HistoryMathML 1 was released as a W3C recommendation in April 1998 as the first XML language to be recommended by the W3C. Version 1.01 of the format was released in July 1999 and version 2.0 appeared in February 2001. In October 2003, the second edition of MathML Version 2.0 was published as the final release by the W3C Math Working Group. MathML was originally designed before the finalization of XML namespaces. However, it was assigned a namespace immediately after the Namespace Recommendation was completed, and for XML use, the elements should be in the namespace with namespace URL
MathML version 3Version 3 of the MathML specification was released as a World Wide Web Consortium#W3C recommendation (REC), W3C recommendation on 20 October 2010. A recommendation of ''A MathML for CSS Profile'' was later released on 7 June 2011; this is a subset of MathML suitable for CSS formatting. Another subset, ''Strict Content MathML'', provides a subset of content MathML with a uniform structure and is designed to be compatible with OpenMath. Other content elements are defined in terms of a transformation to the strict subset. New content elements include which associates bound variables () to expressions, for example a summation index. The new element allows structure sharing. The development of MathML 3.0 went through a number of stages. In June 2006 the W3C rechartered the MathML Working Group to produce a MathML 3 Recommendation until February 2008 and in November 2008 extended the charter to April 2010. A sixth Working Draft of the MathML 3 revision was published in June 2009. On 10 August 2010 version 3 graduated to become a "Proposed Recommendation" rather than a draft.Mathematical Markup Language Version 3.0 W3C Recommendation
Presentation and semanticsMathML deals not only with the ''presentation'' but also the ''meaning'' of formula components (the latter part of MathML is known as "Content MathML"). Because the meaning of the equation is preserved separate from the presentation, how the content is communicated can be left up to the user. For example, web pages with MathML embedded in them can be viewed as normal web pages with many browsers, but visually impaired users can also have the same MathML read to them through the use of screen readers (e.g. using the MathPlayer Plug-in (computing), plugin for Internet Explorer or Firefox, Opera (web browser), Opera 9.50 build 9656+ or the Fire Vox extension for Firefox). Newer versions of JAWS (screen reader), JAWS support MathML voicing as well as braille output.
Presentation MathMLPresentation MathML focuses on the display of an equation, and has about 30 elements. The elements' names all begin with . A Presentation MathML expression is built up out of ''tokens'' that are combined using higher-level elements, which control their layout (there are also about 50 attributes, which mainly control fine details). Token elements generally only contain characters (not other elements). They include: * – identifiers; * – operators; * – numbers. * – text. Note, however, that these token elements may be used as extension points, allowing markup in host languages. MathML in HTML5 allows most inline HTML markup in mtext, and is conforming, with the HTML markup being used within the MathML to mark up the embedded text (making the first word bold in this example). These are combined using layout elements, that generally contain only elements. They include: * – a horizontal row of items; * , , and others – superscripts, limits over and under operators like sums, etc.; * – fractions; * and – roots; * – surrounding content with fences, such as parentheses. As usual in HTML and XML, many character entity reference, entities are available for specifying special symbols by name, such as and . An interesting feature of MathML is that entities also exist to express normally-invisible operators, such as (or the shorthand ) for implicit multiplication. They are: * U+2061 FUNCTION APPLICATION; * U+2062 INVISIBLE TIMES; * U+2063 INVISIBLE SEPARATOR; * U+2064 INVISIBLE PLUS. The full specification of MathML entities is closely coordinated with the corresponding specifications for use with HTML and XML in general. Thus, the expression requires two layout elements: one to create the overall horizontal row and one for the superscripted exponent. Including only the layout elements and the (not yet marked up) bare tokens, the structure looks like this:
Content MathMLContent MathML focuses on the semantics, or meaning, of the expression rather than its layout. Central to Content MathML is the element that represents function application. The function being applied is the first child element under , and its operands or parameters are the remaining child elements. Content MathML uses only a few attributes. Tokens such as identifiers and numbers are individually marked up, much as for Presentation MathML, but with elements such as and . Rather than being merely another type of token, operators are represented by specific elements, whose mathematical semantics are known to MathML: , , etc. There are over a hundred different elements for different functions and operators. For example, represents and represents . The elements representing operators and functions are empty elements, because their operands are the other elements under the containing . The expression could be represented as
Wikidata annotation in Content MathMLAccording to the OM Society, OpenMath Content Dictionaries can be employed as collections of symbols and identifiers with declarations of their semanticsnames, descriptions and rules. A 2018 paper presented at the Special Interest Group on Information Retrieval, SIGIR conference proposed that the semantic knowledge base Wikidata could be used as an OpenMath Content Dictionary to link semantic elements of a mathematical formula to unique and language-independent Wikidata items.
Example and comparison to other formatsThe well-known quadratic formula: : would be marked up using LaTeX syntax like this:
Embedding MathML in HTML/XHTML filesMathML, being XML, can be embedded inside other XML files such as XHTML files using XML namespaces. Browsers such as Firefox 3+ and Opera 9.6+ (support incomplete) can display Presentation MathML embedded in XHTML.
The area of a circle is .
The area of a circle is .
Other standardsAnother standard called OpenMath that has been designed (largely by the same people who devised Content MathML) more specifically for storing formulae semantically can also be used to complement MathML. OpenMath data can be embedded in MathML using the element. OpenMath ''content dictionaries'' can be used to define the meaning of elements. The following would define ''P''1(''x'') to be the first Legendre polynomial