The rise of the World Wide Web in the late 20th century inspired the vision of a Digital Mathematics Library (DML). Its primary aim is, in a very broad sense, to digitize and store the entire corpus of mathematical research literature, and to implement new features like searching, linking, and computing. The DML is committed to openness, ensuring global access for research and education communities.
The DML vision was codified by the General Assembly (GA) of the International Mathematical Union in 2006, by endorsing a statement, “Digital Mathematics Library: A Vision for the Future“ proposed by the CEIC. Its core mission was formulated as follows:
„The Committee on Electronic Information and Communication (CEIC) of the International Mathematical Union endorses this vision of a distributed collection of past mathematical scholarship that serves the needs of all science, and encourages mathematicians and publishers of mathematics to join together in implementing this vision.
The Digital Mathematics Library should include a substantial part of the past literature, and, most importantly, its components should be connected, both to each other and to the current literature. This can begin most easily by focusing on journals. The ultimate goal is to create an enduring network of digital literature, most of which can be seamlessly traversed by all scientists engaged in mathematical research and scholarship.“
Mathematicians think of themselves as a world-wide community. A successful DML has ultimately to be a shared global good provided and curated by the community for the community, meeting the needs of the community.
The challenges in realising DML were, and are, tremendous. To name just a few:
Quickly, the DML concept was picked up by many countries and institutions, and got permanently adapted, developed, and refined. This results in a zoo of acronyms that include DML or versions of it (some to be named below) that may be confusing a the beginning; but in fact, they all bear witness to the appeal of the DML concept and of its universality.
Thinking about DML, even if far from being realised, has inspired many scholars and institutions to reflect how they want to publish, to interact, to be read, and how not. Thus, the influence of the DML Vision goes far beyond its implementation.
Many of the essential resources for today's working mathematician have actually been around for less time than we realise. In the late 1990s it was still common to look up keywords in card catalogues in libraries, the quality of which depended heavily on the skills of the librarians. Reprints of articles were requested from colleagues by postcard, and once a month a researcher would go to the library to read the latest issue of `Zentralblatt Mathematik' or `Mathematical Reviews', which contain short reviews of all recent publications, to see what's new in their field.
The situation changed rapidly, as a brief review shows:
Mathematical Reviewing services: In 1996, both main reviewing services, Zentralblatt Mathematik and Mathematical Reviews, started offering a subscription based online version in addition to the print issue. It took them several years of effort to retrodigitize old issues (partly only in non-searchable scanned format).
The rise of preprint servers: Probably the world's most famous preprint server was founded in 1991 as a free central repository at the Los Alamos National Laboratory (LANL), accessible via ftp under the name "LANL preprint archive". To this day, it stores only TeX / LaTeX files, thus minimising the required storage capacity. In 2001, founder Paul Ginsparg changed the institution to Cornell University and the name of the repository to arXiv.org, also known as " the arXiv". By 2007 it had more than 50,000 submissions per year.
The first digital library: The first digital library to be created was JSTOR in 1994, as a digital alternative for libraries that lacked the space and money to purchase print copies of journals. Today JSTOR content is provided by more than 900 publishers, and the database contains more than 12 million journal articles, in more than 75 disciplines. Most access is by subscription, but some of the site is public domain and available free of charge.
It is not surprising, therefore, that in this period of significant change, the mathematical community decided that there was a need for a committee to assess these developments, form an opinion and make recommendations. As explained in our mission statement, this was the birth of CEIC in 1998.
Many scholars in the community devoted a great deal of effort to the creation of the first digitisation projects of mathematical literature. We cite a few of them:
NUMDAM: NUMDAM is the French digital reference library in mathematics assembled by MathDoc with the help of a network of partners. The service began in 2000 with the pilot digitization of 5 journals, and was first put online in January 2003. The digitization program, which is still active, has continued to expand both geographically (European journals) and thematically (mathematics, physics, statistics, computer science and related sciences).
EUDML: EuDML (The European Digital Mathematics Library) was a project funded by the European Commission. Together with several partners a collaborative digital library service was developed. EuDML makes mathematics literature available online in the form of an enduring digital collection, developed and maintained by a network of institutions.
GDZ: this is the Göttinger Digitalisierungszentrum founded and maintained by SUB, the Göttingen State and University Library. It is one of the few projects initiated by a library.
As it turned out, securing continuous funding is one of the most serious challenges faced by all these projects. This leads regularly to unused knowledge and infrastructure and the need to keep starting afresh in a different context.
In 2012, CEIC organised the International Symposium on "The Future World Heritage Digital Mathematics Library". The Conclusions of the meeting explore practical mechanisms, challenges, and capabilities required for the realisation of the GDML.
At the 2014 ICM in Seoul, IMU President Ingrid Daubechies convened a working group to consider the actions needed to advance the prospects for a Global Digital Mathematics Library. The GDML Working Group decided to establish a not-for-profit organisation, the International Mathematical Knowledge Trust (IMKT).
The International Mathematical Knowledge Trust (IMKT) was created as a step towards a global digital mathematics library with a grant from the Alfred P. Sloan Foundation. It IMKT was legally constituted in December 2017 in Waterloo, Canada under the Canada Not-for-profit Corporations Act. As a consequence of the pandemic in 2020-21, however, IMKT activities were disrupted and encountered difficulties to be started again. Nevertheless, it is fully dedicated to the long-term goal of creating a comprehensive mathematical knowledge base for the international community.
The GDML concept involves different aspects: An index, a collection of available digital items, and, above all, an interface to access them and more sophisticated tools to advanced research applications.
GDML_0 is meant to be the initial interface and index. The best currently existing foundation for GDML_0 is zbMATH Open, which is the online version of Zentralblatt and is now freely available worldwide. Its transition to an open access database was explicitly motivated by the IMU’s GDML vision, as acknowledged on their website:
“After a concerted effort by zbMATH stakeholders, the Joint Science Conference (Gemeinsame Wissenschaftskonferenz) agreed in the first week of December 2019 that the Federal and State Governments of Germany would support FIZ Karlsruhe to transform zbMATH into an open platform. As a result zbMATH Open has become a freely accessible research tool for the mathematical community worldwide since January 2021.
This step was inspired by the International Mathematical Union’s 2014 vision of a Global Digital Mathematics Library: ‘to provide a coherent and sustainable open platform in which all mathematicsrelevant information and data can be brought together, comprehensively accessed and used free of charge under a uniform interface’.”
All of the data compiled or created by zbMATH itself is available under a Creative Commons BY-SA license (an open access license allowing reuse with attribution, provided that the results are also made available under the same terms), while some bibliographic data supplied by publishers is more restrictively licensed.
Among freely available databases, zbMATH Open has by far the best and most accurate coverage of mathematics, and it therefore constitutes an ideal portal to the GDML.