November 25, 1999

This is the text of a talk to be presented at the conference on the Future of Mathematical Communication at MSRI, Berekeley Dec. 1999. |

In this short note we look at the “Future of Mathematical Communication (over Telecommunication Media)” from the perspective of mathematicians working in India. There is a likelihood that the comments herein would also apply to mathematicians working elsewhere; such as Sri Lanka, Pakistan, Nigeria and so on. To start with we look at things from the end-user’s point of view. Next we look at the services that can be provided and finally we explore some possible plans for expanding mathematical activities on the internet and elsewhere.

The primary access that most mathematics departments in India have to
internet services is through a dial-up link at 38.4 KBps or less. Thus
it is of some importance that mathematical content that is intended
for this audience should take such bandwidth into account. This means
limiting the use of graphics, streaming audio/video and other forms of
multimedia^{1} .
However, I feel this should not affect mathematical communication much for the
following reasons.

- While pictures “speak a thousand words” the quality of mathematical exposition is judged by its precision and rigor. Both these qualities call for less bandwidth utilisation!
- Very few mathematical papers even today use the two dimensional nature of print, let alone three or four dimension provided by high-end graphics and multimedia. By the time these tools acquire the precision required to communicate mathematics we should have a more equitable world order in terms of bandwidth availability.

Most mathematicians would like to see the thought/calculation/program that produced a particular graphical result and not be limited to the result itself. Thus it would be far preferable (in mathematical communication) to embed in a document the actual steps of computation rather than the result of the computation alone. This assumes that the receiver has access to computational facilities comparable to those of the sender. (Examples of such use are sending compressed text, use of Java, Perl or other multiplatform languages to send the program). An assumption of reasonable computing power at the finger-tips of the end-user is far more valid today than the assumption that all the end-users have access to similar network bandwidth.

Research and academics has always been an area of open access. This accessability has to be retained and if possible enhanced. Access to new research has increased by using the internet to access preprints containing latest research. However, there are certain opposite trends. For example, when a traditional library buys a book or journal any visitor can read/browse the collection. A sibling library can get the document through inter-library loans. On the other hand on-line access to journals is often much more restricted. The archived information is also much more difficult to access. This leads us to the discussion of copyright and other issues that have already been discussed by W. Hodges.

With the above points in mind I have always felt the importance of duplicating the
availability of mathematical literature which can be freely copied. Thus we
have already set up a mirror of www.arXiv.org at the IMSc, Chennai. In
addition, a replication or “mirror” of the Math-Net services is also in the
pipeline^{2} .

One of the features that would be a nice addition to the preprint service (and which is perhaps implementable via Math-Net) is e-print reviews. This could further be extended to “annotated” documents. Thus instead of Prof. X. Pert’s links to “interesting papers dealing with . . . ” we could have a student’s guide to reading these papers (similar to J. F. Adam’s Student’ Guide to Algebraic Topology). Hypertext links would allow one to give clear references within the relevant texts. We also need to accomodate “legacy” documents or others which would not provide hypertext pointers. This would require the possiblity of HTML or meta-data enhancements allowing one to “seek” into an existing document. All such use would lead to copyright issues which need to be resolved.

Another project that would enhance the mathematical worth of computer based information would be if one could wed the philosophy of Bourbaki (a bad word nowadays!) with that of software documentation projects such as the LDP (Linux Documentation Project). The idea would be to provide a complete exposition of a given research topic. Such expositions would have a “current maintainer” who keeps the guide up-to-date with proofs and or detailed references. One of the obvious enhancements would be that gaps, errors, additional examples or counter-examples would become available to a new entrant from a “standard” source. The maintainers job would have to be voluntary but would probably be rotated in some way.

All the above ideas require a lot of work to be put in, in the areas of exposition and documentation. To put either these ideas or others like them to work at least some of us must let go of the maxim “those who can do and those who can’t teach”. The great burst of mathematical research over the last 100 years and more will lie unread in research papers unless we improve the art of mathematical communication.