# Mathematical Markup Language (MathML) Version 2.0

## W3C Recommendation 21 February 2001

This version:
  http://www.w3.org/TR/2001/REC-MathML2-20010221
  Also available as: HTML zip archive, XHTML zip archive, XML zip archive, PDF (screen), PDF (paper)
Latest version:
  http://www.w3.org/TR/MathML2
Previous version:
  http://www.w3.org/TR/2001/PR-MathML2-20010108
Editors:
  David Carlisle (NAG)
  Patrick Ion (Mathematical Reviews, American Mathematical Society)
  Robert Miner (Design Science, Inc.)
  Nico Poppelier (Penta Scope)
Principal Authors:
  Ron Ausbrooks, Stephen Buswell, Stéphane Dalmas, Stan Devitt, Angel Diaz, Roger Hunter, Bruce Smith, Neil Soiffer, Robert Sutor, Stephen Watt

Copyright © 1998-2001 W3C® (MIT, INRIA, Keio), All Rights Reserved. W3C liability, trademark, document use and software licensing rules apply.

## Abstract

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 World Wide Web, just as HTML has enabled this functionality for text.

This specification of the markup language MathML is intended primarily for a readership consisting of those who will be developing or implementing renderers or editors using it, or software that will communicate using MathML as a protocol for input or output. It is not a User's Guide but rather a reference document.

This document begins with background information on mathematical notation, the problems it poses, and the philosophy underlying the solutions MathML 2.0 proposes. MathML can be used to encode both mathematical notation and mathematical content. About thirty of the MathML tags describe abstract notational structures, while another about one hundred and fifty 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 characters and their relation to fonts.

While MathML is human-readable, it is anticipated that, in all but the simplest cases, authors will use equation editors, conversion programs, and other specialized software tools to generate MathML. Several early versions of such MathML tools already exist, and a number of others, both freely available software and commercial products, are under development.

## Status of this document

This section describes the status of this document at the time of its publication. Other documents may supersede this document. The latest status of this document series is maintained at the W3C.

This document has been reviewed by W3C Members and other interested parties and has been endorsed by the Director as a W3C Recommendation. It is a stable document and may be used as reference material or cited as a normative reference from another document. W3C's role in making the Recommendation is to draw attention to the specification and to promote its widespread deployment. This enhances the functionality and interoperability of the Web.

This document has been produced by the W3C Math Working Group as part of the activity of the W3C User Interface Domain. The goals of that W3C Math Working Group are discussed in the W3C Math WG Charter (revised February 2000 from original of 11 June 1998). A list of participants in the W3C Math Working Group is available.

The MathML 2.0 specification was reviewed extensively during its development, as provided by the W3C Process. During end of that period the W3C Math Working Group members encouraged implementation using the specification and comment on it; a report on Implementation and Interoperability experiences and issues has been made public. It is intended that this will be updated from time to time by the continuing work of the W3C that oversees the MathML 2.0 Recommendation. The W3C Math Working Group maintains a public Web page http://www.w3.org/Math/ which contains further background information.

Public discussion of MathML and issues of support through the W3C for mathematics on the Web takes place on the public mailing list of the Math Working Group (list archives). To subscribe send an email to www-math-request@w3.org with the word `subscribe` in the subject line.

Please report errors in this document to www-math@w3.org. The list of known errors in this document is available at http://www.w3.org/2001/02/MathML2-errata.

The English version of this specification is the only normative version. Information about translations of this document is available at http://www.w3.org/2001/02/MathML2-translations.

The MathML 2.0 Recommendation is made available in different formats. In case of a discrepancy between any of the derived forms and that found in the W3C's archive of Recommendations the definitive version is naturally the archived Recommendation.

A list of all current W3C Technical Reports can be found at http://www.w3.org/TR.

MathML 2.0 is a revision of the earlier corrected W3C Recommendation MathML 1.01. It differs from it in that all chapters have been updated and two new ones and some appendices added.

Chapters 1 and 2, which are introductory material, have been revised to reflect the changes elsewhere in the document, and in the rapidly evolving Web environment. Chapters 3 and 4 have been extended to describe new functionalities added as well as smaller improvements of material already proposed. Chapter 5 has been newly written to reflect changes in the technology available. The major tables in Chapter 6 have been regenerated and reorganized to reflect an improved list of characters useful for mathematics, and the text revised to reflect the new situation in regard to Unicode. Chapter 7 has been completely revised since Web technology has changed. A new Chapter 8 on the DOM for MathML 2.0 has been added; the latter points to new appendices D and E for detailed listings.

The appendices have been reorganized into normative and non-normative groups. Appendices D, E and G are completely new.

## Table of contents

1 Introduction
1.1 Mathematics and its Notation
1.2 Origins and Goals
1.3 The Role of MathML on the Web
2 MathML Fundamentals
2.1 MathML Overview
2.2 MathML in a Document
2.3 Some MathML Examples
2.4 MathML Syntax and Grammar
3 Presentation Markup
3.1 Introduction
3.2 Token Elements
3.3 General Layout Schemata
3.4 Script and Limit Schemata
3.5 Tables and Matrices
3.6 Enlivening Expressions
4 Content Markup
4.1 Introduction
4.2 Content Element Usage Guide
4.3 Content Element Attributes
4.4 The Content Markup Elements
5 Combining Presentation and Content Markup
5.1 Why Two Different Kinds of Markup?
5.2 Mixed Markup
5.3 Parallel Markup
5.4 Tools, Style Sheets and Macros for Combined Markup
6 Characters, Entities and Fonts
6.1 Introduction
6.2 MathML Characters
6.3 Character Symbol Listings
6.4 Differences from Characters in MathML 1
7 The MathML Interface
7.1 Embedding MathML in other Documents
7.2 Conformance
7.3 Future Extensions
8 Document Object Model for MathML
8.1 Introduction

### Appendices

A Parsing MathML
A.1 DOCTYPE Declaration for MathML
A.2 MathML as a DTD Module
A.3 Namespace prefix declarations
A.4 Use of MathML without a DTD
A.5 SGML
A.6 The MathML DTD
B Content Markup Validation Grammar
C Content Element Definitions
C.1 About Content Markup Elements
C.2 Definitions of MathML Content Elements
D Document Object Model for MathML
D.1 IDL Interfaces
D.2 MathML DOM Tables
E MathML Document Object Model Bindings (Non-normative)
E.1 MathML Document Object Model IDL Binding
E.2 MathML Document Object Model Java Binding
E.3 MathML Document Object Model ECMAScript Binding
F Operator Dictionary (Non-normative)
F.1 Format of operator dictionary entries
F.2 Indexing of operator dictionary
F.3 Choice of entity names
F.4 Notes on `lspace` and `rspace` attributes
F.5 Operator dictionary entries
G Sample CSS Style Sheet for MathML (Non-normative)
H Glossary (Non-normative)
I Working Group Membership and Acknowledgments (Non-normative)
I.1 The Math Working Group Memberships
I.2 Acknowledgments
J Changes (Non-normative)
K References (Non-normative)