W3C WD-math-980106

Mathematical Markup Language

W3C Working Draft

This version:
6-Jan-1998: http://www.w3.org/TR/WD-math-980106
Latest version:
6-Jan-1998: http://www.w3.org/TR/WD-math
Previous version:
10-Jul-1997: http://www.w3.org/TR/WD-math-970710
Patrick Ion <ion@math.ams.org>
(Mathematical Reviews / American Mathematical Society)
Robert Miner <rminer@geom.umn.edu>
(Geometry Center / University of Minnesota)
Principal Writers:
Stephen Buswell, Stan Devitt, Angel Diaz, Nico Poppelier,
Bruce Smith, Neil Soiffer, Robert Sutor, Stephen Watt


This specification defines the Mathematical Markup Language, or MathML. MathML is an XML application for describing mathematical notation and capturing both its structure and content. The goal of MathML is to enable mathematics to be served, received, and processed on the Web, just as HTML has enabled this functionality for text.

This document begins with background information on mathematical notation, the problems it poses, and the philosophy underlying the solutions MathML proposes. MathML can be used to encode both mathematical notation and mathematical content. About 25 of the MathML tags describe abstract notational structures, while another 75 provide a way of unambiguously specifying the intended meaning of an expression. Additional chapters discuss how the MathML content and presentation elements interact, and how MathML renderers might be implemented and should interact with browsers. Finally, this document addresses the issue of MathML entities (extended characters) and their relation to fonts.

Status of this document

This is a stable document derived from the 10 July working draft of the MathML specification. This document has been produced as part of the W3C HTML Activity. The publication of this document does not imply endorsement by the Consortium's staff or Member organizations.

At the time of this writing, the fundamental Extensible Markup Language (XML) specification is not yet been adopted as a W3C Recommendation. Should future changes in the XML specification necessitate changes in the MathML specification, it is the intention of the HTML-Math Working Group to issue a revision of the MathML specification. However, considering that the XML specification has been submitted as a Proposed Recommendation, any changes are very unlikely to be substantial in nature.

Most of this document represents technology tested by multiple implementations. A summary of MathML rendering and authoring software is described on the HTML-Math Working Group home page. A small number of features that have not had the benefit of extensive implementation experience. Nonetheless, the experience of the Working Group members with analogous features in other domains has resulted in consensus that these features belong in this specification.

The HTML-Math Working Group intends further development of recommendations for mathematics on the Web, as set out below and in its Charter. In particular, work is under way on several matters, such as macro mechanisms, input syntaxes, and fonts. A future report covering these and other considerations is planned for May 1998.

A list of current W3C Working Drafts can be found at http://www.w3.org/pub/WWW/TR.

Table of Contents

Extended Table of Contents

Chapter 1. Introduction
Chapter 2. MathML Fundamentals
Chapter 3. Presentation Markup
Chapter 4. Content Markup
Chapter 5. Mixing Presentation and Content
Chapter 6. Entities, Characters and Fonts
Chapter 7. Implementing MathML

Appendix A. DTD for MathML
Appendix B. Glossary
Appendix C. Operator Dictionary
Appendix D. Working Group Membership
Appendix E. Informal EBNF Grammar for Content Elements