Mathematical Markup Language (MathML) Version 2.0 (Second Edition)
W3C Recommendation 21 October 2003, superseded 7 March 2023
- This version:
- https://www.w3.org/TR/2023/SPSD-MathML2-20230307/
- Latest MathML 2 version:
- https://www.w3.org/TR/MathML2/
- Latest MathML Recommendation:
- https://www.w3.org/TR/MathML/
- Previous version:
- http://www.w3.org/TR/2003/REC-MathML2-20031021/
- 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, David Carlisle, Stéphane Dalmas, Stan Devitt, Angel Diaz, Max Froumentin, Roger Hunter, Patrick Ion, Michael Kohlhase, Robert Miner, Nico Poppelier, Bruce Smith, Neil Soiffer, Robert Sutor, Stephen Watt
Please refer to theerratafor this document, which may include some normative corrections.
In addition to theHTML version, this document is also available in these non-normative formats:diff marked HTML version,XHTML+MathML version,PDF (paper formatted) version,PDF (screen formatted) version,zip archive of XML sources and stylesheets, and zip archive of (X)HTML documents.
See alsotranslations.
Copyright © 1998-2003W3C® (MIT,ERCIM,Keio), All Rights Reserved. W3Cliability,trademark,document use andsoftware licensing rules apply.
Abstract
This specification defines the Mathematical Markup Language, orMathML. MathML is an XML applicationfor describing mathematical notation and capturing both its structure andcontent. The goal of MathML is to enable mathematics to be served,received, and processed on the World Wide Web, just asHTML has enabled this functionality fortext.
This specification of the markup language MathML is intendedprimarily for a readership consisting of those who will be developingor implementing renderers or editors using it, or software that willcommunicate using MathML as a protocol for input or output. It isnot a User's Guide but rather a reference document.
This document begins with background information on mathematicalnotation, the problems it poses, and the philosophy underlying thesolutions MathML 2.0 proposes. MathML can be used to encode bothmathematical notation and mathematical content. About thirty of theMathML tags describe abstract notational structures, while anotherabout one hundred and fifty provide a way of unambiguously specifyingthe intended meaning of an expression. Additional chapters discuss howthe MathML content and presentation elements interact, and how MathMLrenderers might be implemented and should interact withbrowsers. Finally, this document addresses the issue of MathMLcharacters and their relation to fonts.
While MathML is human-readable, it is anticipated that, in all butthe simplest cases, authors will use equation editors, conversionprograms, and other specialized software tools to generateMathML. Several versions of such MathML tools already exist, anda number of others, both freely available software and commercialproducts, are under development.
Status of this Document
This section describes the status of this document at the timeof its publication. Other documents may supersede this document. Alist of current W3C publications and the latest revision of thistechnical report can be found in theW3C technical reports index athttp://www.w3.org/TR/.
This specification is a Superseded Recommendation. A newerspecification exists that is recommended for new adoption in place ofthis specification.
For purposes of the W3C Patent Policy, this SupersededRecommendation has the same status as an active Recommendation; itretains licensing commitments and remains available as a reference forold – and possibly still deployed – implementations, butis not recommended for future implementation. New implementationsshould follow the latest version of the MathML specification. (This isfurther explainedinObsoleting and Rescinding W3C Specifications.
This is a revised edition of a document that has been reviewed by W3C Members and other interestedparties and has been endorsed by the Director as aW3CRecommendation.
This document has been produced by theW3C Math Working Group as part ofW3CMathActivity.The goals of the W3C Math Working Group arediscussed in the W3C Math WGCharter (revised February 2000 and June 2001 from the original of 11June 1998). A list ofparticipants in the W3C Math Working Groupis available.
The MathML 2.0 (Second Edition) specification was reviewed extensively during its development, as provided by the W3C Process. During that period the W3C Math Working Group participants encouraged implementation using the specification and comment on it; a report onImplementation 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 Activity maintains a public Web pagehttp://www.w3.org/Math/ which contains further background information.
The preparation of a Second Edition of the MathML 2.0 Specification allows the revision of that document to provide a coherent wholecontaining corrections to all the known errata and clarifications of some smaller issues that proved problematic. It is not the occasionfor any fundamental changes in the language MathML 2.0. To clarify this adiff-marked HTML version of this Second Editionis made available.
Public discussion of MathML and issues of support through the W3Cfor mathematics on the Web takes place on the public mailing list of the Math WorkingGroup (list archives).To subscribe send an email towww-math-request@w3.orgwith the wordsubscribe in the subject line.
Please report errors in this document towww-math@w3.org.
Patent disclosures relevant to this specification may be found on the Math Working Group'spatentdisclosure page.
The basic structure of this document is the same as that ofthe earlier MathML 2.0 Recommendation[MathML2], withthe addition of an index in the new Appendix L.MathML 2.0 itself was a revision of the earlier W3C Recommendation MathML 1.01[MathML1]. It differed from it in that all chapters were updated andtwo new ones and some appendices were added.
Since MathML 1.01,Chapters 1 and 2, which are introductory material, have been revisedto reflect the changes elsewhere in the document, and in the rapidlyevolving Web environment. Chapters 3 and 4 have been extended todescribe new functionalities added as well as smaller improvements ofmaterial already proposed. Chapter 5 has been newly written to reflectchanges in the technology available. The major tables in Chapter 6have been regenerated and reorganized to reflect an improved list of characters useful for mathematics, and the text revised to reflect thenew situation in regard to Unicode. Chapter 7 has been completelyrevised since Web technology has changed. A new Chapter 8 on the DOM forMathML 2.0 has been added; the latter points to new appendices D and E fordetailed listings.
The appendices have been reorganized into normative andnon-normative groups. The material in Appendices D, E, G and L was not present in MathML 1.01.
