Documents and Specifications - Software - Mathematics on the Web - Working Group - Background - Activity Statement - MathML Test Suite - Member Area - MathML Conference
MathML 2.0 , a W3C Recommendation was released on 21 Feb 2001. A product of the W3C Math working group, MathML is a low-level specification for describing mathematics as a basis for machine to machine communication. It provides a much needed foundation for the inclusion of mathematical expressions in Web pages [more].Try it!
17 implementations of MathML are available (browsers and authoring tools), many of which are open source software. Go to the software section for descriptions and pointers, or read the Implementation and Interoperability report.
The MathML Test Suite has over 400 tests of various functions in the MathML 2.0 specification. An interface is being developed to permit additions to the set by the user community.
The Candidate Recommendation period is one of stability when implementation prototypes and trials of interoperability are encouraged. The Candidate Recommendation period for MathML extends until December 14, 2000. It is this short because in fact there are already several significant prototype implementations of MathML underway. Reports of the experience with the specification in practice will determine when the MathML specification will be put forward as a Proposed Recommendation. Please take a look.
The successful first conference entirely dedicated to MathML and Math on the Web took place October 20-21, 2000, Urbana-Champaign, IL, USA. [There are some transcripts and slides of talks available.]
MathML is intended to facilitate the use and re-use of mathematical and scientific content on the Web, and for other applications such as computer algebra systems, print typesetting, and voice synthesis. MathML can be used to encode both the presentation of mathematical notation for high-quality visual display, and mathematical content, for applications where the semantics plays more of a key role such as scientific software or voice synthesis.
MathML is cast as an application of XML. As such, with adequate style sheet support, it will ultimately be possible for browsers to natively render mathematical expressions. For the immediate future, several vendors offer applets and plug-ins which can render MathML in place in a browser. Translators and equation editors which can generate HTML pages where the math expressions are represented directly in MathML will be available soon.
Although the mark-up language HTML has a large repertoire of tags, it does not cater for math. With no means of using HTML tags to mark up mathematical expressions, authors have resorted to drastic means. For example, a popular method involves inserting images - literally snap shots of equations taken from other packages and saved in GIF format - into technical documents which have a mathematical or scientific content.
W3C has been working with a number of companies with experience in editing and processing math on computers, as well as other specialist organizations. This work has culminated in a markup language called MathML, and W3C released MathML 1.0 as a Recommendation in April 1998. On July 7, 1999 the Math Working Group posted MathML 1.01, a revised version of the MathML 1.0 Recommendation.
The present Math WG has been working on an extension of MathML which has further customization possibilites, and which is in harmony with the recent developments in Web markup technology. The results of this effort have been a series of Working drafts of MathML 2, the most recent of which is highlighted at the top of this page.
For more information about MathML and the activities of the W3C Math working group, consult the W3C Math Activity Report or the MathML FAQ, by Stephen Buswell et. al. (a wealth of introductory and background information on MathML).
MathML consists of a number of XML tags which can be used to mark up an equation in terms of its presentation and also its semantics. MathML attempts to capture something of the meaning behind equations rather than concentrating entirely on how they are going to be formatted out on the screen. This is on the basis that mathematical equations are meaningful to many applications without regard as to how they are rendered aurally or visually.
XML is closely related to HTML and assumes a very similar, but not identical syntax. One distinction is that in XML you cannot omit end tags. Furthermore, tags for elements which don't have any content are specially marked by a slash before the closing angle bracket.
MathML is a low-level format for describing mathematics as a basis for machine to machine communication. MathML is not intended for editing by hand, but is for handling by specialized authoring tools such as equation editors, or for export to and from other math packages.
MathML is intended to facilitate the use and re-use of mathematical and scientific content on the Web, and for other applications such as computer algebra systems, print typesetters, and voice synthesizers. MathML can be used to encode both mathematical notation, for high-quality visual display, and mathematical content, for more semantic applications like scientific software, or voice synthesis.
This simple example of MathML gives you an idea of how it works. The equation in question is:
x2 + 4x + 4 =0
and below are two ways that this can be represented, first using presentational tags, then using semantic tags. The presentational tags generally start with "m" and then use "o" for operator "i" for identifier "n" for number, and so on. The "mrow" tags indicate organization into horizontal groups.
<mrow>
<mrow>
<msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo>
<mrow>
<mn>4</mn>
<mo>⁢</mo>
<mi>x</mi>
</mrow>
<mo>+</mo>
<mn>4</mn>
</mrow>
<mo>=</mo>
<mn>0</mn>
</mrow>
The semantic tags take into account such concepts as "times", "power of" and so on:
<apply>
<plus/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<times/>
<cn>4</cn>
<ci>x</ci>
</apply>
<cn>4</cn>
</apply>
Combined with a style sheet to specify other aspects of layout, MathML should eventually be used by browsers without the use of plug-ins. At present, several vendors offer applet and plug-ins which can render MathML in place in a browser. Translators and equation editors which can generate HTML pages with images of the mathematical expression from HTML with embedded MathML code will be available soon. A detailed survey of some software applications that render and make use of MathML (including screen shots of MathML in action) is available.
Additional Working Group Information:
This section points to mathematical resources on the Web, not necessarily related to MathML
The Math working group is co-chaired by Patrick Ion of AMS (Mathematical Reviews), and Angel Diaz of IBM Research. There is a great deal of activity in the W3C Math working group at the moment.
Both co-chairs are fully informed, and intimately involved in the activities of the working group. Contact either of the co-chairs if you are interested in joining the group, or need other information about the W3C Math Working Group.
| Name | Status | Company |
|---|---|---|
| Ausbrooks, Ron | Mackichan Software | |
| Bernardin, Laurent | Waterloo Maple | |
| Brutzman, Don | TBD | Web3D |
| Buswell, Stephen | Stilo Technology Ltd | |
| Carlisle, David | Invited expert | NAG |
| Dalmas, Stéphane | INRIA | |
| Devitt, Stan | Invited expert | Stratum Technical Services |
| Diaz, Angel | Co-chair | IBM |
| Dooley, Sam | alternate | IBM |
| Froumentin, Max | W3C contact | W3C |
| Gayley, Todd | alternate | Wolfram Research |
| Hunter, Roger | Alternate | MacKichan |
| Ion, Patrick | Co-chair, Invited expert | MR/AMS |
| Kohlhase, Michael | DFKI | |
| Linetsky, Gene | Alternate | Saba |
| Lovell, Douglas | observer | IBM |
| Miner, Robert | Invited expert | Design Science |
| Padovani, Luca | alternate | University of Bologna, Italy |
| Philips, Ivor | The Boeing Company | |
| Raman, T.V. | observer | IBM |
| Robson, Robby | Saba | |
| Sargent, Murray | Microsoft | |
| Schena, Irene | University of Bologna, Italy | |
| Soiffer, Neil | Wolfram Research | |
| Topping, Paul | alternate | Design Science |
| Travis, Leopold | MathSoft | |
| Watt, Stephen | Invited expert | Univ. of Western Ontario |
Subscription information can be found at The W3C mailing list administrivia page.
| Date | Document |
| Feb 21, 2001 | Mathematical Markup
Language (MathML) 2.0 Recommendation
Also available as: |
| MathML Test Suite | |
| Feb 20, 2001 | Implementation and Interoperability Report |
| July 07, 1999 | Mathematical
Markup Language (MathML) 1.01 Recommendation
Note: it is recommended that users and implementors adopt MathML2.0. This link is provided for mostly historical and compatibility purposes |
| June 11, 1998 | W3C Math Working Group Charter - Angel Diaz, Patrick Ion |
| June 11, 1998 | Briefing Package for W3C Math Activity - Angel Diaz, Patrick Ion |
| May 14, 1998 | MathML Requirements - Paul Topping |
| April 07, 1998 | Mathematical Markup Language (MathML) 1.0 Specification (replaced by 1.01) |
| Date | Document |
| January 08, 1998 | Mathematical Markup Language Working Draft |
| May 26, 1998 | EzMath - an easy to use textual format based upon how you would read mathematical expressions over the phone [Dave Raggett, W3C] |
| April 11, 1997 | HTML Math Working Group Charter |
| June 22, 1996 | MINSE - a concise medium-independent notation for math [Ka-Ping Yee,University of Waterloo] |
| May 31, 1996 | Wolfram
Proposal for HTML-Math
|
| August 30, 1995 | Unicode, Rich Text, and Mathematics - Murray Sargent, Microsoft |
| March 01, 1995 | HTML 3.0 Internet Draft (Expired) |
| August 10, 1994 | AsTeR - Audio System For Technical Readings [T. V. Raman, Adobe] |
| August 10, 1994 | Unicode Plain-Text Encoding of Mathematics - Murray Sargent, Microsoft |
| June 01, 1993 | ISO 12083 Math DTD and explanatory text |
| Browser Interface Requirements for HTML Math - Robert Miner | |
| Thoughts on HTML Math - Bruce Smith Wolfram Research | |
| A letter on medium-independence of layout schema - Bruce Smith Wolfram Research | |
| An HTML Native Proposal | |
| Standard dtd's and scientific publishing , N.A.F.M. Poppelier, E. van Herwijnen, C.A. Rowley | |
| Entity sets of TR 9573 | |
| Tables of Mathematica 3.0 characters | |
| Notational test examples | |
|
Design of a User Interface for Computer Algebra Systems - Neil Soiffer, Wolfram Research |
|
| A more semantically oriented Math DTD due to Roy Pike |
Some useful general information about putting math on the web:
