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


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