are just some of
the existing venues for electronic publishing and searching of mathematics.
But the level between graduate textbooks and research papers
is not well served at present.
We propose two parallel initiatives:
creation of a network of open access survey journals across
all areas of mathematics, and creation of a network of web sites
on particular topics (e.g. bottom-level MSC topics), each site
maintained by an expert editor using the ease of modern
software tools, providing both an "encyclopedia entry"
for the topic and updated links to electronic resources. An
is already in operation.
Mathematical publication today
Textbooks and monographs on one side, and peer-reviewed research journals
on the other side, are the most familiar categories of mathematical
publication. They have not changed in essence for 50 or 100 years, and
likely will not change much in the near future -
the transition of journals from paper to electronic
facilitates physical access
without changing the roles of authors, referees and editors
and (as yet) without resolving contentious issues of price.
But cyberspace provides opportunity for a much broader spectrum of types of
publication. One can already find online, for instance
peer-reviewed research papers
peer-reviewed survey papers
monographs and polished lecture notes
lectures recorded by slide presentations, scribe notes, and videos
retroactive digitization of old print literature
descriptions by individuals or groups of their ongoing research
encyclopedias at an elementary level.
We applaud this variety of content, but find three unsatisfactory
features of its structure.
Cost of journals.
Commercial publishers impose ever-increasing subscription costs on their ejournals, thereby restricting access, with negligible compensating advantages.
The totality of mathematical material in cyberspace is at present
neither well linked together nor intelligently searchable.
Seeking a readable account of Topic X, one could use a search engine like
But Google treats a mathematics page as just another page
on the Web, having no conception of the logical interrelationships of
mathematics. The new
service restricts the search to
the scholarly literature, accessing the content of many copyrighted books and
journals as well arXiv and other open access sources.
But it is not easy to restrict such a search to expository material.
enable basic searches like "find papers by author A in subject S".
But there is no resource currently available for a search like
"find a survey on topic X accessible to a first year graduate student".
Designing a system which can respond to such queries seems to require
more human intervention.
As another instance,
when you post your lecture notes on subject S,
you currently have no systematic way of providing links
to your material which make it easily accessible to
someone searching for material on subject S.
Research progress continually increases the gap between research
frontiers and first-year-graduate-textbook level material,
and the gaps between different disciplines.
Monographs help fill these gaps, but we see an increasing need for
At present, writing of expository survey papers carries insufficient prestige, and
such papers are often scattered in hard-to-find conference proceedings and
Writing high-quality surveys should be encouraged, to help organize mathematical
knowledge in accessible form, and to facilitate interdisciplinary work.
Instead of tackling each of these three difficulties separately,
we have a bold proposal which attempts directly
to solve the problems of fragmentation and compartmentalization, and
indirectly to reduce the cost of commercial journals, by promoting the value
of openly accessible content.
We propose the formation of a large collection of open access
electronic survey journals in mathematics, with articles
indexed by subject for ease of access.
We expect the main organization of survey journals to correspond to the
different branches of mathematics, but we hope that
national mathematics societies may contribute to the effort by supporting
open access publishing of high quality survey papers in all fields of mathematics.
The authors work in the field of probability, which
(as measured by papers in Math Reviews)
is about 1/25 of mathematics.
We describe our plan to survey the field of probability and stochastic processes,
with the idea that its structure may be copied (and tinkered with) about 25 times to
cover all of Mathematics. The Mathematics Survey is our vision of
such a system of surveys, one for each major branch of mathematics.
As the foundation for a survey of probability and stochastic processes, we have
started the new open access electronic journal
with support from the
Institute of Mathematical Statistics and the
This is a peer-reviewed electronic journal, with a basic user interface similar to that
of existing ejournals such as Geometry and Topology
and The Electronic Journal of Probability.
Survey articles can be of
various size and scope, ranging say from a
five page write up of a conference talk on recent developments
(or a five page account of some unjustly neglected classical topic)
to a several hundred page monograph.
They are posted on the web as accepted, with bundling into volumes of
convenient size for web display.
Papers are to be kept in a format like PDF or its successors, intended
to be printed out for reading rather than read on-screen.
We note that if high quality survey papers are provided an open access electronic outlet,
they should be widely cited, hence appear near the top of a citation ranked search
of scholarly articles such as now provided by Google Scholar.
An open access survey journal which already exists in
another branch of mathematics is Living Reviews in Relativity, supported by the Max Planck Institute.
We plan to promote the development of such journals in all branches of mathematics,
with the help of various organizations.
As a second encyclopedia layer of a survey of probability and stochastic
processes, we plan to exploit the structure of the 2000 Math Subject Classification
much like David Rusin's
but eventually may allow finer subclassifications and new overlapping classifications.
For instance topics such as
60J: Markov processes
60J80: branching processes
60J80-brw: branching random walk
would conceptually be nodes of the encyclopedia layer.
Initially, we imagine this to be just a
tree structured index, like that provided by
MPRESS for preprints,
which would allow the reader to easily browse lists of survey articles and other
open access material classified by subject. The structure of such an index is technically
quite light: a web-page for each node of the MSC can easily be generated by a script, with
some human-specified links, and the rest done by automated pointers to
e.g. MathSciNet, Zentralblatt MATH, and
A prototype for such a distributed system of scripted web pages, with authors instead of subjects,
and navigation by the author collaboration graph instead of a more complex graph
describing interrelations between subjects, is provided by the BibServer system.
A typical subject node would initially be generated by scripted links to existing resources.
As the content at a subject node expands, we intend that control over its arrangement
be provided by one or more associate editors who should develop a web site devoted to that subject.
For a relatively small fraction of subjects, such sites already exist, and
their maintainers should for the most part be willing to maintain content
consistently with requirements of the navigation system. The value of such
sites should be obvious enough that they will be created in areas where there
These sites and their maintainers would serve three interrelated purposes.
First, the site would contain original content designed to be read on-screen - minimally
a one page "encyclopedia entry" describing the subject, but this could be
expanded arbitrarily according to the energy of contributors.
Second, the site would assemble links to related content
available on the web, including relevant papers in the survey journal
and subject bibliographies.
Third, the maintainers of subject specific sites would typically be willing to
serve as associate editors of the survey journal.
Once this structure is set up, we expect it to quickly and
automatically become the canonical place to look for links to
graduate and research level mathematics: people who post
material on the web are ipso facto wanting others to
be able to look at their material, and will be happy to
take one minute to transmit the link to the associate editor
of the relevant node.
The kind of material on the existing
- links to personal home pages of probabilists, journals,
conferences etc - would become part of the material
associated with the top-level (60: Probability) node.
Along with the link structure, it should be straightforward to
search the collection of all sites linked to the Survey.
Is the project feasible?
Consider e-mail, TEX/LATEX, and the WWW.
Each started with individuals yet became indispensable,
because their usefulness was obvious and because
enough people were motivated to help implement them.
Similarly, the usefulness of a
is (we hope) obvious. But why do we expect people to contribute to it?
By emphasizing survey papers, for which few publication venues exist,
we expect that
will quickly become the definitive place
for authors to publish survey papers in probability.
Joining the project doesn't require a huge commitment of time
If you are an active researcher then you typically are
an expert on some subject node.
To get started as an associate editor maintaining a subject site, all that's needed is to write a one page description of that subject, insert it into a
suitable template and insert links to, and brief descriptions of, other online
material on that subject.
But these are all things you already know - it's just one
Continuing that theme, most people are happy to write about
their research speciality, so we hope that eventually
a large proportion of active researchers will participate as
subject node associate editors,
and will contribute occasional survey articles.
Indeed, provided the quality of the survey journals is well maintained,
as is in the obvious interest of the profession,
being invited to edit a subject node should convey
the prestige of being "an established research mathematician"
akin to receiving tenure.
We envisage dynamic interaction with one's professional work,
in that on the occasions when one needs to write research overviews - as
part of organizing a workshop, planning a monograph, assembling
a research group, making a grant proposal, giving a talk - one
takes the opportunity to make the intellectual content be
openly available on the web rather than hidden in private documents.
Why this particular approach?
Let us imagine three different projects;
(i) a survey ejournal of mathematics
(ii) an online encyclopedia of mathematics
(iii) a site which indexes and searches online mathematics.
In our opinion, each project is in one sense "too big" - it's
too difficult to cover all of mathematics under any centralized scheme - while being
in another sense "too small", in that it would just add an
extra category to the existing categories of mathematical
publication in cyberspace.
We are ambitious in that we are proposing all three projects
at once. But we hope that the obvious synergy between these projects
will sustain self-reinforcing growth into a new feature in the landscape of
We start with probability
as demonstration, because
there is a reasonably small, tightly knit community of probabilists,
with a strong sense of the identity and importance of their subject in the
larger scheme of mathematics and science (exemplified by specialist societies,
the Bernoulli Society
and the Institute of Mathematical Statistics.
We think it essential that the project be perceived as being run
by the mathematical community as a whole, so we expect that
individuals' involvement in the project should be largely self-organizing,
with only a small degree of hierarchical structure.
Perhaps controversially, we regard it as undesirable for the project to be
controlled by any single scholarly society, for three reasons.
Existing mathematical societies (AMS, SIAM, ...) comprise
geographically- and subdiscipline-bounded
subsets of the very broadly defined mathematical sciences community,
and such boundaries are anachronistic in cyberspace.
Societies have bureaucratic structures, which make them slow to innovate or create.
And most of them derive revenue from existing publications, causing
a perceived conflict of interest with the principle of free access underlying
We do appreciate however that AMS has encouraged authors and editors to use
its extremely useful
MR Lookup and
facilities by pledging to maintain
these services on an open access basis.
This and other developments, such as the general support for open access
provided by the European Mathematical Society through
and by the International Mathematical Union through its
offer hope that within a few years time a significant fraction of the
mathematical literature may be navigable on the web without gates or tolls.
The mathematics survey project could only ever represent a tiny proportion of
all journal publication, so it would not directly ameliorate the systemic
problem of journal costs. But every successful open access project
is progress toward the tipping point when expensive journal subscriptions
More about the project
1. The survey journal is intended to be non-competitive; any
submission reaching the required standard of scholarship will be accepted.
Refereeing is intended to improve quality of exposition and to ensure that
the paper does a reasonably complete job of surveying the subject
(whether broad or narrow) that it claims to survey.
2. The encyclopedia layer is not enslaved to the MSC classification.
If an individual perceives some topic as an interesting research area
and can articulate that perception clearly, then they can create a new node
for that topic in the encyclopedia layer.
Indeed, as one of many barely-foreseeable side benefits of the project
once established, a listing of recently-created nodes may become the
best list of "hot topics" in mathematics.
Obviously it will be necessary to provide some technical organization
of format for web pages and the survey journal and their cross-links,
but that sort of thing is becoming easier and easier to automate on
a wide scale. Moreover, web crawlers such as CiteSeer
and Google Scholar
do much to compensate for lack of uniformity of various sites.
We seek to minimize requirements for administration of people.
Being an editor of Probability Surveys
or a sibling survey journal
may entail effort and responsibility comparable to being editor
of a major research journal. We expect these sibling editors to communicate,
but a formal structure seems unnecessary.
4. There is little hope for any human endeavor predicated upon
100% altruism and 0% self-interest. But with regard to self-interest,
we have already mentioned prestige, added to which there is the opportunity to
publicize one's own view of a mathematical area.
Another aspect (addressed to U.S. readers but surely with analogs elsewhere)
is that N.S.F. funding programs increasingly seek a
"contribution to infrastructure",
for individual, group, interdisciplinary and VIGRE-type grants.
Involving postdocs and advanced graduate students in the writing of
encyclopedia entries and survey papers can perhaps be counted as contributing
to the "informational infrastructure" of the Mathematics Survey,
as well as to "human infrastructure" in that we are training them to write well.
How to help
The first volume of Probability Surveys was posted online in 2004.
We hope to launch the encyclopedia layer soon. We would appreciate
technical assistance with design and content management for a generic subject
site. We encourage mathematicians in other fields to take the
initiative of starting up sister survey journals in their fields,
and we will do what we can to facilitate this process.
Please contact us at firstname.lastname@example.org, and
see http://mathsurvey.org/ for
more information about the project.
A talk based on this article was given by Jim Pitman at the
Special Session on Electronic Publications at the Joint AMS-SMM International
Meeting, Houston, May 13, 2004. The article appears also in the volume
New Developments in Electronic Publishing of Mathematics
edited by Hans Becker, Kari Strange and Bernd Wegner, and published by Fiz Karlsruhe, 2005.
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