Mathematics

As of November 2025, the Directory of Open Access Journals (DOAJ) listed 815 entries under Mathematics.

Article processing charges (APCs) are often viewed critically. For this reason, open access mathematics journals often use business models without APCs. Many of these journals are published directly by scientific institutions or professional associations.

Examples include:

• Journal de l'École Polytechnique – Mathématiques
• Documenta Mathematica

Because, as mentioned above, older literature is of great importance in mathematics, older journal volumes are often made freely available online even if the current volumes are closed access and thus subject to a fee. In these cases, the moving- wall model is often used: for a certain period of time (e.g. the first five years after publication) access is fee-based; after expiry of this embargo period, access is free. 

When publishing works in open access journals, care should be taken – also in mathematics – to avoid predatory publishing. 

The most important repository in mathematics is arXiv, a preprint server for physics, mathematics, and related disciplines (see our Physics page). As arXiv grew in importance, the once-longstanding practice whereby authors published their preprints on their institutions’ websites was abandoned. Many repositories in mathematics no longer publish any new preprints (one exception: the Max Planck Institute for Mathematics’ MPIM Preprint series). 

Mathematics research data can be conveniently deposited in Zenodo or in disciplinary repositories, which can be found, for example in the Registry of Research Data Repositories, re3data.

In addition, there are a number of open access repositories with retrodigitised mathematics literature, the most important of which are:

• Göttinger Digitalisierungszentrum (GDZ): contains, among other things, theCollection Mathematica, in which the Göttingen State and University Library’s entire historical mathematics collection up to and including the year 1900 is made accessible.
• NUMDAM: is located at the Université Grenoble Alpes and contains many French and Italian journals. Although access is free, embargo periods vary from journal to journal.
• The University of Michigan Historical Mathematics Collection: contains monographs published in the 19th and early 20th centuries.
• Historical Math Monographs (Cornell University Library)
• Project Euclid (Cornell University): hosts e-journals, many of which are open access.

The Open Directory of Open Access Repositories (OpenDOAR) provides an overview of these and other repositories.

Mathematical methods are also increasingly being applied successfully in interdisciplinary research and are therefore widespread. For example, mathematical models, parameters, data, and numerical algorithms are used in machine learning. Mathematical research data have thus become very complex, multifaceted, and unwieldy. The publication of these resources in open access is therefore highly beneficial for interdisciplinary research. However, especially in the area of data sciences, huge computing capacity is sometimes required (see the Mathematical Research Data Initiative, MaRDI, 2021).

Traditionally, proving theorems is a central element of the publishing culture in mathematics. These proofs must be completely understandable to readers within the contribution itself. In open access publications, all content is already freely available. For a long time, there was therefore no need to provide supplementary research data. However, as digitalisation advances, automated theorem-proving procedures, visualisations, and other types of mathematical research data are increasingly emerging, and the open accessibility of these resources is becoming more and more important.

Mathematical research data are very complex and diverse. The MaRDI Knowledge Graph, which is currently being developed, links many open access sources of mathematical research data. Besides the Knowledge Graph, other research data services tailored to the mathematics community can be found on the MaRDI Portal.

Software developed in mathematics is often versioned and made available via Github, which has been part of Microsoft since 2018. Public GitHub repositories can be accessed without prior registration. However, to upload one’s own data, registration is necessary; the basic functions of the service are available free of charge. Many universities and research institutes offer Git instances of their own, based, for example, on the open source platform GitLab.

Some journals that cover the computationally intensive areas of mathematics, for example numerics, already check the reproducibility of the code and software components of papers. One example is Computational Science and Engineering, a gold open access journal with its own Code Review Board. Efforts are being made to extend this to other areas of mathematics.