The Math Working Group is chartered to continue the task of
facilitating the use of mathematics on the Web, both for science and
technology and for education. This involves the maintenance of the recent
version 2.0 of the MathML
specification (W3C Recommendation, 21 February 2001), encouragement of its
wider deployment, preparation of any revisions or addenda appropriate,
continued liaison with other Working Groups within the W3C to ensure that the
potential of MathML is realized, and relations with other organizations, all
designed to strengthen the position of MathML and enhance the use of
mathematics on the Web. MathML can be of value as a test case in the
deployment of some of the newer W3C initiatives.
This means that the use of MathML in Web documents is encouraged by the
W3C, to which the MathML specification belongs, and should significantly
contribute to the usefulness of the Web for science, technology and education.
The continuation of the work on mathematics on the Web falls within the scope
of the User Interface Domain.
- Maintaining and clarifying the MathML 2.0 Recommendation.
- Ensuring ongoing compatibility between MathML and the new and evolving
- Working with other W3C groups to develop generally applicable solutions
for XML in preference to specific extensions to MathML.
- Encouraging development of software that facilitates the creation,
display and use of documents using MathML for mathematics. Examples are
visual and audio browsers, translators from older encodings (such as
TEX and ISO 12083), tools (possibly using customized input
syntaxes) and editors.
- Employing MathML in appropriate contexts to express mathematics in W3C
- Developing mechanisms to improve on any deficiencies noted in the use of
- Preparing possible revisions and addenda to MathML.
Criteria for Success
- Maintenance of the W3C Math site pages as a center for information on
the deployment of MathML, a W3C product, including an up-to-date Implementation and Interoperability
- Maintenance of the Test Suite and Validation Services for MathML
provided at the W3C site, and of the associated Compliance
- Preparation of reports on updates to MathML containing improved
features, and of addenda to the specification as necessitated by
developments at the W3C or outside.
- Continued full compatibility of MathML with relevant W3C specifications
which are still evolving.
- Expansion of acceptance and use of MathML, as measured by the number of
products released supporting its features.
- Promotion of the essential role of MathML for communicating math through
the Web, and its employment in the production of mathematically rich
documents and services. The success of this can be measured by its spread
This group commences in June 2001 and is scheduled to persist 24 months,
terminating at the end of May 2003.
The group will create
- Working Draft documents which contain specifications for updates or
extensions of the MathML specification and use of mathematics on the Web.
- A schema for MathML
- An outline of modularization of MathML
- a system for profiles in MathML
- adjustment to the MathML Test Suite
- clarity on the implications of this for MathML's extension
- Presentation and Content markup updates
- Guidelines for graphics and MathML
- A DOM API for MathML Revision
- Spoken mathematics using XSL Style Sheets (Voice XML)
- Examples of Web Services for Mathematics using MathML (XML
- Tutorial and introductory materials to encourage adoption of the MathML
- Guideline documentation for implementors of MathML.
- Promotional activity and materials on behalf of MathML.
- Minutes of telephone conferences and face-to-face meetings.
The group will produce a Proposed Revision of the MathML Recommendation,
evolved from stable Working Drafts, and will put that forward for
consideration as a W3C Recommendation, if that proves appropriate.
Minutes of teleconferences and face-to-face meetings will also be available
from the WG page (members
work of the Working Group, and in particular, its document
production will be in accord with the guidelines set down in the W3C
Coordination Group (members only)
- The Math WG will coordinate its work at a high level with other
Working Groups primarily through participation in the Hypertext
Coordination Group where it is represented by its chair(s).
- XML Coordination Group
- The Math WG will coordinate its work in the XML sphere through
participation in the XML Coordination Group, which is intended to
improve communication beyond the level the previous Math WG
- XML Working Group (XML
Schema, XLink, XML Protocol, XML Query, XML Encryption) (members
- The Math WG is naturally affected by changes to XML syntax. MathML is
written in XML 1.0, with the addition of XML namespaces. MathML is
presently described by a DTD, which should be replaced by a schema with
at least equivalent value. However, the MathML specification would
benefit from being supplemented by a schema able to express formally
more of the constraints presently only expressible in the prose of the
specification. For this reason the Math WG has a strong interest in
cooperation with the XML Schema WG, which has already started. The
topics of data types, replacement of character entities and structural
expressions are all on the table. In addition, the details of the
deployment of namespaces and MIME, which are within the purview of this
WG, types have implications for the embedding of MathML in browsers that
are relevant today. The MathML revision format will use the results of
XLink group working on linking for internal hyperlinking, linking into
and out of mathematical parts of a Web document. The expansion of the
capacities of linking and querying may interact with MathML. Whether the
mathematics of XML Encryption can usefully be expressed in MathML is to
be investigated, in the W3C spirit of using its own recommendations.
There are already on the Web a number of mathematical services: it seems
entirely appropriate to set out their Discovery, Description and Service
Integration according to the developing XML Protocols.
- Document Object
Model (DOM) (members only)
- MathML content is accessible from the XML Document Object Model. The
Math WG is directly concerned with some details of the DOM. The previous
Math WG has made some of MathML's natural requirements known and
representatives collaborated on a DOM. Such work will continue
especially on the Embedded DOM model.
- W3C Web Accessibility
- The work of the Math WG was from the start intended to be helpful in
promoting the wider accessibility of math, and MathML 1.0 was designed
with that in mind. It is hoped that now a real implementation of a
non-visual renderer for MathML can be achieved through collaboration
with the WAI WG and suitable implementors. This goal has proved to be a
long-term one, although there are already demonstrations of some
non-visual rendering of formulas based on MathML. However voice
rendering of mathematics is now ready to be done.
- CSS & FP Working
Group (members only)
- The Math WG continues to look to the style-sheet mechanism under
development for platform independent rendering of MathML. There are
demands upon CSS&FP implicit in the requirements for MathML. Members
of the previous Math WG participated in the inter-WG Style Task Force
and this will continue.
- XSL Working
Group (members only)
- The Math WG looks to style-sheet mechanisms for platform independent
rendering of MathML. Again, there are demands upon XSL implicit in the
requirements for MathML. Of particular interest in XSL are the scripting
and macro mechanisms planned. Suggested FOs for mathematics have already
been put forward. The XSL Requirements Summary anticipates support of
- The use of graphics in mathematics is commonplace at all levels, yet
the Math WG in developing MathML consciously left aside dealing with
drawing for mathematics. Many in the community clamored for it, and the
WG did consider the questions early on, but decided that resources did
not permit addressing the need. With the successful development of SVG,
presently a W3C Candidate Recommendation, many of the tools to do
graphics for mathematics seem to be at hand. How these are to be
integrated with XHTML and MathML in practice remains to be worked out in
detail. The WG will need contact with the W3C Graphics activity, and in
particular SVG and any corresponding group working on three-dimensional
- Semantic Web
- This new initiative of the W3C offers more opportunities to use the
formal structures of the RDF to try and capture more of mathematics at
levels above that of a single formula, which is what MathML in essence
- I18N Working
Group (members only)
- Mathematics is an international language, and may be incorporated in
documents in all natural languages. The Math WG must cooperate with the
internationalization efforts of the I18N Working Group. The character
model settled upon is important to mathematics. If examples of the use
of mathematical notation in conjunction with bi-directional writing
systems are found which are not fully compatible with MathML 2.0 then
attention will be given to their requirements.
The Math WG coordinates its work with other groups or organizations insofar
as they may be directly concerned with mathematics on the Web, or as their
activities may have a direct impact on the usefulness of MathML.
- The Unicode Consortium
and ISO WG2
- The Unicode Consortium and ISO WG2 have already been very responsive
to the needs of mathematics on the Web, and additions to Unicode and ISO
10646 are expected in versions 3.1 and 3.2 that have been made expressly
for mathematics on the Web. Coordination with these groups will
- The OpenMath community, based around the OpenMath Society, and its
contracts under the European Community's ESPRIT project contributed
measurably to the development of MathML 2.0. Contact with this community
- The TEX
- The previously dominant composition system in the academic community
has been TeX. In fact TeX can work well with MathML, either as an input
syntax which is widely known, or as a mathematical composition engine
with which much experience has been gathered. The TeX Users Group and
the LaTeX3 project will be kept informed of progress on the MathML
front. Fonts from the TeX community may be helpful in rendering MathML
in browsers. Projects for the conversion of legacy TeX material to
MathML have already been started, but are not yet of `production
- IEEE LTSC
- The IEEE Learning Technology Sub-Committee has approached the W3C Math
WG with the idea that they might endorse MathML as the preferred
standard for mathematical encoding in their standards. This avenue of
cooperation, which has the potential of helping the spread of MathML
within the US educational community will be explored. The LTSC also has
done work on mathematical metadata, but not in exactly the RDF
- There is a large initiative supported by ANSI which aims at
formalizing the exchange of scientific, technical and engineering
information for manufacturing. In fact their section 50 is a way of
transcribing mathematical material, mostly geometrical. Its relation to
the Recommendation of MathML should be understood, and cooperation with
the STEP initiative, which is part of ISO standardization, undertaken if
- The STIPUB group of Publishers of Scientific and Technical Information
is making available a public set of fonts to cover all those characters
in Unicode needed for their publishing needs. We need to remain informed
of their progress.
- An cooperative European effort of this name has been set up with the
intention of promoting training and education in the use of the Web for
education in mathematics, and in particular in MathML. Liaison with
XMath is obviously desirable. Perhaps they will be able to help with the
public educational materials needed. Note this is not to be confused
with other products and projects with very similar names.
- This consortium has been developing an XML version of VRML, a markup
for three-dimensional graphics. The Math WG was approached by them
because of the obvious interest of mathematics in such advanced
graphics, and of the mathematical nature of the descriptions of surfaces
and higher-dimensional objects.
One or more public Working Drafts will be produced covering each of the
|Document or Event
|MathML Implementation and Interoperability
|MathML User and Implementation Primer
||WD 1: Schema
|MathML Test Suite
||WD 2: Modularization
||WD 3: DOM API
|Second MathML User Community Conference
|MathML Web Services
|MathML User and Implementation Primer
||WD 3: Presentation and Content Modules
|MathML Spoken using XSL Stylesheets
|MathML Test Suite
|MathML User and Implementation Primer
|includes final forms of all components
|MathML Test Suite
|MathML Conformance Document
|MathML User Primer
|MathML Implementation Primer
Note that the list given necessarily cannot foresee all that will come out
of the work done by the WG, and that it does not take into account the phases
of putting forward a specification for consideration as a W3C Recommendation.
The decision to offer such will have to be taken by the new Math WG after a
time of work. It might be that another way of adopting revisions to MathML
will be more suitable.
The archived mailing list firstname.lastname@example.org is used for public
discussion of mathematical markup and related issues, and WG members are
encouraged to subscribe. In a phase of expanding adoption of a specification
it is essential that the Working Group be organized so that responses on the
public mailing list are timely and helpful.
There is a public page on W3C Math
Activity, maintained by persons designated by the chair. It tracks the
evolving use of MathML, and supports it with information on implementations,
FAQ, and access to the MathML Test Suite and Validator. There is also a private Math Group page (members only),
maintained by the chair.
The Group works by consensus. In the event of failure to achieve consensus,
the Group may resort to a
vote as described in the Process Document. If the issue is resolved by
consensus during the voting period, the vote is cancelled.
Participants (W3C Member representatives, Invited Experts, and W3C Team
members) are required not to disclose information obtained during
participation, until that information is otherwise publicly available.
meeting attendance and timely response are described in the Process
document. Participation (meetings, reviewing and writing drafts) is expected
to consume time up to one day per week.
W3C Members may also offer to review one or more working drafts from the
group for clarity, consistency, technical merit, fitness for purpose and
conformance with other W3C specifications. They are required to provide the
review comments by an agreed-upon date but are not required to attend
As decided on a case-by-case basis, invited experts may attend a single
meeting or a series; they may in some cases be subscribed to the Group mailing
list. For the duration of their participation, invited experts are encouraged
to adopt the same requirements for meeting attendance and timely response as
are required of W3C Members.
W3C team ensures that the mailing lists and Group page are adequately
maintained and that public Working Drafts are made available on the Technical Reports page. A W3C team member
provides liaison between any non-team document editors and the W3C team.
W3C team are expected to adopt the same requirements for meeting attendance
and timely response as are required of Working Group Members. The expected
commitment from the W3C is therefore at least 20% of a full time person, plus
5% of an administrative person.
At present Max Froumentin is providing the support and liaison mentioned
The proceedings of the Working Group are conducted in an open working
environment in accordance with the W3C's policy
on intellectual property (IPR) issues
Members of the Math Working Group, and of any other Working Group
constituted within the Math Activity, are expected to disclose any
intellectual property claims they have in this area. Any technology essential
to implement specifications produced by this Activity must, at the very least,
be available for licensing on a royalty-free basis. At the suggestion of the
Working Group, and at the discretion of the Director of W3C, technologies may
be accepted if they are licensed on reasonable, non-discriminatory terms.
Members disclose patent and other IPR claims by sending email to an
archived mailing list that is readable by Members and the W3C team:
email@example.com. Members must disclose all IPR claims at least to
this mailing list.