MathML

MathML 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 http://www.w3.org/1998/Math/MathML. When MathML is used in HTML (as opposed to XML) this namespace is automatically inferred by the HTML parser and need not be specified in the document.

MathML 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 plugin for Internet Explorer or Firefox, Opera 9.50 build 9656+ or the Fire Vox extension for Firefox). Newer versions of JAWS support MathML voicing as well as braille output.[6]

  <mrow>
    a &InvisibleTimes; <msup>x 2</msup>
    + b &InvisibleTimes; x
    + c
  </mrow>

  <mrow>
    <mi>a</mi> <mo>&InvisibleTimes;</mo> <msup><mi>x</mi><mn>2</mn></msup>
    <mo>+</mo><mi>b</mi><mo>&InvisibleTimes;</mo><mi>x</mi>
    <mo>+</mo><mi>c</mi>
  </mrow>

<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE math PUBLIC "-//W3C//DTD MathML 2.0//EN"
         "http://www.w3.org/Math/DTD/mathml2/mathml2.dtd">
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>a</mi> <mo>&InvisibleTimes;</mo> <msup><mi>x</mi><mn>2</mn></msup>
    <mo>+</mo><mi>b</mi><mo>&InvisibleTimes;</mo><mi>x</mi>
    <mo>+</mo><mi>c</mi>
  </mrow>
</math>

<math>
    <apply>
        <plus/>
        <apply>
            <times/>
            <ci>a</ci>
            <apply>
                <power/>
                <ci>x</ci>
                <cn>2</cn>
            </apply>
        </apply>
        <apply>
            <times/>
            <ci>b</ci>
            <ci>x</ci>
        </apply>
        <ci>c</ci>
    </apply>
</math>

(plus
  (times a (power x 2))
  (times b x)
  c)

The well-known quadratic formula:

${\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}$

would be marked up using LaTeX syntax like this:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

in troff/eqn like this:

x = {-b +- sqrt{b sup 2 – 4ac}} over 2a

in Apache OpenOffice Math and LibreOffice Math like this (all three are valid):

x = {-b plusminus sqrt {b^2 – 4 ac}} over {2 a}
x = {-b +- sqrt {b^2 – 4ac}} over {2a}
x = {-b ± sqrt {b^2 – 4ac}} over {2a}

in AsciiMath like this:

x = (-b +- sqrt(b^2 - 4ac))/(2a)

The above equation could be represented in Presentation MathML as an expression tree made up from layout elements like mfrac or msqrt elements:

<math mode="display" xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
  <mrow>
    <mi>x</mi>
    <mo>=</mo>
    <mfrac>
      <mrow>
        <mo form="prefix">&minus;</mo>
        <mi>b</mi>
        <mo>&pm;</mo>
        <msqrt>
          <msup><mi>b</mi><mn>2</mn></msup>
          <mo>&minus;</mo>
          <mn>4</mn><mo>&it;</mo><mi>a</mi><mo>&it;</mo><mi>c</mi>
        </msqrt>
      </mrow>
      <mrow>
        <mn>2</mn>
        <mo>&it;</mo>
        <mi>a</mi>
      </mrow>
    </mfrac>
  </mrow>
  <annotation encoding="application/x-tex"><!-- TeX -->
     x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}
  </annotation>
  <annotation encoding="StarMath 5.0">
     x = {-b plusminus sqrt {b^2 - 4 ac}} over {2 a}
  </annotation>
  <!-- More annotations can be written: application/x-troff-eqn for eqn, application/x-asciimath for AsciiMath... -->
  <!-- Semantic MathML go under <annotation-xml encoding="MathML-Content">. -->
 </semantics>
</math>

This example uses the <annotation> element, which can be used to embed a semantic annotation in non-XML format, for example to store the formula in the format used by an equation editor such as StarMath or the markup using LaTeX syntax. The encoding field is usually a MIME type, although most of the equation encodings don't have such a registration; freeform text may be used in such case.

Although less compact than TeX, the XML structuring promises to make it widely usable, allows instant display in applications such as Web browsers, and facilitates an interpretation of its meaning in mathematical software products. MathML is not intended to be written or edited directly by humans.[14]

MathML, 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.

<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html  PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN"
  "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
  <head>
    <title>Example of MathML embedded in an XHTML file</title>
    <meta name="description" content="Example of MathML embedded in an XHTML file"/>
  </head>
  <body>
    <h1>Example of MathML embedded in an XHTML file</h1>
    <p>
      The area of a circle is 
      <math xmlns="http://www.w3.org/1998/Math/MathML">
        <mi>&#x03C0;<!-- π --></mi>
        <mo>&#x2062;<!-- &InvisibleTimes; --></mo>
        <msup>
          <mi>r</mi>
          <mn>2</mn>
        </msup>
      </math>.
    </p>
  </body>
</html>

A rendering of the formula for a circle in MathML+XHTML using Firefox 22 on Mac OS X

Inline MathML is also supported in HTML5 files in the current versions of WebKit (Safari and JavaFX/WebView ), Gecko (Firefox). There is no need to specify namespaces like in the XHTML.

<!DOCTYPE html>
<html lang="en">
  <head>
    <meta charset="utf-8">
    <title>Example of MathML embedded in an HTML5 file</title>
  </head>
  <body>
    <h1>Example of MathML embedded in an HTML5 file</h1>
    <p>
      The area of a circle is 
      <math>
        <mi>&pi;</mi>
        <mo>&InvisibleTimes;</mo>
        <msup>
          <mi>r</mi>
          <mn>2</mn>
        </msup>
      </math>.
    </p>
  </body>
</html>

Of the major web browsers, Gecko-based browsers (e.g., Firefox) have the most complete native support for MathML.[15][16]

While the WebKit layout engine has a development version of MathML,[17] this feature is only available in version 5.1 and higher of Safari,[18] Chrome 24[19][20] but not in later versions of Chrome.[21] Google removed support of MathML claiming architectural security issues and low usage do not justify their engineering time.[22] As of October 2013, the WebKit/Safari implementation has numerous bugs.[23]

JavaFX/WebView. Also based on WebKit, the JavaFX embedded web browser supports MathML starting with JavaFX 8 Update 192 and JavaFX 11 versions. Support is broken, in JavaFX 8 previous versions, JavaFX 9 and JavaFX 10.

Opera, between version 9.5 and 12, supports MathML for CSS profile,[24][25] but is unable to position diacritical marks properly.[26] Prior to version 9.5 it required User JavaScript or custom stylesheets to emulate MathML support.[27] Starting with Opera 14, Opera drops support for MathML by switching to the Chromium 25 engine.[28]

Microsoft Edge does not support MathML, nor are there plans to add support.[29]

Internet Explorer does not support MathML natively. Support for IE6 through IE9 can be added by installing the MathPlayer plugin.[30] IE10 has some crashing bugs with MathPlayer and Microsoft decided to completely disable in IE11 the binary plug-in interface that MathPlayer needs.[31] MathPlayer has a license that may limit its use or distribution in commercial webpages and software. Using or distributing the MathPlayer plugin to display HTML content via the WebBrowser control in commercial software may also be forbidden by this license.

The KHTML-based Konqueror currently does not provide support for MathML.[32]

The quality of rendering of MathML in a browser depends on the installed fonts. The STIX Fonts project have released a comprehensive set of mathematical fonts under an open license. The Cambria Math font supplied with Microsoft Windows had a slightly more limited support.[33]

According to a member of the MathJax team, none of the major browser makers paid any of their developers for any MathML-rendering work; whatever support exists is overwhelmingly the result of unpaid volunteer time/work.[34]

In 2015 the MathML Association was founded to support the adoption of the MathML standard.[35]

Another 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 <annotation-xml encoding="OpenMath"> element. OpenMath content dictionaries can be used to define the meaning of <csymbol> elements. The following would define P₁(x) to be the first Legendre polynomial

<apply>
  <csymbol encoding="OpenMath" definitionURL="http://www.openmath.org/cd/contrib/cd/orthpoly1.xhtml#legendreP">
    <msub><mi>P</mi><mn>1</mn></msub>
  </csymbol>
  <ci>x</ci>
</apply>

The OMDoc format has been created for markup of larger mathematical structures than formulae, from statements like definitions, theorems, proofs, or example, to theories and text books. Formulae in OMDoc documents can either be written in Content MathML or in OpenMath; for presentation, they are converted to Presentation MathML.

The ISO/IEC standard Office Open XML (OOXML) defines a different XML math syntax, derived from Microsoft Office products. However, it is partially compatible[40] through relatively simple XSL Transformations.

• CSS
• List of document markup languages
• Comparison of document markup languages
• Formula editors
• LaTeX2HTML
• LaTeXML
• KaTeX – JavaScript library that converts LaTeX to MathML
• MathJax – JavaScript library that converts LaTeX to MathML

• W3C Math Home – Contains the specifications, a FAQ, and a list of supporting software.
• Pavi, Sandhu (12 December 2002). "The Mathml Handbook". Charles River Media. Retrieved 2 October 2015.
• web-xslt, a collection of XSLT programs for handling MathML (e.g. converting Content MathML to Presentation MathML, converting Presentation MathML to TeX)