# Briefing Package for W3C^{TM} Math Activity

## 1. Executive Summary

This document sets the stage for the continuation of development and support for the World Wide Web Consortium (W3C) Mathematical Markup Language (MathML) 1.0 Specification. MathML 1.0 provides a solid foundation for representing mathematical expressions. However, a number of critical requirements dating back to the original HTML-Math Working Group Charter remain to be accomplished, and other goals developed as a result of MathML implementations or of feedback from the community remain to be met. With MathML 1.0 in hand, we are offered a unique opportunity to ensure effective math on the Web through its widespread acceptance, and it seems very desirable to maintain the present MathML 1.0 Recommendation, and to further develop the specification. The current Math Working Group proposes that the W3C establish a new Math Working Group to continue the work of the W3C Math activity. The proposed revision MathML aims to reduce the overhead involved in publishing scientific and technical Web content, while increasing its scope to accommodate new areas of science. We expect that as a result of a new MathML the suite of tools for authoring, managing, transforming and rendering MathML will continue to evolve and leverage the relationship between MathML and other W3C specifications.

## 2. Current W3C Status

### 2.1 Existing work

W3C has an existing Math Working Group which by charter shall finish its work in June 1998. The MathML 1.0 Specification is a product of the W3C's Math Working Group and was issued as a W3C Recommendation on the 7th of April 1998. MathML is an XML application for representing mathematical expressions, their presentation, their semantics, or both. MathML consists of approximately 100 elements and their attributes, which can be divided into two major categories: presentation elements and content elements. Presentation elements may be used to express the two-dimensional layout of mathematical expressions. Content elements are used to express the semantics of mathematical expressions up to the level of calculus. Content elements have a default presentation but may be combined with presentation elements to customize the layout of expressions. ( Some MathML examples.)

The proposed new working group is positioned as a continuation of the present Math Working Group and would be chartered within the W3C User Interface Domain.

### 2.2 Architectural Constraints

The relationship between MathML and other W3C technologies is crucial. The Math Working Group has made available a separate requirements document that describes the demands that MathML makes on browsers, eXtensible markup Language(XML), the Document Object Model (DOM), style mechanisms --- eXtensible Style Language (XSL), Cascading Style Sheets (CSS), etc. ---, and rendering. The requirements that MathML makes of these mechanisms, and of browsers generally, are not unique to MathML and are useful in other W3C contexts. If necessary this document will be updated as the group progresses.

## 3. Proposal: Mathematical Markup Language Working Group

### 3.1 Introduction

Efforts to define a specification for mathematics in HTML have been underway in the W3C for several years. Dave Raggett made a proposal for math in HTML in 1994. Although that proposal was not ultimately incorporated into HTML 3.2, a panel discussion at the WWW IV Conference in April 1995, and representation by W3C members, demonstrated that there was clear interest in pursuing a specification for mathematics on the Web. A group was formed to discuss the problem further.

In the intervening years, the W3C and the math working group have both evolved substantially. The small informal math group has grown, and has been formally reconstituted as the W3C HTML-Math Working Group, later shortened to the W3C Math Working Group. The current Working Group is composed of experts from commercial publishers and software vendors, as well as not-for-profit publishers and research organizations from both Europe and North America.

The W3C Math Working Group's main achievement thus far has been the production of the MathMLTM 1.0 specification. MathML is well-suited to markup emphasizing the presentational quality, as well as the semantic aspect of math formalism. It can serve as markup for high-quality math composition. MathML has been outfitted with enough special XML elements to carry much of the meaning of mathmath up to roughly the beginning of college level. Furthermore, since it is an XML application, it offers itself naturally to the commercial publishing realm which wishes to use the same source for electronic browsable copy, as well as for high-quality rendering through traditional print.

The MathML 1.0 specification is a powerful low-level language primarily aimed at facilitating the building of tools for communicating math over the Web. As a consequence, it is rather complex, and experience has shown that end users expecting complete solutions for authoring and publishing scientific documents on the Web are easily overwhelmed. To reach its full potential as a framework for sharing mathematical information over the Web, further support for MathML both in software and in other Web standards is required. This in turn requires active maintenance and development of the MathML specification itself.

We propose that the World Wide Web Consortium establish a Math Working Group as described in this briefing package. The Math Working Group should be directed to make further progress following the work of the W3C Math Working Group which shall have finished its charter in summer 1998. The Math Working Group should work through the remaining open issues identified by that Math Working Group as still of importance. In particular, the Math Working Group shall be responsible for the maintenance and updating of the MathML 1.0 Specification adopted as a recommendation by the W3C following upon the efforts of the foregoing Math Working Group, and shall continue the push towards making the work of science and mathematics more readily communicable and accessible through the WWW.

### 3.2 Scope of the Activity

This briefing package is being issued because of strong member interest. We divide the scope of the Math Working Group activity into three sections.

#### 3.2.1 General support

To work toward the effective spread and adoption of MathML it is desirable to have a center where those who are using it can turn for advice on some of the perhaps subtle points of the specification. In addition, to promote MathML's use a suite of typical examples of MathML in action has to be devised and the standard has to be maintained. There will be errors to be corrected and extensions to be made.

More generally, an outline of implementation strategies needs to be prepared.

MathML is not intended as a direct authoring language. The Math Working Group decided not to endorse a single input syntax since it determined there could not be one that would suit all. Instead, the Math Working Group decided that it should encourage interested parties to develop tools for authoring, generating, translating, or exporting MathML. However, it is important to the success of MathML that input syntaxes purporting to feed into MathML actually do so reasonably. If not the usefulness of MathML as a language will be degraded. We will offer support to organisations working on input syntaxes.

#### 3.2.2 Presentation

In order to realize the full potential of the presentation markup of MathML, it is necessary that the placement of inclusions within an HTML or XML document be subject to better control. This is also needed by other formatting driven applications. The Document Object Model, which is undergoing refinement by the DOM WG, should be monitored to ensure that it is understood how to use it to realize MathML rendering in Web browsers.

The promise of style sheets, and in particular of CSS and XSL, is that they might be used to provide a platform-independent rendering mechanism for MathML. The Math Working will work with the XSL Working Group toward inclusion of such things as sufficient math flow objects to render MathML and other scientific formulas.

A very new development has been the submission of Notes to the W3C concerning two-dimensional vector graphics languages. The probable chartering of a Scalable Vector Graphics (SVG) Working Group within the Graphics Activity of the User Interface Domain of the W3C is welcomed by the present Math Working Group. The PGML and VML Notes submitted to the W3C, seem to advocate a graphics language rich enough to support the finest nuances of MathML rendering. If such an SVG Working Group is formed then it would be a task of the Math Working Group to serve as a liaison between implementors of the MathML Specification as they may be affected by the developing SVG specification.

#### 3.2.3 Content

Though the content tagging already in MathML 1.0 does support most of math up to early college level, there are simple extensions that have already been suggested. How to make such extensions, and which to choose to endorse as recommended requires a body to oversee the process reliably.

In addition, a large-scale effort which is oriented toward the semantic encoding of math is OpenMath, with which the Math Working Group already has collaborated. OpenMath has so far adopted some of the work that was done by the Math Working Group. It may be expected that some of the content tagging of MathML should be adjusted in the light of the experience gained on the semantic front through OpenMath work.

The mathematical properties of content elements are largely conveyed through default attributes values. The management of these attributes exactly parallels the management of attributes of flow objects as found in CSS2 and the current work on XSL. Mechanisms such as macros or style sheets for managing these default attributes need to be investigated.

### 3.3 Market for the activity

The target market segment remains the same as the original working group with several additions due to recent W3C activities. Indeed, the potential audience for a mathematics specification for the Web is quite large, encompassing students and teachers at nearly all educational levels, professional researchers from many different scientific disciplines, software vendors, scientific publishers, etc.

Publishers have an immediate need for displaying mathematical content on the Web. Publishers have legacy data in TeX and/or SGML and presently have very limited options for displaying such documents on the Web. The Math Working Group should encourage the development of converters of legacy data. There is presently work afoot here.

Software vendors who wish to link their products for manipulating mathematical expressions with mathematics in Web pages are served by MathML. This might be accomplished by cutting and pasting a mathematical expression from a Web page into the mathematical software, or by other more direct means.

With the emergence of the DOM, web component developers will be able to control the actions of MathML rendering applications. A new market for scientific web components that interact with MathML renderers is beginning to emerge.

### 3.4 Structure of Activity

A new working group will be formed, charged to continue to work of the current W3C Math Working Group, in the User Interface domain. The proposed charter includes the list of deliverables, the start and end dates and the level of commitment required to participate in the work.

Involvement with other W3C activities and working groups will be an important part of the MathML continuation effort. This involvement will be accomplished by cross membership and interest group involvement as well as making use of the W3C Hypertext Coordination Group. The MathML Working Group charter and requirements document detail the expected relationships with other working groups.

### 3.5 Resource Statement

#### 3.5.1 W3C Resource Commitment

The proposed W3C Math WG requires a minimum of resources from the Consortium, as is the case with the current Math working Group. In particular, the proposed group requires

- A W3C staff contact to serve as liaison to the W3C team. As is currently the case, this staff contact need only devote a small fraction of his or her time to monitoring the MathML activity.
- Access to a W3C teleconference bridge every other week.
- Logistic support for planning face to face meetings twice a year.
- An archived mailing list for WG use, and a public archived mailing list.
- Space on the W3C web site.

#### 3.5.2 Member Resource Commitment

Working Group members will need to make a commitment of preferably 20% of their time, for one year, to qualify as a fully participating member. As the Math Working Group sees fit it may accept participants with special expertise who can contribute no less than 10% of their time.

It is expected that the members of the W3C who have contributed personnel resources to the successful work of the present W3C math WG will wish to continue their involvement with math on the Web. The vote approving MathML as a Recommendation suggested a wider interest in using MathML than just those directly involved in the Working Group writing it, as, of course, it should be. Therefore we may expect new involvement.

W3C Members may also undertake to review one or more working documents without fully participating in the Working Group activity. There is no participation requirement for this, apart from timely delivery of review comments for the draft in question.

The proposed Working Group schedule is for 18 months. At a minimum contribution of 20% of a full time equivalent per principal member, with 10 such members the overall resources contributed to this working group would thus be 3 person-years.

Participation requirements by W3C members, by the W3C team and by invited experts are described in the charter.

### 3.6 Projected Schedule

The Working Group, if approved, will commence work at the beginning of September 1998 by establishing a mailing list and by then holding the first of its face-to-face meetings in October 1998.

The Working Group will hold bi-weekly teleconferences as described in the charter, and will work to the following schedule:

- First public requirements document: May 1998 (by previous Math Working Group)
- New Math Working Group meeting: October 1998
- Working Group meeting: April 1999
- First Working Draft of MathML revision: May 1999
- Working Group meeting: August 1999
- Second Working Draft of MathML revision: October 1999
- Working Group meeting: November 1999
- Proposed Recommendation for revised MathML: Jan 2000
- Working Group termination: February 2000

The Working Group will terminate in February 2000, after comments arising from the revised MathML Proposed Recommendation ballot have been incorporated.

## 4. Annex

### 4.1 Existing Information

The following resources may be of use as background material

- Cascading Style Sheets, level 2
- http://www.w3.org/TR/REC-CSS2
- Document Object Model (DOM)
- http://www.w3.org/DOM/Group
- Extensible Markup Language, version 1
- http://www.w3.org/TR/REC-xml
- Hypertext Coordination Group
- http://www.w3.org/Markup/CoordGroup
- W3C Math Activity Report
- http://www.w3.org/Math/Activity.html
- Mathematical Markup Language (MathML) 1.0 Specification
- http://www.w3.org/TR/REC-MathML/
- MathML Requirements
- http://www.w3.org/Math/Group/needs/MathMLRequ.HTML
- Namespaces in XML
- http://www.w3.org/TR/WD-xml-names
- W3C Web Accessibility Initiative
- http://www.w3.org/WAI/
- XML Linking Language
- http://www.w3.org/TR/WD-xlink
- XSL Working Group
- http://www.w3.org/Style/XSL/Group

### 4.2 Participant Lists

The following organizations, most already members of the W3C, have expressed their interest in MathML through their involvement in the current Math Working Group. We expect their support for the proposed new activity:

- Adobe
- American Mathematical Society
- Design Science Inc.
- Elsevier Science
- Geometry Technologies, Inc.
- IBM Research Division
- American Mathematical Society
- University of Waterloo
- INRIA (the SAFIR Research Group)
- Stilo Technologies
- SoftQuad, Surrey, BC
- University of Western Ontario
- Waterloo Maple Inc.
- Wolfram Research

The chairs of the new Working Group will be Patrick Ion <ion@ams.org> (American Mathematical Society / Mathematical Reviews) and Angel Diaz <aldiaz@us.ibm.com> (IBM Research Division).