The Future of Mathematical Communication - Abstracts

Patrick D. F. Ion, Mathematical Reviews, American Mathematical Society

Lessons from the past of Mathematical Communication

We can perhaps usefully look at some past events in the history of mathematical communication to remind us of some pitfalls that may lie between us and its wonderful future. A story about attempts to provide universal mathematical encoding may be relevant to some of today's efforts. The tragic tale of a wonderful bibliography and its loss may remind us of the importance of conscious archiving and multiplexing. Some of the excesses of notation standardization may remind us of present trends. Other instances will be mentioned as time permits.

June Lester, Centre for Experimental and Constructive Mathematics

Communicating with Interactivity

For mathematical communication, the great promise of computers is interactivity, the ability to make mathematical objects respond to user actions. Thus an equation transforms at a mouse click into an equivalent form, a geometric configuration retains its integrity when its components are dragged to new positions, or a graph changes shape continuously as the parameters describing it are changed. New modalities are still to come: what sound would a curve make, for example?

I look at questions of *communicating* with interactivity, i.e. the process of designing, refining and confining interactivity appropriately in order to demonstrate a given mathematical idea, or to focus the reader experience in a chosen direction. Numerous examples of gratuitous, ineffective or misleading interactivity can be found on educational CDs, on the web and elsewhere. I'll look at some of them, and attempt to formulate some general design principles of interactivity for effectively communicating mathematics.

Jeremy Gunawardena, BRIMS, Hewlett-Packard Labs

WebSeminars

Technology now allows us to do something we've never been able to do before: to capture much of the content of a seminar or lecture or tutorial and make it available to anyone with access to the Internet. Where previously you had to coincide in space-time with such an event, now you dont. In fact, it is not that simple and, like most consequences of digitalisation, it will probably bring mixed blessings. I'll discuss our experiences in making WebSeminars at BRIMS and speculate about where these trends will take us.

Howard Ratner, Springer-Verlag, New York, Inc.

Reference Linking Using DOI

Online publishing of serial articles is quickly becoming commonplace. The most common form of pointers to other pieces of content is the reference citation. Digital Object Identifiers (DOI) are one way to facilitate this online linking. DOI-X is an implementation of a reference linking system utilizing: an XML DTD for batch upload of DOIs and associated metadata to a centralized database; batch loader and query facility.

Robby Robson, Dept. of Mathematics, Oregon State University

Metadata for Mathematical Resources: Show and Tell

Metadata is "data about data." It is provides a way of labeling an electronic resource with familiar types of information, such as title, author, copyright, language, and subject classification, as well as with information such as technical specifications, level, difficulty, duration, and approach that speak to its utility in a specific environment and to a specific user. In the print world metadata is familiar from the spines of books and library card catalogues. In the electronic world metadata are more complex, more powerful, and more essential. During the past year, several major metadata efforts have converged and are producing metadata specifications which are on their way to becoming standards through the IEEE learning technology standards committee. A mathematics metadata working group with a focus on broad pedagogic applications has been working within this framework to develop a set of metadata standards for mathematics. The emphasis of this work to date has been on subject taxonomies for levels of mathematics not addressed by the MSC, on metadata elements that will need particular attention from the mathematical community, and on supporting the integration and enhancement of digital libraries. This talk will give an overview of structured metadata, demonstrate a vision for its use in educational settings, discuss the working group's approach to mathematical subject taxonomies, show some of the taxonomic work that is due for more public review in early 2000, and demonstrate how the metadata under development is being implemented and used in digital libraries.

Eberhard Hilf, Dept. of Physics, Carl von Ossietzky University, Oldenburg, Germany

Distributed Science Online Services by Distributed Workforce

-- Plans and experiences in Worldwide Physics Communication and Information 1. Professional (metadata driven) home pages for Individuals and Institutions --experiences, prospects of add on services 2. The distributed network of all worldwide Physics Institutions -- general information, documents, theses 3.Research field specific 'portals' for information and communication. -- concept and status 4. Ongoing active virtual research workfields -- the role of researchers and lurkers 5. Distributed teaching and teachers: the distributed virtual University.

Alexei Zhizhchenko, Russian Academy of Sciences

Integrated System of Information Resources of RAS

The Current State of the Implementation: At the moment the first version of the ISIR is implemented and is accessible by the address 'http://isir.ras.ru/' for Russian version and 'http://isir.ras.ru/en' for the English one.

The system is implemented as a digital library and supports different types of resources that are essentially data types of digital objects kept in the digital library.

Resources are closely related with each other and these relations are supported by the system.

The system supports the following resource types: person, organization, department, publication, and project.

Resources organization and department have the following attributes: full and short names, organization type, address, phone, e-mail, URL, the way to access, historical remarks, activity, picture, staff.

Resource person has the following attributes: full name, academic degree, position, activity, picture.

Resource publication has the following attributes: title, annotation, date, publishing house, theme, full text.
Resource project has the following attributes: title, description, dates, theme, key words.

The system is multilingual, but at the moment only information in Russian and English is loaded. To support hierarchical relations and different thematic classifiers special navigation mechanisms are implemented that take resource types into account. It is possible to search resources by values of their attributes, to edit them using Web interface.

It is possible to navigate through space of resources, looking the resource properties, loading their contents. Different levels of access control are provided.

Resource metadata are kept in a relational database, resource contents is kept either in RDBMS, or in a file system, depending on resource type. A resource can have a number of copies that can have different formats.

The system is currently implemented under UNIX (S) and MS Windows NT, with the use of RDBMS Oracle and Oracle Web-server. The implementation for MS-SQL Server and Access is now under development.

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Zsuzsa Koltay, Coordinator of Electronic Publishing, Cornell University Library

Project Euclid

Project Euclid is Cornell University's initiative to advance effective and affordable scholarly communication in theoretical and applied mathematics and statistics. We recently concluded a planning grant, sponsored by the Andrew W. Mellon Foundation, to define our focus. The planning process included needs assessment and a scan of the field of journal publishing in mathematics. I will discuss our findings, our vision of the future, our goals for the project, and what our next steps will be.

Martin Grötschel, Konrad-Zuse-Zentrum für Informationstechnik and Technische Universität Berlin

MathNet: A Model for the Future Role of the Mathematical Community in Information and Communication?

Scholarly publication, information, and communication is in a stage of a possibly far-reaching transformation. This change is based on a revolution in computing and communications technology. Several questions come up immediately:

Should mathematicians ''sit and wait'' to see how this ''market'' is going to develop? What should the mathematical community actively do? What role should the mathematical societies assume in the future?

My answer is: Engage proactively!

In this talk I will first give a short review of the current developments and my analysis of the chances and dangers arising. My conclusion (and I hope that this vision is shared by many others) is that we need an open, high-quality, distributed, user-driven and -friendly electronic information and communication system that integrates the worldwide avtivities of various groups of mathematicians, librarians, publishers, etc. in an unbiased way. The system should allow easy navigation and retrieval, in particular, precise browsing and search to provide efficient support for research, teaching, and the use of mathematics by others.

I will provide scientific, technical, and political reasons why I think that all these attributes are necessary. I will also argue that such a system has to be developed and maintained within some organizational framework, which, however, must provide sufficient openness and flexibility to integrate efforts and activities of diverse groups, e.g., groups that do not necessarily see their own contributions within an organized (and thus somewhat bureaucratic) structure.

I suggest that the International Mathematical Union (IMU) provides this frame. IMU is an organization that has - in its 50 years of existence - proven to be able to steer international collaboration within mathematics, despite politically rough times. IMU is the best possible choice to monitor the system development and define the standards, e.g., for mathematical data and documents and the interoperability of software. Through its organizational structures, IMU has the possibility to assure participation of mathematical societies from all over the world.

I will outline the technical and organizational concepts underlying the MathNet system developed in Germany in the recent years. I propose to use the German MathNet as a prototype for the system to be set up under the auspices of IMU. The persons and groups in Germany involved in the MathNet project are willing to contribute their achievements and experiences to the new international system.

For detailed information on MathNet see: http://www.mathnet.de/

The final result of all these efforts could be as follows: All partners (i.e., mathematical departments and other institutions, mathematical societies, individuals, publishers, libraries, etc.) make their electronic resources (e.g., preprints, papers, lecture notes, books, information about research projects, personal information, job offers, software, data of practical applications) that they are willing to make freely accessible available in the internet in structured form. The data structures are set up in such a way that mathematical information of a specific type can be gathered automatically (e.g., by robots). The system has to be designed in such a way that various types of relevant services can provided (that are up-to-date and of high quality with respect to the standards the system targets for). Existing services in the German MathNet system are: a preprint index (MPRESS), a collection of mathematical persons (PERSONA MATHEMATICA), an institution NAVIGATOR, and some others.

No insurmountable technical difficulties (e.g. high storage capacity, network and computer speed) arise in this context. Appropriate and not too costly hardware is available. Even open software, such as HARVEST, on which such a communication and information system can be based is on-hand. The hardest part is, most likely, of organizational nature. Will we be able to convince sufficiently many ''players'' to particpate? Will they regularly contribute their resources in an orderly fashion and will they maintain this service?

I believe that a system such as the one outlined above can be set up and maintained. I also believe that such a system would be of great help for the working mathematician. Today, very many institutions and individuals make their electronic resources visible in the internet. If everybody adds an epsilon of effort to structure the information a little more the whole world could search and find mathematical information much more effectively.

CALL: Let's not wait until others have decided what is good for mathematics. I, thus, propose to form - under the auspices of IMU - a community of mathematical institutions and individuals dedicated to develop and maintain a mathematical information and communication system as sketched above. Let's launch the initiative at the Berkeley workshop and build up the necessary infrastructure!

Loki Jorgenson Digital Editor, Canadian Mathematical Society

Prospects for Open Source Scholarly Publishing

The Open Source phenomenon, made famous by Linus Torvald's Linux project, has offered the promise of a more democratic, grass roots approach to many undertakings. In the context of software development, the term "open source" has acquired specific meaning. But what does it mean to publishing and, in particular, scholarly communications? Is it still about software, meaning the underlying systems supporting delivery and publication? Or is it about the authoring process, allowing many hands to contribute to a single work? Or is it about distributing the functions of editting, referring and review? Does it apply only to the Internet or does it apply to hardcopy too? And who profits? And how?

Bernd Wegner, Technische Universitaet Berlin

Projects in Electronic Information and Electronic Publication supervised by EMS

Literature databases, scientific journals and communication between researchers on the electronic level are rapidly developing tools in mathematics having high impact on the daily work of mathematicians. They improve the availability of information on all important achievements in mathematics, speed up the publication and communication procedures and lead to enhanced facilities for the preparation and presentation of research in mathematics.

The European Mathematical Information Service (EMIS) tries to bundle several of these facilities in a joint offer, to extend them by innovative components and to distribute them in a system of replicators for the benefit of mathematicians worldwide. EMIS has been founded by the European Mathematical Society (EMS) and is run under their supervision with support from the office of Zentralblatt MATH in Berlin. It is based on the voluntary supply of input from sources distributed worldwide.

The aim of the lecture is to give a more detailed report on one of these projects, the so-called EULER porject developing a search engine for distributed mathematical sources in the web, and to survey related activities like the databases MATH and MATHDI and the JFM-project for the indexation and digitalization of classical literature in mathematics. Additional projects like the Electronic Library, offering a variety of freely accessible electronic journals in mathematics, and the preprint index MPRESS will be subject of other lectures.

John Ewing, Executive Director, American Mathematical Society

Predicting (and Protecting) the Future

Robert Miner,

The Surprising Success of MathML

The World Wide Web Consortium issued the Mathematical Markup Language (MathML) Specification as a Recommendation in April 1998. In the ensuing months, a variety of software applications have implemented MathML support, and work on native support for MathML rendering in web browsers is well underway. Several large publishers of technical material have begun migrating their production over to MathML. In addition, MathML has had a significant impact on related Web technologies such as Unicode, CSS, XSL, and DOM. This talk will review the current status of MathML adoption, and examine some of the factors behind its surprising success in the arena of Web technology, in spite of the apathetic response it has sometimes met with in the mathematics research community.

Ursula Martin, University of St Andrews/SRI International http://www-theory.dcs.st-and.ac.uk/~um

The role of computational logic in mathematical communication

Computational logic means the use of computers to produce formal proofs in a given logical system, a dream of logicians such as Russell and Hilbert, which (Gödel's theorem aside) has only really become feasible with today's computer support. It ranges from implementations of automatic procedures, through collections of strategies for the machine to try which will not necessarily find a proof, to programs which check line by line whether or not the input generated by the user or another program is a valid proof. Computational logic software systems such as Otter, Mizar and PVS have been used, for example, to prove conjectures and generate on-line journals of mechanically verified mathematics, and companies such as Intel and Cadence are investing heavily in such technology for modelling hardware.

Yet this work has had little impact on mainstream mathematics, perhaps because of apparently naive claims sometimes made by non-mathematicians, traditional misgivings about the place of formal proof in mathematics, or an unwillingess to divert scarce resources into reworking known material inside a computational logic system.

I shall argue that it is time for the mathematical community to revisit computational logic: - for its immediate application as an effective component of mathematical software such as Maple or for representing mathematical knowledge as part of endeavours like OpenMath - to share in ownership of a technology that is becoming increasingly important in applications of mathematics, such as hardware design, e-commerce protocols or network analysis, that require the highest assurance of correctness - to develop a strategy for the representation, validation and communication of mathematics in a future where the opportunities and challenges of digitally embodied knowledge may radically change scholarship and scientific discourse

Professor Ursula Martin PhD MA CEng holds degrees from Cambridge and Warwick Universities, and following posts at Urbana-Champaign, Manchester and London is now Professor of Logic, Algebra and Computation at the University of St Andrews in Scotland, where she heads a research group working on the theory and applications of computational logic and symbolic computation. She is currently spending a sabbatical at the Computer Science Laboratory at SRI International in Menlo Park, investigating the application of computational logic to continuous mathematics. She has served on the Council of the London Mathematical Society 1994-1999, and initiated and coordinated from 1996 to 1999 EPSRC/LMS MathFIT, a joint initiative of the LMS and the UK national science research council to promote interdisciplinary research in mathematics and computer science.

Konrad Polthier,

Online Experiments and Visualization with JavaView

The talk is a case study on our web-based geometric research experiments, and on creating an online publication of the results. All the numerical experiments are done in a web browser, therefore, the current research could be simultaneously done in Berlin and in Kobe/Japan together with my coauthor Wayne Rossman.

For the numerics and visualization of geometric experiments my group in Berlin has developed a Java based software JavaView, which is the basis of our numerical experiments. We encountered the problem, that our newest research should be published as an online-paper including the experiments as Java applets, but currently there does not exist the possibility of a reviewed publication yet.

Some experimental pages with JavaView applets are accessible at http://www-sfb288.math.tu-berlin.de/vgp/

Ulli Kortenkamp

Communicating Interactive Geometry

We would like to present "The Interactive Geometry Software Cinderella", a Java-based software for dynamic Geometry comparable to Geometer's Sketchpad or Cabri Geometry II. Cinderella enables anybody to create really interactive webpages containing constructions, animations or guided exercises. This makes it the ideal tool for geometry communication via the Internet. The advanced features of Cinderella are based on a blend of 19th century mathematics (complex Projective Geometry, Cayley-Klein geometries, ...) and new theory developed by the authors (Complex Tracing & Randomized Theorem Checking). Only with the help of a solid mathematical foundation and a state-of-the-art implementation it was possible to create a tool that can be used by students of all grades as well as in research.

More Information about Cinderella can be found on the Cinderella website at http://www.cinderella.de

Paul S. Wang, Institute for Computational Mathematics, Department of Mathematics and Computer Science Kent State University

Internet Accessible Mathematical Computation: A Progress Report

Internet Accessible Mathematical Computation (IAMC) is a distributed system to make mathematical computing widely available on the Internet. Accessing mathematical information and computation can be as easy as visiting a Web page. Through the GUI of an IAMC client, a user performs interactive computation with an IAMC server anywhere on the Internet. Mathematical results obtained can be stored and sent directly to other IAMC servers for further processing. The current system architecture, the Mathematical Computation Protocol (MCP), the design of IAMC client and IAMC server, the server interface to compute engine are presented.

Rob Corless, University of Waterloo

Software Tools for Mathematical Communication

This talk explores some surprising aspects, which perhaps may be called emergent behaviour, of the use of apparently simple-to-build software tools for mathematics. In particular, we look at some new insights which can be gained into old subjects when viewed through a computational lens. Depending on time and interest of the audience, the talk may cover elementary Riemann surfaces, linear algebra and analysis, and/or a new/old function now known as the Lambert W function. The talk will end with speculations on the effects of MathML and OpenMath, reasoning by analogy with what we have seen in the past decade for other subjects.

Mark Steinberger,

Journal Quality

We explore issues of quality in mathematics journals, from purely electronic features like linking and indexing to more traditional features like typesetting and copy editing. We explore the interrelationships between the creation of these features and show, among other things, how linking can improve the editorial quality of the finished product (in the traditional sense).

Andre Kuzniarek,

Mathematical Communications Initiatives from Wolfram Research

Since the release of Mathematica Version 3 in 1996, Mathematica notebook technology has been at the forefront of electronic technical document delivery systems. We are in the final stages of development for a product called Publicon which puts Mathematica's authoring features into an inexpensive package that will appeal to the publishing community and technical societies in general. I will demonstrate one of our prototypes and some associated authoring tools, along with some other interesting technology in the works related to mathematical communication.

Michael Doob

The Mathematician-Publisher interface: the recent past, the near future, and the potholes in the road.

Much has been discussed and written about emerging technologies and their economic implications for both publishers and libraries. On the other hand, almost nothing has been said about the change in mathematicians and their relationship with publishers. In this presentation we consider their mutual expectations, both great and small, and how they have changed over the last several years. We then (dangerously) extrapolate to see how the mathematician-publisher relationship might change in the near future.

Olga Caprotti,

OpenMath: Accessing and Using Mathematical Information Electronically

James Davenport, London Mathematical Society

Electronic Publishing and OpenMath, and what to do about LaTeX

Electronic publishing offers the options of far greater searching capability than is available even with services like MathSciNet. However, text-based searching, while still a great improvement, is not the whole answer. How do we search the formulae? OpenMath offers at least the possibility of representing the semantics of the mathematics, rather than just the layout of the mathematics on the page. This poses two questions:

(1) How practicable is this?

(2) Most submissions, in practice, are in TeX dialects, rather than in XML/MathML/OpenMath: what do we do about this? I will report on some preliminary experiments conducted with the LMS Journal of Computation and Mathematics.

Nathalie Sinclair, Queen's University

Survival of the Fit: Communicating with our future mathematicians

We often take a rather formalist approach to mathematics communication in education, one that stresses operations, syntax, and form. Not only does this impede mathematical understanding, the putative goal of communication, it provides students with little insight into the way that mathematics is constructed, forms our thinking and shapes the world we live in.

Children, like mathematicians, search for patterns, try to find ways to make things "fit." These ways will surely involve their visual, spatial, kinesthetic, and intuitive facilities, as well as their logical symbolic ones. As educators, we need to harness the tools and languages that will help children use these facilities to become not only consumers but creators of mathematics.

I will discuss the contributions that new technologies (the Internet, dynamic geometry software, Javabeans) can make in: --helping students gain a better and deeper understanding of the traditional mathematics curriculum; --opening the door to more sophisticated mathematics; and, --helping students to make judgments about what is valuable, relevant and beautiful in mathematics.

Thorsten Bahne, Günter Törner

Changing the Representation Medium - Changing the Standards? The Case of Electronic Dissertations in Germany

This presentation is based on the project "Dissertation Online", funded by the German Research Foundation (DFG) (see http://www.educat.hu-berlin.de/diss_online/englisch/index1e.html) and initiated by a subgroup within the Initiative of the German Learned Societies for the Advancement of Digital Information and Collaboration, (see http://elfikom.physik.uni-oldenburg.de/IuK/index.html.en) ("IuK-Initiative")

Gary Taubes

Difficulty n Getting Good Press on Good Science

A potentially serious look at the realities of modern journalism and the reasons why it will always be easier to get good press with bad science than with good.

David Morrison, Duke University

Future uses of the mathematics arXiv

Robion Kirby, Dept. of Mathematics, University of California at Berkeley

Competing with the commercial journals

I will provide an update on my 1997 data giving the price/page for math journals, and then discuss the problems with beginning a high quality, free, electronic journal with a printed version (Geometry & Topology).

Ulf Rehmann

DOCUMENTA MATHEMATICA: Efficient Production of Mathematical Literature

Electronic tools can be used to increase speed and to significantly reduce costs of the production process for mathematical and, more general, scientific literature.

If all scientific journals and books were produced that way, this could stop the trend of permanent increase of scientific library budgets, without reducing the quality of literature support.

As an electronically produced and fully refereed journal, DOCUMENTA MATHEMATICA uses highly automated software tools in order to minimize production time and work.

They way DOCUMENTA MATHEMATICA is managed was recently described in the report

http://www.mathematik.uni-bielefeld.de/~rehmann/bericht-eng.html

by its Managing Editors.

The software tools developed for DOCUMENTA MATHEMATICA have also been used in order to produce the Proceedings of the International Congress of Mathematicians 1998 (ICM) as an Extra Volume of that journal.

The scientific part of these proceedings (ca. 2200 pages consisting of 186 manuscripts written by the Invited Speakers of the ICM with ca. 160 embedded graphics) was produced - by one person - during the time from July 1, 1998 ( = deadline for manuscript submission ) through July 15, 1998 ( = submission date of the final postscript file to the printer).

During that time, manuscripts were formated in a uniform layout and recycled to the authors for final corrections. Moreover, the tables of contents, the author indexes, and the postscript versions for the final volumes were built. These postscript files were the input for the printer in order to produce the printed volumes.

Thanks to the new electronic production methods it was possible, for the first time in the hundred year history of the ICM, to publish two of the three volumes - as printed books - already before the congress started, while the volume containing the reports on the ICM ceremonies appeared still in the same year 1998.

Main ingredients for the production were standard software building tools like the well known Unix program "Make", but also "Perl", "Emacs", some standard format converters, and, of course, electronic mail.

All the necessary programs are freely available, standard, and universal. They have proven their capability of maintaining computer related software-"literature", like compilers and other tools, for many years; but they can - and should - also be used for producing and maintaining scientific literature in general.

Bill Casselman, Dept. of Mathematics, University of British Columbia

A survey of mathematical exposition in Java

I will attempt to give a survey of how Java has been used on the Internet in the exposition of mathematical ideas. This is potentially a huge undertaking, and I will concentrate on examining a few typical projects critically, outlining several problems for the future.

Andrew Odlyzko, AT&T Labs - Research

The rapid evolution of scholarly communication

In scholarly publishing, "... journals are not where the interesting action is." When we look at usage of non-traditional sources of online information, such as preprint servers and home pages, we do see rapid growth rates, rates so high that very soon these sources will be the dominant methods for scholarly comunication. These growth rates and their implications will be discussed in this talk.

Wilfrid Hodges,

What do you want from your publisher?

An annotated checklist for mathematical authors, in non-legal terms but with some comments on the legal possibilities and pitfalls.

Peter Michor,

Electronic services offered by the European Mathematical Society

This short talk will present the services for the mathematical community offered or organized by the European Mathematical Society: EMIS (European Mathematical Information Service) containing: The electronic library of Mathematics. The Jahrbuch der Mathematik Project. First three hits free when asking Zentralblatt-MATH online.

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