[1]W3C

Mathematical Markup Language (MathML^(TM)) 1.01 Specification

W3C Recommendation, revision of 7 July 1999, superseded 7 March 2023

   REC-MathML-19980407; revised 19990707

   This version:
          [2]https://www.w3.org/TR/2023/SPSD-MathML-20230307/

   Latest version:
          [3]https://www.w3.org/TR/REC-MathML

   Previous version:
          [4]http://www.w3.org/1999/07/REC-MathML-19990707

   Editors:
          Patrick Ion [5]
          (Mathematical Reviews / American Mathematical Society)
          Robert Miner [6]
          (Geometry Technologies, Inc.)

   Principal Writers:
          Stephen Buswell, Stan Devitt, Angel Diaz, Patrick Ion, Robert Miner,
          Nico Poppelier, Bruce Smith, Neil Soiffer, Robert Sutor, Stephen Watt

   [7]
   Copyright © 1999 [8]W3C ([9]MIT, [10]INRIA, [11]Keio), All Rights Reserved. W3C
   [12]liability, [13]trademark, [14]document use and [15]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 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 proposes.
   MathML can be used to encode both mathematical notation and mathematical content.
   Twenty-eight of the MathML tags describe abstract notational structures, while
   another seventy-five 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.

   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 specification is a Superseded Recommendation. A newer specification exists
   that is recommended for new adoption in place of this specification.

   For purposes of the W3C Patent Policy, this Superseded Recommendation has the
   same status as an active Recommendation; it retains licensing commitments and
   remains available as a reference for old - and possibly still deployed -
   implementations, but is not recommended for future implementation. New
   implementations should follow the latest version of the MathML specification.
   (This is further explained in [16]Obsoleting and Rescinding W3C Specifications.)

   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.

   The fundamental [17]eXtensible Markup Language (XML) 1.0 specification upon which
   MathML is based has 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 W3C Math Working Group to issue a revision of the MathML
   specification. However, any changes are very unlikely to be substantial.

   Most of this document represents technology tested by multiple implementations. A
   summary of MathML rendering and authoring software is described on the [18]W3C
   Math Working Group home page.

   The [19]www-math mailing list is a public forum for questions and comments about
   MathML and issues related to putting math on the Web.

   The W3C Math Working Group intends further development of recommendations for
   mathematics on the Web, as set out [20]below.

   A list of current W3C Recommendations and other technical reports can be found at
   [21]http://www.w3.org/TR.

   This document is a revised version of the document first released on 7 April
   1998. [22]Changes from the original version are only editorial in nature. The
   present W3C Math Working Group is working on further improvements of MathML.

  Available formats

   The MathML 1.01 W3C Recommendation is made available in different formats from
   the [23]W3C Math WG's site. 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 Recommendation. At first it is expected that zipped and
   gzipped bundles will be made available, but such easily printable formats as
   PostScript or PDF may be supplied.

  Available languages

   The English version of this specification is the only normative version. However,
   for translations of this document, see
   [24]http://www.w3.org/MarkUp/mathml101-updates/translations.html.

  Errata

   The list of known errors in this specification is available at:
          [25]http://www.w3.org/MarkUp/mathml101-updates/errata.html.

   Please report errors in this document to [26]www-math@w3.org.

Table of contents

   [27]Extended Table of Contents
     * [28]Chapter 1. Introduction
     * [29]Chapter 2. MathML Fundamentals
     * [30]Chapter 3. Presentation Markup
     * [31]Chapter 4. Content Markup
     * [32]Chapter 5. Mixing Presentation and Content
     * [33]Chapter 6. Entities, Characters and Fonts
     * [34]Chapter 7. Implementing MathML

     * [35]Appendix A. DTD for MathML
     * [36]Appendix B. Glossary
     * [37]Appendix C. Operator Dictionary
     * [38]Appendix D. Working Group Membership
     * [39]Appendix E. Informal EBNF Grammar for Content Elements
     * [40]Appendix F. Default Semantic Bindings for Content Elements
     * [41]Appendix G. MathML 1.0 Changes

     * [42]References

References

   1. https://www.w3.org/
   2. https://www.w3.org/TR/2023/SPSD-MathML-20230307/
   3. https://www.w3.org/TR/REC-MathML
   4. https://www.w3.org/1999/07/REC-MathML-19990707
   5. mailto:ion@ams.org
   6. mailto:rminer@geomtech.com
   7. https://www.w3.org/Consortium/Legal/ipr-notice#Copyright
   8. https://www.w3.org/
   9. http://www.lcs.mit.edu/
  10. http://www.inria.fr/
  11. http://www.keio.ac.jp/
  12. https://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer
  13. https://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks
  14. https://www.w3.org/Consortium/Legal/copyright-documents
  15. https://www.w3.org/Consortium/Legal/copyright-software
  16. https://www.w3.org/2016/11/obsoleting-rescinding/
  17. https://www.w3.org/pub/WWW/TR/REC-xml
  18. https://www.w3.org/Math
  19. http://lists.w3.org/Archives/Public/www-math
  20. https://www.w3.org/TR/REC-MathML/chapter1.html#goals
  21. https://www.w3.org/TR
  22. https://www.w3.org/TR/REC-MathML/appendixG.html
  23. https://www.w3.org/Math
  24. https://www.w3.org/MarkUp/mathml101-updates/translations.html
  25. https://www.w3.org/MarkUp/mathml101-updates/errata.html
  26. mailto:www-math@w3.org
  27. https://www.w3.org/TR/REC-MathML/toc.html
  28. https://www.w3.org/TR/REC-MathML/chapter1.html
  29. https://www.w3.org/TR/REC-MathML/chapter2.html
  30. https://www.w3.org/TR/REC-MathML/chap3_1.html
  31. https://www.w3.org/TR/REC-MathML/chap4_1.html
  32. https://www.w3.org/TR/REC-MathML/chapter5.html
  33. https://www.w3.org/TR/REC-MathML/chapter6.html
  34. https://www.w3.org/TR/REC-MathML/chapter7.html
  35. https://www.w3.org/TR/REC-MathML/appendixA.html
  36. https://www.w3.org/TR/REC-MathML/appendixB.html
  37. https://www.w3.org/TR/REC-MathML/appendixC.html
  38. https://www.w3.org/TR/REC-MathML/appendixD.html
  39. https://www.w3.org/TR/REC-MathML/appendixE.html
  40. https://www.w3.org/TR/REC-MathML/appendixF.html
  41. https://www.w3.org/TR/REC-MathML/appendixG.html
  42. https://www.w3.org/TR/REC-MathML/refs.html