The International Math Union's Electronic Initiatives

Jonathan Michael Borwein, FRSC
Shrum Professor and Canada Research Chair

Director, Simon Fraser CoLab

Centre for Experimental and
Constructive Mathematics
Simon Fraser University, Burnaby, V5A 1S6, BC





·      Great changes are underway in the way we compute and communicate. This extended and annotated introduction discusses a few of the changes that impinge especially on the mathematical sciences, concentrating on the initiatives of the IMU.


·      The full CEIC Report to the General Assembly is available on line in Word and PDF at


·      This is a complicated world, for example, the Canadian Mathematical Society adheres to the IMU within the International Council of Scientific Unions (ICSU, via the Canadian National Research Council (NRC)!


·      And as Mathematicians we are growingly powerless to effect our future.

·            As evidence of the changes, I refer to two recent issues of Computers in Science and Engineering, a journal that is jointly published by the ACM and the IEEE. The first, in February 2000, was on the Top Ten Algorithms having

"the greatest influence on the development and practice of science and engineering in the 20th century".

See also the Science News coverage at

( entitled `Algorithms for the Ages'.


·       A follow up issue in May 2001 was on Tomorrows’ Hardest Problems


It  includes my article with P. Borwein, discussing

"Challenges in Mathematical Computing."

 A true preprint -- the editor actually edited -- is available at

·      Therein, we make the claim that


"Almost all interesting mathematical algorithmic questions relate to NP-hard questions and such computation is prone to explode exponentially. More space, more speed and processors, and even say massive parallelism will have an impact but it will be largely at a `micro not macro' level. We anticipate the greatest benefit accruing from mathematical platforms that allow for highly computer assisted insight generation (more `aha's' per cycle), not from solution of grand challenge problems."


·      While I talk primarily from the perspective of a researcher, it is important to remember how many `players' there are and how small a part of the scheme mathematical science publishing and computing really is.


·      Though we, like Tom Lehrer, know math is everywhere, in reality even the bioscience disciplines are likely to tread over us.


·       For example, Nobel Laureate Richard J. Roberts recently wrote in "PubMed Central: The GenBank of the published literature", Proc. Natl. Acad. Sci. USA, Vol. 98, Issue 2, 381--382, January 16, 2001


"What is a reasonable delay? I would argue that 6 months seems a reasonable time for a journal to monopolize the content. Most of us would not dream of scanning the contents of a journal published 6 months ago unless we were searching for a specific article. Thus it seems unlikely that a large number of subscriptions would be lost if 6-month-old issues were made freely available. I think rather few worthwhile journals would be adversely affected if they were to institute such a policy."

·      Such an outcome would destroy most current mathematics society publishing. Despite that, such issues are not high on mathematicians’ agendas. For example, only a handful out of over ten thousand mathematicians have chosen to grant the AMS permission to publish rather than transfer copyright, since they were offered the choice more than five years ago.

·      Nor do we often take care to distinguish public ventures from purely commercial initiatives like (which actively hides its Elsvier roots).


Neutrality (Nature, Sep 6 , 2001)

"But PMC and E-Biosci highlight the urgent need to index the full text of papers and their metadata and not just abstracts, as is the practice of PubMed and other aggregators.


The reality is that all of those involved in scientific publishing are in a period of intense experimentation, the outcome of which is difficult to predict (see Tim O'Reilly, Information wants to be valuable). Getting there will require novel forms of collaboration between publishers, databases, digital libraries and other stakeholders. It would be unwise to put all of one's eggs in the basket of any one economic or technological 'solution'. Diversity is the best bet."


·      As Lawrence Lessig cogently points out, innovation and freedom are under digital threat at content, code and concrete levels.


I finish this introduction by quoting Lessig quoting Jefferson on the nature of ideas.



``If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of everyone, and the receiver cannot dispossess himself of it. [2] Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lites his taper at mine, receives light without darkening me.



 [3] That ideas should freely spread from one to another over the globe, for the moral and    mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density at any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement, or exclusive appropriation. [4] Inventions then cannot, in nature, be a subject of property.’’



·       Letter from Thomas Jefferson to Issac McPherson (August 13, 1813), in The Writings of Thomas Jefferson 6, quoted from page 94 of The Future of Ideas by Lawrence Lessig, Random House, 2001. 





·      To further set the stage:

``The work then proceeds in a manner unique to science. Because practitioners publish their work electronically, through the e-print archives at the Los Alamos National Laboratory in New Mexico, the entire community can read a paper hours after its authors finish typing the last footnote. As a result, no one theorist or even a collaboration does definitive work. Instead, the field progresses like a jazz performance: A few theorists develop a theme, which others quickly take up and elaborate. By the time it's fully developed, a few dozen physicists, working anywhere from Princeton to Bombay to the beaches of Santa Barbara, may have played important parts.''

Gary Taubes, ``String Theorists Find a Rosetta Stone," Science July 23 (1999) 513.


·      I next draw attention to various specific CEIC activities:


a.   Our statement on copyright and related copyright activities; and more generally on current Best Practices;


b.      Our plans for development of personal collected works and;


c.      Our attempts at propagating secondary home-pages -- such as CECM's at:   ---  and my own personal home page

       See also the Installation Interface:


d.   I also note the growing attempts to collect mathematical data in ``global data-bases" such as arXiv:


e.   The arXiv has grown out of the Los Alamos preprint server, which has now moved to Cornell


and so should mesh better with the various World and Digital Library Initiative (s), Euclid, and like projects.


·      I especially note CEIC's own involvement with:


1.                    MPRESS: through international extension of the German Math-Net:


2.                    Persona Mathematica:


3.                    Other services still to be set up, in accord with the MathNet Charter:


·      These, and like topics, will be covered by many other speakers today. They were described in some detail in Swanzl and Sperber's contribution to the 2001 Linz meeting: MathNet: Semantics, Visualization and Internalization.

·      I conclude by discussing our hopes to further develop tools for coordinating these efforts -- and the issues and obstacles involved.

For example, in our mandate we were asked to "consider transferring the World Directory of Mathematicians to an electronic freely accessible form". For logistic and IP reasons, we have recommended not now doing so.


·      More generally, I would see our future as less technological and more advisory:  providing a clearing house and an advisory role on these  and similar complicated issues.  

Our Best Practice and Copyright documents are already serving as models for other disciplines.

·      In each case the active endorsement of the IMU Executive has proven invaluable.



·      The period in which we as academics might ensure control of any significant part of this rapidly changing environment is rapidly slipping away.


·            Despite the obstacles, the rewards can be amazing:

`` Three years ago, said Dr. Zanelli in Chile, one of his own students posted a paper and the next day received an e-mail message from Dr. Witten. The student was at first so shocked that he accused Dr. Zanelli of playing an elaborate practical joke.

We learned that great physicists do read the archives daily and they browse through all the preprints,' Dr. Zanelli said, `even if they come from an obscure place in the end of the world.'

Dr. Witten's instant response, Dr. Zanelli said, `was like having the pope drop by for tea.' ''

James Glanz, ``Web Archive Opens a New Realm of Research,'' New York Times, April 30, 2001.


July 5, 2002