The World Wide Web Consortium (W3C) blessed version 3.0 of the MathML standard as an official "recommendation" in October of 2010. There are no major surprises in the revision, but software support has only started to catch up in recent months. Firefox 4 is the first browser to support MathML 3.0 directly, and new releases of the Firemath equation editor and STIX fonts enable in-browser editing and rendering, respectively. Widespread use of MathML may continue to elude scientists and educators in the near term, however, due to lackadaisical support in the other major browsers.
Let there be math
MathML is an XML-based specification for serving and rendering mathematical notation on the web. There are two ways to mark up mathematics in MathML, known as "presentation" MathML and "content" MathML. Presentation MathML focuses on making expressions human-readable, for use in web pages intended only to be read and understood. As a result, its fundamentals offer considerable control over the layout of the math, but do not try to capture its semantic meaning. Content MathML is designed to encode the semantic mathematical meaning of every expression, so it could be parsed and correctly understood by a computer algebra system.
For example, it is sufficient in presentation MathML to write
<msup> <mi>x</mi> <mn>2</mn></msup>
which simply renders the 2 as a superscript. But
content MathML must encode the meaning of that relationship, and thus uses
a different set of entities entirely:
<apply> <power/><ci>x</ci> <cn>2</cn> </apply>
Both markup systems delimit individual "tokens" including literal numbers, variables, and operators, plus separator characters such as parentheses, braces, fraction lines, and matrix brackets. In most cases, whether the notation or the functional structure is most important dictates which system the author should use, but they can be mixed together so long as sufficient care is taken.
Given that web-based computer algebra systems are scarce, presentation MathML is where most of the effort is focused. MathML's major historical competitor is TeX formatting, which predates MathML considerably. There are numerous conversion scripts to render TeX and LaTeX expressions into inline images, which was generally regarded as the "safe" option for self-publishing as well as for content management systems. In recent years, however, conversion scripts for transforming TeX notation into MathML are making a strong showing.
MathML 3.0 does not introduce major changes to MathML syntax, although there are new elements in presentation MathML to support elementary-level math notation, such as vertical addition, multiplication, and long division. The
mstack element is used to align such stacked rows of digits and operators; the related
mscarries elements support horizontal lines between rows and special borrow/carry rows. The
mlongdiv element is used to mark up a long division, with quotient, denominator, and properly-aligned intermediate calculation steps. Because long division notation varies considerably between regions, the element supports a
longdivstyle attribute with ten variations.
Most of MathML 3.0's changes address outstanding roadblocks to its adoption in the field. For starters, MathML 3.0 is officially part of HTML5, which means it can be delivered inline in HTML documents. MathML 2 required that the document be XHTML, delivered by the web server as application/xhtml+html, and linked to the W3C's MathML DTD. Until more HTML5 browsers support MathML, the old DTD as well as a new Relax NG schema are still available, and MathML MIME types have been registered, which is expected to push forward adoption in office applications and other non-browser environments.
The specification's definitions of content MathML elements have also been reorganized to better explain their alignment with the OpenMath semantic algebra system — an alignment that was part of previous revisions of MathML, but poorly documented. Finally, 3.0 explicitly supports mixing MathML with bi-directional text, closing a longstanding bug with the right-to-left text layout used in Arabic and Hebrew.
The Gecko 2.0 rendering engine at the heart of Firefox 4 supports the majority of presentation MathML 3.0, including tokens and general layout elements, and most (but not all) modifying attributes. Still unimplemented are the new elementary math layout elements, line-breaking attributes, and the ability to embed hyperlinks within MathML expressions. Mozilla maintains a status page where users can follow the progress of individual elements.
A more practical resource for those needing MathML support today is the demos page, which links to pages showcasing support for individual elements, plus tests of Firefox's CSS support for MathML. By default, Gecko renders different MathML tokens according to different rules. Single letters (which often appear as variables) are rendered in italics, while multi-character strings (which often represent functions, such as sin() or tan()) are rendered in non-italic style. But MathML allows the page author to style the typography of any element, which is useful for highlighting one term or part of an equation, but also provides fine control where necessary, such as to differentiate between n and n.
MathML itself supports writing non-alphanumeric symbols via HTML character codes, but to take advantage of them, the browser needs fonts that supply Unicode's mathematical operators and symbols. Mozilla's demos are written to support the limited character coverage of the Symbol font, but the project's recommended solution is to install the STIX font set, which provides a much larger set of symbols, and in multiple styles. Internally, Firefox uses the
font.mathfont-family configuration variable to choose the font used to display MathML, which uses a "fallback" list of math-supporting fonts
to select the most appropriate option, so neither the page author nor the user needs to manually set a font preference.
STIX also supports "stretchy" elements, such as integrals, radicals, vertical bars, various braces, and arrows that are expected to expand to whatever size is needed to delimit the accompanying expression. In late 2010, however, a regression crept in to Firefox's STIX support that broke stretchy separators. The fix required both a patch to Firefox (which made it in to the 4.0 release) as well as an update to the STIX fonts. The STIX fonts are available under the SIL Open Font License, but as of 2011 are provided only in OpenType format. Type 1 (for PostScript) and TrueType versions are on the roadmap for future releases.
Rendering support is excellent in Firefox, but MathML's syntax is still verbose enough that writing it by hand is infeasible for all but the simplest expressions. In addition to the weight added by marking up individual tokens, operators, and layout elements, MathML uses invisible elements such as
moverunder to carefully align the elements in every expression vertically and horizontally.
Fortunately, the Firemath extension provides a WYSIWYG MathML expression editor as a Firefox add-on. The latest edition, version 0.4.0.2, was released in March, with support for Firefox 3 and 4. Once installed, Firemath can be launched from the Tools menu. The editor runs inside a tab or browser window; the basic usage scenario consists of creating an equation or expression in the Firemath tab, copying it to the clipboard, then pasting the result as MathML into a page or external editor.
As one might anticipate, the editor itself reserves a large swatch of
space for a table of math operator and element buttons — enough are
provided that the main library panel breaks them into six tabs. But the
most common expressions and functions are separated out into a separate
toolbar at the top-left. The editor component itself consists of three
panes: the active WYSIWYG editor itself, a "live" render pane showing the
contents of the editor, and a source view, which shows the underlying
The WYSIWYG editor displays a rendering of the current expression, too, but it places small pink dots at available entry points in the MathML. Some of the toolbar buttons insert operators or elements into the expression at these entry points, while others (such as sub- or super-scripts) require you to select an existing element first. Thus, writing an expression can be tricky if you are a Firemath newbie. The interface does its best to distinguish between these different classes of button by separating them with empty space, but it still takes some getting used to.
Editing an existing expression is also on the tricky side, as the keyboard arrow keys permit movement but not selection, and selecting the right element with the mouse can be difficult (particularly with stacked and nested elements). There is also a toolbar delete key, but it is not mapped to the keyboard delete, which seems like an oversight. In my own experiments, I found it frustrating that the normal copy-paste-cut and undo/redo functions are not supported in the editor, and that several of the toolbar buttons used bitmaps rather than text labels — bitmaps obviously designed for a light-colored background and unreadable in my dark GTK theme.
Still, one must expect to learn one's way around a new tool, and to that end the Firemath online documentation and examples proved helpful, but sparse. It is clear some of the editing conventions supported grew out of necessity, such as holding down the Control key while inserting "fence" elements such as braces. Using modifier keys to place objects on the screen is a common choice in graphics editors; it is simply uncommon for a text editor. On the other hand, a more complete glossary of the supported functions and operators would be helpful — not everyone will have the entire mathematical symbol Unicode block memorized — and it would be helpful for those less skilled in MathML to show the cursor position in the source code view as well as in the WYSIWYG editor. It is easy to misjudge a few pixels of vertical spacing on the pink dot, but much harder to misjudge the location of the actual HTML tags.
In addition to the basic elements, you can click the toolbar's "attribute" button to bring up a separate editor where you can change MathML attributes, including font script, size, foreground and background color, and even add user-defined CSS classes. This is also the only way to make horizontal spacing adjustments, through changing the attributes of the
When your work is perfected in the editor, Firemath can copy it to the clipboard as MathML or as an image (in PNG or JPEG format), or save it with the same output options. The MathML output can be exported as fully marked-up HTML5, XHTML, an inline equation, or a block-level
Firemath only produces presentation MathML, and at present has not added support for MathML 3.0's new elements. Its output, however, is valid in HTML5 documents for the syntax unchanged since MathML 2. You can also manually add newer attributes through the attribute editor, if desired, and Firemath will preserve them.
In just a few minutes of working with Firemath, the distinction between
presentation and content MathML becomes crystal clear (if it wasn't
already) — you can use the editor to craft any mathematical-looking
expression your heart desires, even if it is semantic nonsense (such as this example). Forcing you into writing semantically correct math is not the job of a display technology like MathML; rendering it correctly with respect to size, position, and alignment is. Firemath makes it easy to write expressions the way you want them to look, which is all that an editor is responsible for doing.
Infinity and beyond
In the sciences, expecting visitors to use Firefox in order to see your published content is probably not a difficult hurdle, but online courseware packages like Moodle target a wider range of users, including school computer labs that may have locked-down environments. Moodle currently uses TeX to format equations in its content editor (rendering them to inline images), but as indicated on the wiki and elsewhere, there is growing interest in supporting MathML, either directly or via TeX-to-MathML converters. For other content management systems, the W3C maintains a list of known MathML plugins, including some for general-purpose CMSes like Wordpress, but the timestamps on many of the entries are getting dangerously old.
Despite those challenges, the MathML community is optimistic. David
Carlisle from the MathML Working Group wrote in a blog
posting in October that the adoption of the standard into HTML5 will
constitute a "massive boost to getting Mathematics into web-based
systems." It is said that the browser vendors' commitment to HTML5
will surely bring more support to MathML, which may be true, but so far
Safari, Chrome, and IE have yet to make a public statement to that effect.
Which means that at the moment, you have exactly one alternative for robust
to post comments)