## Open Access in mathematics

Mathematicians endeavour to preserve and classify literature and to make it accessible. In contrast to their colleagues in many natural sciences and technical disciplines, mathematicians have a very direct interest in old mathematical literature, not only for the purpose of documenting the history of the discipline but also for current research contexts. It therefore comes as no surprise that, in mathematics, open access (OA) is not restricted to current research results but also includes older literature. Retrospective digitization and free access to this digital content play an important role in this regard.

Once proven, a mathematical proposition remains correct, and very often it also continues to play an important role in the discipline. Hence, even in current mathematical research papers, the historical citational depth is comparatively great: works from the 19th century and earlier are also consistently used and cited.

In 2006, Grigori Jakolewitsch Perelman was awarded the Fields Medal on the basis of a series of papers offering proof of the Poincaré conjecture, which he made publicly available only on the preprint server arXiv between 2002 and 2003. Although these papers never underwent classical peer review, the fact that they were made openly accessible meant that they could be examined by teams of experts within the mathematical community. (By the way, Perelman turned down the Field Medal, which is the equivalent of the Nobel Prize in mathematics.)

Especially in mathematics, criticism of the costs of journal subscriptions is very pronounced. It is not surprising, therefore, that The Cost of Knowledge appeal for a boycott of the scholarly publisher Elsevier was initiated by a mathematician, Timothy Gowers.

Because of unreasonable costs and subscription conditions, the executive board of the Center for Mathematics of the Technische Universität in Munich (TUM) decided to cancel all subscriptions to Elsevier journals with effect from 2013.

## Open Access journals

Many mathematicians take a critical view of paying publication fees. It is not surprising, therefore, that the majority of OA journals in this discipline employ business models that do not involve such fees.

Because older literature is also of great importance in mathematics, it is gratifying that many journals make older volumes freely accessible online, even when the current volumes are not OA. The moving wall model is frequently employed here: for a certain period (e.g. five years) after publication, access is fee-based, after which it becomes free of charge.

Examples of journals that use this model are

- Journal für die reine und angewandte Mathematik (1826-1997 free of charge)

- Mathematische Annalen (1869-1996 free of charge)

- Annales scientifiques de l'École Normale Supérieure (1864- free of charge, with the exception of the last four volumes)

Within the framework of the Swiss project retro.seals.ch, scholarly journals are being retrospectively digitized and made freely accessible online. The focus is on journals published in Switzerland; historical issues are also covered. Several journals in mathematics are covered, for example the Commentarii Mathematici Helvetici; all volumes from Volume 1 (1929) onwards are made freely accessible five years after print publication.

Because of the large number of titles in mathematics, the individual OA journals and other texts will not be listed here. Instead, a list of directories and repositories will be provided:

- The European Mathematical Information Service (EMIS) provides access to countless opera omnia, and to many journals, conference proceedings, monographs, and lecture notes

- Project Euclid (Cornell University) offers electronically published journals, many of which are OA

- The DML: Digital Mathematics Library directory maintains a list with links to retrospectively digitized mathematics literature (as of February 2015: 4,608 monographs and 576 journals from over 50 repositories), many of which are freely accessible. Over 4.9 million pages of digitized literature are indexed.

List of OA journals in mathematics:

- Electronic Journals Library (EZB) (the green traffic light symbol indicates availability of full-text access)

## Disciplinary repositories

### arXiv

The disciplinary repository of physics and neighbouring disciplines arXiv has been operated by Cornell University Library since 2001. The preprints are either drafts of journal articles before refereeing and publication, or preliminary findings or discussion papers that have not yet been published elsewhere. When submitting preprints for the first time, authors are, as a rule, required to get a so-called endorsement from an established arXiv author who has written a certain number of papers from within the so-called endorsement domain of an arXiv archive or subject class. Authors with recognized academic affiliations may be exempt from this requirement. arXiv is a disciplinary repository with simple functionalities and – compared to peer review – reduced mechanisms of quality assurance. Many publishers in physics enable manuscripts deposited in arXiv to be directly submitted to their journals.

There are a number of dedicated mathematics preprint servers besides the central preprint server arXiv. These servers are either limited to a sub-field or are operated by a faculty or institute. Examples include

- K-theory Preprint Archives (University of Illinois)

- Linear Algebraic Groups and Related Structures (Universität Bielefeld)

- The preprint server of the Faculty of Mathematics of the Technische Universität (TU) Darmstadt

- MPIM Preprint series (Max-Planck Institut für Mathematik)

Die bedeutendsten Open-Access-Repositorien retrodigitalisierter mathematischer Literatur sind

- The Center for Retrospective Digitization Göttingen (GDZ) with numerous journals and monographs, including the Kollektion Mathematica, in which Göttingen State and University Library’s (SUB) entire historic holdings of mathematics literature up to and including 1900 is made accessible.

- NUMDAM, Grenoble with many French and Italian journals (free access with a moving wall that depends on the journal in question)

- The University of Michigan Historical Mathematics Collection with monographs (19th and early 20th century)

- Historical Math Monographs, Cornell University Library, with monographs

## Literature searches in mathematics

In addition to the disciplinary mathematics databases that are not freely accessible, there are diverse possibilities to search free of charge for information in mathematics. Important OA services in mathematics include

- Electronic Research Archive for Mathematics (ERAM) Jahrbuch Database Projekt

- ViFaMath, Virtual Library of Mathematics

- EuDML, The European Digital Mathematics Library

## Key players

In mathematics, individual scientists often play an important role and call for OA to scientific literature. By way of example, two key players will be mentioned here. First, Timothy Gowers, the initiator of The Cost of Knowledge appeal, who is a strong advocate of OA. He also operates a mathematics blog at https://gowers.wordpress.com/. Second, Martin Götschel of the Technische Universität Berlin, who is president of the Zuse Institute Berlin (ZIB). Götschel is actively committed to OA, also in his capacity as secretary general of the International Mathematical Union (IMU).

In its recommendations, the Committee on Electronic Information and Communication (CEIC) of the International Mathematical Union (IMU) advocates that the publications of mathematicians should be made freely accessible to the public.

In Germany, the German National Library of Science and Technology (TIB) supports OA by assuming responsibility for financing the German universities’ contribution to arXiv in the network arXiv-DH. Together with the Max Planck Society and the Helmholtz Association, it thereby ensures the payment of the German community’s share of arXiv’s costs.

## Open Science

The Episciences.org project provides a free platform on which OA articles that have not yet been peer reviewed (which is often the case with preprints in mathematics, for example in arXiv) can undergo peer review. The goal is to give articles that have been made publicly available only on preprint servers the possibility of scientific quality assurance and to eliminate the disadvantage of preprint servers compared to peer-reviewed journals.

Within the framework of the IMU’s CEIC, there are efforts to develop a World Digital Mathematics Library (WDML) that would contain the entire mathematics literature and make it freely accessible and re-usable on a permanent basis. The aim is to make as much past literature available as possible and to link it with current literature.

Content editor of this web page: Dr. Gernot Deinzer, UB Regensburg.