias Boege, René Fritze, Christiane Görgen, Jeroen Hanselman, Dorothea Iglezakis, Lars Kastner, Thomas Koprucki, Tabea Krause, Christoph Lehrenfeld, Silvia Polla, Marco Reidelbach, Christian Riedel, Jens Saak, Björn Schembera, Karsten Tabelow, Marcus Weber
Year of publication: 2022
Preprint available at arxiv:2211.12071 [math.HO].