Workshop overview

The Committee on Electronic Information and Communication (CEIC) of the International Mathematical Union (IMU) will host a 2.5 day meeting to discuss the goal of a World Digital Mathematics Library (WDML). The purpose of this meeting is to develop the outlines of a viable plan of action to realize the long standing dream of a universally accessible repository for the world’s mathematics literature. The workshop will bring together the major stakeholders — academic, corporate, learned societies, foundations, funding agencies, software developers — to discuss the scope and practical requirements for a successfully realized WDML project, the financial and computing resources required, the formatting and metadata standards needed to form a fully functional version, and related issues.

While the establishment of a WDML is not a new idea, having its genesis as the power of the internet became apparent to mathematicians and others worldwide, the practical difficulties of digitization, the primitive state of software needed to adequately connect and interface existing literature, and the lack of visibility of successful models of digital storage and access to scientific works, such as arXiv and JSTOR, led to frustration and discouragement of some of the early proponents of such a project. However, the vast range of material that has now been digitized, albeit in differing formats and level of accessibility, the rise of new technologies, both hardware and software, the increasing scope and sophistication of online access to scientific and other material (arXiv, University preprint repositories, Google books, the newly envisioned Digital Public Library of America, and many more), and even the appearance of social online media (blogs, Twitter, Polymath projects, Mathoverflow, etc.) have helped to resurrect the WDML vision, and give hope that, with seed funding and a serious, wide-ranging dialog among the key contributors — academic, government, foundation, commercial — the time is now ripe for revisiting the early vision, building on past successes and frustrations, and devise a realistic plan for the near and long term future, leading to prototypes and eventually fully functioning versions, that will gradually encompass a significant fraction of the freely available mathematical literature.

The meeting will be coordinated with the National Academies' Board on Mathematical Sciences recent grant from the Sloan Foundation to assemble a Committee of experts to study how a Mathematics Heritage Library could be established and develop a report. The outcomes of the workshop and discussions therein would thus serve as a point of reference and catalyst for the NA-BMS Committee to facilitate its deliberations on how to practically achieve their goal. The IMU and NA-BMS will fully cooperate and coordinate throughout the course of these interconnected initiatives, coordinating the two activities to leverage one another's efforts and maximize impact. The IMU's international perspective, through its member countries, International Congress, and its committees, to the broad range of mathematical societies and key individuals throughout the world makes its role in such a project particularly appropriate.

The CEIC itself continues to play a leading role in promoting the establishment of a World Digital Mathematics Library. In 2006, the General Assembly of the International Mathematical Union endorsed a recommendation of the CEIC describing its vision of a distributed collection of past mathematical scholarship that will serve the needs of all science, and encourages mathematicians and publishers of mathematics to join together in implementing this vision.

Clearly, in the intervening 5 years , technology has proceeded at a breakneck pace, and an updating of the vision, incorporating linking, indexing, and computable searching, must be included in any new standards. Indeed, the recent development of intelligent computable search technology, as epitomized by Wolfram Alpha, makes the usability and impact of such a library considerably greater than its previous vision, being a key reason for revisiting and re-igniting the enthusiasm of the mathematical community for such an endeavor. There is a need to take stock of where we currently are, the successes and failures over the past decade, and the lessons learned by preliminary attempts, including digitization projects, search algorithms, etc., for formulating a realistic and attainable plan for the future.

Mathematics occupies a unique position among the sciences that makes its literature particularly apt for such a repository. Researchers in mathematics and its many applications continue to make essential use of not just recent literature, but the full range historical papers and books, some dating back two centuries or more. Connections between different parts of mathematics have proven to be of increasing importance to understanding deep relationships between previously disparate areas of research, and thereby lead to unanticipated advances on current problems. To be successful, a Digital Mathematics Library must include a substantial part of the past literature, and, most importantly, its components should be interlinked, both to each other and to the current literature. The ultimate goal is to create an enduring network of digitized mathematical literature, most of which can be seamlessly traversed by all scientists engaged in mathematical research and scholarship.

A critical issue is to come up with realistic estimates of the costs, sustainability, and scale of the project — which literature should be included, e.g. is a paper appearing in, say, a learned society proceedings mathematics or not? Where does one draw the boundaries in applied mathematics, e.g. would statistics be included? If not, where is the line between probability and statistics? Would only non-copyrighted material be included, at least initially, or will the library have a goal of negotiating with publishers to include older material they currently own? Of course, the overall scope would be a dynamic target, with initial implementations concentrating on older recognized mathematics journals, but this needs a full discussion. Also, to avoid conflicts with commercial publishers — although their incorporation into the program underscores the importance of brining them into the discussions from the beginning — the initial phases of the library will be to use out-of-copyright older mathematical sources, which is still a very valuable resource for working mathematicians and those who apply mathematics to real-world applications.

Further issues to be explored: Will the library also include monographs? Will it be research level material, or also textbooks and educational papers? If not, how does one draw the line? Do citation rates play a role in sorting out material for inclusion? What sort of metadata, mathematical algorithms, and software will be required to provide full functionality for the broad range of users? There is currently an increasingly large amount of digitized mathematics available online — see for a fairly complete list of currently available Retrodigitized Mathematics Journals and Monographs. However, digitization involves far more than the mere capturing of pixels: for example, OCR, formula recognition, 2D parsing, disambiguation of references, and smart indexing are all important components in the process of "comprehending the digitized". Integration of all these disparate and incomplete digitization efforts will an important aspect of the eventual Library.

In addition, a realistic assessment of the benefits of such a digital library needs to be done. One method would be to selectively survey the global mathematics community, including libraries, to understand who would use a WDML, what their expectations and desires might be, etc. Access to the literature from developing countries, with substandard research infrastructure and limited funds, is especially important, ensuring that the common mathematical heritage of all mankind is not limited to the privileged few. The IMU's Commission for Developing Countries, recently formed by merging existing committees, will be an important resource for obtaining input from those parts of the mathematical world. Similar arguments can be made for researchers in smaller, less well endowed schools within the developed world. Indeed, the unfortunate and accelerating decline in physical libraries, subject to increasingly unsustainable budget cuts, lends added urgency to this enterprise.

The organizational aspects are an essential component — perhaps a consortium of societies and commercial players, a guarantee of sustainable funding sources, hosting and mirrors, and staff and volunteers, all need to be dealt with. How would the project connect with and make use of other initiatives, e.g. various digitization projects, Wolfram alpha, Google books, etc.? Thus, a key goal is, based on the results of these discussions, to devise a realistic and implementable business plan, both short- and long-term, including issues of sustainability and maintenance, which will be an essential component of its eventual realization.

In order to lay the groundwork for the meeting, this wiki-based web site will be used to present the questions that we hope the meeting will answer, and have the invited participants prepare position statements, with the opportunity for the community at large to post comments. Moderators will ensure that the online discussion remains relevant and focussed on the main issues concerning a World Digital Mathematics Library.

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