Communication of mathematical research and scholarship is undergoing
profound change as new technology creates new ways to disseminate and
access the literature. More than technology is changing, however; the
culture and practices of those who create, disseminate, and archive
the mathematical literature are changing as well. For the sake of
present and future mathematicians, we should shape those changes to
make them suit the needs of the discipline.

For this reason, we have identified a number of "best practices" for
those involved with the mathematical literature mathematicians,
librarians, and publishers. Many of these are practices that apply to
other academic disciplines as well. Although we focus primarily on
mathematics, we recognize that we can learn from each other as we
move forward, and that no single discipline should act in isolation.

Our advice is meant to guide practice as it changes rather than to
set forth a collection of firm rules and admonitions. The
recommendations concern all forms of scholarly publishing and do not
promote any particular form. Indeed, the authors of this document
hold many differing views on the future of scholarly publishing. The
common principle used to formulate our recommendations is that those
who write, disseminate, and store mathematical literature should act
in ways that serve the interests of mathematics, first and foremost.

This is advice that is meant to ease the transition in scholarly
communication for present mathematicians. Most importantly, however,
it is advice aimed at protecting mathematicians in the future.

**1. Structure and Format.** Logically structured documents
correctly reflect the content of a mathematician's work, setting
forth results, arguments, and explanations to make them
understandable to readers. But a logical structure also makes it
possible to retrieve and eventually to update the document.
Identifying the constituent parts of an electronic document is
essential in order to move from one format to another without human
intervention. Authoring documents should be more than setting down
mathematical research in a pleasing format.

Authors are encouraged to provide the structure necessary to use
their documents now and in the future. The aim is to create a master
file from which the various other formats can be derived. [In
mathematics, LaTeX is a congenial and accessible way to give
documents some structure without adding unreasonable burdens on the
author.]

**2. Linking and Enrichment.** An electronic publication can offer
much more than a print publication. Electronic publication gives the
user the ability to move effortlessly among the various parts of a
paper or even from one paper to another. In order to make this
possible, however, someone must add the necessary information to
establish links in the electronic version.

Adding links is easier when authors provide the information necessary
to establish them. [Correct cross-referencing and citation in LaTeX
transforms readily into hyperlinks, yielding enriched electronic
versions of one's work. Hyperlinks may be used in PDF files as well.]

Moreover, electronic publication is not restricted by the constraints
of the traditional print medium. This provides an opportunity to
detail material that might otherwise be dismissed as "well known''
and to add explanatory appendices. A little less easily, whenever
appropriate, one may include graphic enhancements, animations,
extensive data, tools to analyze that data, or even active examples
that may be varied by the reader.

**3. Versions.** Online publication can lead to severe problems in
citation, because the posted paper can be updated continuously until
it bears little resemblance to the original, as an author corrects,
adds, and deletes material without indicating that changes were made.
As the mathematical literature grows, references to non-existent
papers and results will eventually jeopardize its coherence.

To avoid this problem, papers that have achieved a sufficiently final
state should be stored in an immutable form. This includes any paper
to which others may make reference, whether published in refereed
journals or posted as a preprint. If revisions subsequently are
necessary, each released version should be clearly labeled with its
own version number and old versions should remain available.

**4. Personal Homepages.** Mathematical communication is more than
merely posting or publishing papers. Information about the
mathematical community and its activities is valuable to all
mathematicians, and it is now easier than ever to circulate and to
find such material.

Mathematicians are encouraged to have their own homepage. Ideally,
basic data on such a page (or on a "secondary" homepage) should be
presented in standard form to allow ready automatic compilation into
databases.

[Material found at http://www.math-net.org/Math-Net_Page_Help.html
describes the Math-Net project, which provides standardized homepages
for departments and institutes.]

**5. Personal Collected Works.** Mathematics ages slowly. Access
to older literature is important for most mathematicians, and yet
much of the older literature is likely to remain unavailable in
electronic form in the immediate future. Mathematicians can change
that by taking collective action.

Whenever legally and technically possible, mathematicians are
encouraged to scan their old (pre-TeX) papers and post them on their
homepages, making their "collected work" readily available to all.
This relatively small effort on the part of every mathematician will
provide enormous benefit to the entire community.

The *Call to Mathematicians* found at http://www.mathunion.org provides
further information.

**6. Preprints and archives.** Mathematical writing is ineffective
if it is not communicated. A generation ago, the photocopier made it
easy to send preprints to one's peers. Today, as a substitute, we
have departmental servers, homepages, and public archives. [The arXiv
(http://www.arxiv.org/) is one prominent example.]

It is a good practice to place one's preprints both on a homepage and
in an appropriate archive. Either copy serves to communicate the
mathematics to one's peers, but the public archive will make it more
likely that others can reference your work in the future.

**7.
Copyright.** While copyright is a complex subject that is far removed
from mathematics, copyright law and policy can profoundly affect the
ways in which mathematics is disseminated and used. Copyright is
important for mathematicians.

Authors should be aware of the basic
principles of copyright law and custom. Decisions about copyright for
one's own work should be made thoughtfully.

The material found at
http://www.ceic.math.ca/ serves as a good reference.

**8. Journal Price and Policy.** Libraries have
limited budgets, which often grow more slowly than the prices of
journals, forcing libraries to cancel subscriptions. The cumulative
effect of cancellations goes beyond individual institutions because
it shifts costs to an ever smaller number of subscribers,
accelerating the process of price increase and cancellation. Journal
prices matter to all mathematicians.

When deciding where to submit a
paper an author may choose to be aware of a journal's standing and
impact, but an author also should take account of a journal's price
(as well as its general policies, including archiving). In addition,
one might consider a journal's price and policies when considering
whether to referee or serve on an editorial board.

**9. Validation.**
Publication and peer review processes are increasingly detached. The
emergence of overlay journals, archival preprint servers, and other
new structures of publication raise new and pressing questions about
the appropriate forms of validation. These are important issues for
all scholarship, but even more important for mathematics since it is
essential to know which parts of the mathematical literature are
valid.

Both mathematicians and decision makers need to be alert to
the distinction between posting and providing validation. Editorial
boards should be explicit about the form and the level of validation
they provide for papers and make this information plain to all users.

**10. Statistics.** Electronic delivery of information has changed the
nature of statistics available to assess the usage and the 'value' of
academic literature. Gathering statistics from the Internet is
notoriously complicated, and even those who are knowledgeable about
the pitfalls can be inadvertently or intentionally misled. As
librarians and other decision makers increasingly rely on web
statistics (such as the number of hits, page accesses or downloads)
it is important to be informed about the nature of such measurements
and the difficulty in gathering and interpreting them. Moreover, the
value of a particular resource is often not best measured by simply
counting the number of times it is currently used in some way. This
is especially true in a field like mathematics in which current
research continues to play such a significant role far into the
future.

Given that statistics, while subject to misuse, are valuable
and will be used, it is important that mathematics researchers and
research librarians are alert to these rapidly changing issues and
are prepared to make appropriate arguments for mathematics.

**11. Partial Access.** Many
journals restrict access to (paying) subscribers. As the web of
mathematical literature grows, however, it will be increasingly
important for all mathematicians to navigate that web, whether or
not they have access to complete articles. This allows
mathematicians to learn basic information about an article, even when
they do not belong to institutions that have the financial resources
to support the journal. It is especially advantageous to
mathematicians from the developing world.

Journals should provide
unrestricted access to tables of contents, abstracts of papers, and
other data, such as keywords. Where practical, journals should also
provide unrestricted access to reference lists with links, allowing
all mathematicians to navigate the web of literature, even when they
don't have access to the fulltext of some parts of that web.

**12.
Eventual Free Access.** The scholarly enterprise rests on the free
exchange of ideas, and scholars need to have easy access to those
ideas. Many journals, however, rely on subscriptions to recover
costs and to provide an incentive to publish, forcing them to limit
access to subscribers. Access should be a balance between those two
needs, of scholars and of publishers.

Limiting access to subscribers
for a fixed period of time after publication may be necessary for
many journals. In order to ensure appropriate accessibility for the
electronic literature, we encourage all journals to grant free
access after that fixed period of time.

**13. Archiving format.**
Ensuring the success of longterm archiving is more than storing the
electronic data on reliable media in multiple locations. As software
and formats change in the future, the data will require modification
and updating. Not all electronic formats are suitable for these
purposes.

In general, electronic documents should be stored in their
most primitive format, that is, the format used to derive subsequent
formats. Any format in which material is stored should follow an
"open standard'' that has a detailed public specification. This will
increase the likelihood that scholars working decades or centuries
from now will be able to use the material.

**14. Archiving
responsibility.** Traditionally, maintaining the older literature has
been the responsibility of librarians rather than publishers. Even in
the electronic age, scholars and the librarians who represent them
have the greatest motivation among all of the affected parties to
ensure the preservation of older material.

We recommend that
electronic archives of the mathematical literature should ultimately
be under the control of the academic community.

**15. Licensing and Bundling.** Some licensing and bundling
arrangements for journals accelerate the transfer of control of our
literature away from mathematicians and research librarians. When
institutions are forced to accept or reject large collections of
scholarly literature covering many different disciplines, the
decisions are less likely to be made by scholars. As a consequence,
the normal processes that promote the highest quality journals become
less effective.

The best protection, as always, comes through
staying well informed and alert to these issues. In general,
decisions about journal adoptions and cancellations should be made by
academics and librarians.

**Postscript on Developing Countries.** Today,
active mathematicians depend on access to electronic information
online journals, databases of reviews, and preprint servers. More
than access, research mathematicians need the tools to create and
edit documents in standard formats [such as LaTeX, Postscript, and
PDF]. This is true for mathematicians everywhere, including those in
developing countries. Implementing many of the recommendations in
the preceding document makes little sense if mathematicians are not
connected to the Internet or have no tools to create electronic
documents.

National mathematical societies and academies in
developing countries need to impress on their governments the need to
establish the infrastructure necessary to provide high speed
connectivity among academic institutions.

The entire mathematics
community should encourage and support specific actions designed to
help in this effort, which include:

- Establishing "mirror" services that provide quick access to users of electronic services within each region.
- Establishing local help and service centers that spread expertise on the use of common standards [for example, LaTeX].
- Creating small groups who tour the region and demonstrate the use of technology for research and study.

*Committee on Electronic Information Communication
International Mathematical Union*

**Remark:** The above recommendations
have been stated in very general form. Whenever reference to existing
formats [e.g., LaTeX, PDF], to archiving systems [e.g., arXiv], or to
information and communication systems [e.g., Math-Net] has been made
this is meant for illustration and not to promote these formats and
systems. The IMU EC has asked CEIC to enhance, whenever appropriate
and useful, individual recommendations by adding links to web pages
that explain some of the technical issues involved, provide
additional information, or contain (possibly controversial)
discussions of the topics addressed. These links will be under the
responsibility of CEIC and are not subject of the IMU EC
recommendations.