Mathematics

As of March 2024, the Directory of Open Access Journals (DOAJ) listed 778 entries under the keyword 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'Ecole Polytechnique – Mathematiques
• Documenta Mathematica DOAJ

Also worthy of mention is the Electronic Library of Mathematics (eLibM), a platform on which open access journals (inter alia Documenta Mathematica) are published.

Because, as mentioned above, older literature is of great importance in mathe­matics, older journal volumes are often made freely available online even though 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.

The following are examples of journals that employ this model:

• Journal für die reine und angewandte Mathematik (1826–1997 free)
• Mathematische Annalen (1869–1996 free)
• Annales scientifiques de l'École Normale Supérieure (With the exception of the last four volumes, all volumes from 1864 onwards are free.)    

Commentarii Mathematici Helvetici (With the exception of the last five vollumes, all volumes from 1929 onwards are free.)

The most important repository in mathematics is arXiv, an e-print 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 (with the exception of the Max Planck Institute for Mathematics’ MPIM Preprint series).

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, the Collection Mathematica, in which 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)
• The European Mathematical Information Service (EMIS): provides access to numerous opera omnia, journals, conference proceedings, monographs, and lecture notes.
• Project Euclid (Cornell University): hosts e-journals, many of which are open access.

An overview of relevant repositories is provided by the Open Directory of Open Access Repositories (OpenDOAR).

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

Proofs of mathematical theorems are an essential element of the pure mathe­matics publication culture. These proofs must be completely comprehensible to readers within the contribution. Consequently, it is not necessary to make supple­mentary data available, because, with the open access publication, all information is freely accessible.