The Global Digital Mathematical Library Working Group (GDML WG)

At the first ICM in 1897 there was a session under the chairmanship of Peano concerned with questions of how to encode mathematical knowledge; see the article by E. Schröder in the ICM1897 Proceedings.

Indeed it was in connection with such efforts that Peano developed his axioms for the natural numbers. At the 1928 ICM in Bologna there was active discussion of how to provide comprehensive bibliographic resources for mathematics to everyone; see the article by R.C. Archibald in the ICM1928 Proceedings.  Now the IMU sees the possibility of realizing the current dream of a Global Digital Mathematical Library or World Digital Mathematical Library.

The adjective digital is important here as it is the new digital technologies that allow better access to the resources of mathematical knowledge than ever before. We are in the presence of a transformative technology and we can capitalize on it to everyone’s benefit. I can imagine that in 16th century Europe, or even earlier in 14th century Korea, when printing from metal type was a brand-new technology, people saw the possibilities of the new forms of book for the recording and dissemination of knowledge. That they were right we all now know. That sort of opportunity is open to us again now.

The adjective global is important too. We all think the truths of our subject to be global, independent of location in this world. We think of ourselves as a world-wide community. This is well demonstrated by our being gathered at the ICM2014 from over 120 countries. A GDML can have a global reach as a result of the digital technology mentioned, particularly the internet. It will be a shared global good. We can hope for global support for the idea and expect that there can be contributions to a GDML from all over the world. It will provide benefits all over the world. The earliest mathematical artifact some think to be from Ishango in Congo, commemorated in a 7m-meter high replica; perhaps this GDML can be a help in Africa. But as the Leelavati lecture emphasized the main goal has to be to offer solutions to problems that the people you serve want solved.

IMU President Ingrid Daubechies and Chair Peter Olver of the IMU’s Committee on Electronic Information and Communication (CEIC) took the initiative to work toward a WDML or GDML through consultations with a broad expert group. This culminated in comprehensive report from a Workshop at the US National Academy of Sciences.  Now a small working group of 8 persons, which I am to chair, has been given the task of making, by the end of this year, concrete proposals for work setting up a GDML. Then resources can be found, so to speak, to virtually break ground on building a GDML.

The GDML WG represents a variety of backgrounds and interests and is about as international as 8 people can be, if where their careers have carried them is taken into account. They are united by a belief that there are opportunities for building a GDML to serve the mathematical community and disseminate mathematical knowledge as widely as it is needed, and by a wish to make that happen starting now. The WG will of course be calling upon the expertise of the community, about the square of 8 in size, that Ingrid Daubechies and Peter Olver have been consulting, as well as on many others. The WG’s activities will be reported on through the IMU’s CEIC web site and we, of course, will be happy to hear from the community of ideas for services a GDML may provide and what problems it may solve. We expect that realizing a GDML will naturally involve both the academic and industrial mathematical communities and collaboration with those who have served it well for a long time — very importantly the publishing business world-wide. The WG’s goal is to get GDML projects defined and started in comparatively short order.

I see essentially four facets to the GDML initiative:

  • Community aspects
  • Literature aspects
  • Knowledge management aspects
  • Administrative aspects

They are all discussed in the NRC report. The WG is to make concrete what’s suggested there on all four fronts.

Some parts of a GDML require work that is understood, or already done in part, but that just takes much time and effort to complete. Other parts require serious investigation and prototyping which also takes time, even nowadays, although the general ideas may seem clear. The WG is made up of members who think now is the time to realize the new opportunities for a GDML.

Members and present locations:

  • Thierry Bouche, Institut Fourier & Cellule MathDoc, Grenoble, France
  • Bruno Buchberger, RISC, Hagenberg/Linz, Austria
  • Patrick Ion, Mathematical Reviews/AMS, Ann Arbor, MI, US
  • Michael Kohlhase, Jacobs University, Bremen, Germany
  • Jim Pitman, University of California, Berkeley, CA, US
  • Olaf Teschke, zbMATH/FIZ, Berlin, Germany
  • Stephen Watt, University of Western Ontario, London, ON, Canada
  • Eric Weisstein, Wolfram Research, McAllen, TX, US

Patrick Ion


Welcome to the World Digital Mathematics Library (WDML) Blog

The ever-increasing ubiquity of the World Wide Web in the waning years of the twentieth century served to catalyze the grand vision of a World Digital Mathematics Library (WDML), that will contain digitized versions of the entire corpus of mathematical research literature, both contemporary and historical, in a distributed system of interlinked repositories.  The unique attributes of mathematics, including the eternal validity of mathematical results and constructions, make a Mathematical Digital Library especially compelling.  More than just a collection of digitized research papers and books, the WDML will include the abilities to search, link, annotate, classify, mine, compute, etc. that will form a wide ranging and dynamic suite of applications that incorporate the desirable features of, but go beyond the current capabilities of MathSciNet, zbMATH, Google Scholar, Wolfram Alpha, etc., and thereby fuel the next generation of mathematical research and its manifold applications.  Moreover, a commitment to openness, ensuring that the WDML is accessible throughout the worldwide research and education communities, lies at the heart of this vision.

The WDML vision was codified by the General Assembly (GA) of the International Mathematical Union (IMU) who, in 2006, endorsed a statement, “Digital Mathematics Library: A Vision for the Future“, of the Committee on Electronic Information and Communication (CEIC) that “… 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.”

While numerous digitization projects gained momentum and scope in the intervening years, while several “local” initiatives, such as the European Digital Mathematics Library (EuDML), Math-Net.Ru,  and several country-based DMLs (e.g. DML-CZ, DML-PL, NUMDAM) have demonstrated proof of (at least some aspects of) the concept, and while many of the required software tools are under active development by a number of groups, both academic and commercial, the overall implementation of a truly Global Digital Mathematics Library has remained tantalizingly out of reach.  Nevertheless, several recent developments have rekindled expectations that we may at last have both the means and the will to realize the WDML within the near future.  These developments include:

On June 1-3, 2012, the CEIC organized the Symposium on The Future World Heritage Digital Mathematics Library held at the US National Academy of Sciences (NAS), involving over 50 participants from throughout the world.  The meeting was supported by a grant from the Alfred P. Sloan Foundation.   Participants, keynote talks, position statements, panel discussions, breakout sessions and more can all be found on the Conference Wiki.

In conjunction with the NAS Symposium, the Sloan Foundation further funded a broad-based committee to write the report “Developing a 21st Century Global Library for Mathematics Research” that explore the practical mechanisms, challenges, and capabilities that are required for the realization of the WDML.  The report was published by the US National Research Council (NRC) in March, 2014, and is also available on arXiv.

On August 17, 2014, in conjunction with the International Congress of Mathematicians in Seoul, South Korea (ICM2014), the IMU and CEIC hosted a meeting of a select group of experts, 13 in person and 8 remote, to plan the next practical steps towards the construction of the Global Digital Mathematical Library (GDML).  As a result, a smaller eight person working group (GDML WG), chaired by Patrick Ion, and under the sponsorship of the IMU, was created and charged with, before the end of the year, designing a road map for the practical next steps towards the GDML, determining its organizational structure, prioritizing the different requirements for its implementation, estimating an incremental budget, both start-up and sustaining funds, and fostering the writing of proposals to funding organizations.  Further details about the WG can be found in the following blog post by Patrick Ion.

Furthermore, the WDML was the topic of a successful and wide-ranging Panel Discussion at ICM2014 in Seoul on August 20.  The panelists were Thierry Bouche, Ingrid Daubechies, Gert-Martin Greuel, Patrick Ion, Rajeeva Karandikar, and June Zhang, with this author serving as moderator.  Further details, including links to the panel brief and background materials can be found on the CEIC web site, while a videotape of the entire panel discussion appears on Youtube.

It is the desire of the CEIC and the IMU that this blog will serve as a means for publicizing the ongoing developments in the planning for the GDML among the world-wide mathematical community, as well as serving as a forum for interested mathematicians and users of mathematics to add their views, suggestions, and vision for the enterprise.  I invite your input to the blog, encourage your conversations with colleagues, and look forward to a wide-ranging and lively discussion of all aspects of this exciting project and its potential impact on mathematics throughout the world.

Peter J. Olver