I'm pleased to report that MathML 3.0 is today published as a W3C Recommendation. Seven years to the day since the last MathML Recommendation, MathML 2.0 2nd edition was published on 21st October 2003.
So, what have we been doing for seven years?
My Working Group colleague, Neil Soiffer has just posted a blog entry describing some of the main features and linking to a nice summary of the main new features in MathML3, so I won't list them all in detail here, however some of the headline features are listed below.
Additions to control bi-directional layout, for Arabic styles in particular
The Arabic Note detailed some extensions to MathML 2.0 that would enable a richer variety of right-to-left layouts as used in typesetting Arabic mathematics. In MathML 3.0 this bi-directional control is fully integrated into the language, allowing the effect of each of the presentation layout elements to be specified in RTL and LTR modes.
Elementary math layouts (long division, etc)
Previously long division and long multiplication etc could be typeset using table layout and a lot of spacing adjustment but this was difficult to produce and very hard to process in an accessible way, by for example a speech renderer. MathML 3 introduces new elements (mstack and mlongdiv, principally) which enable a much more natural and accessible encoding of these layout schemes.
Linebreaking of mathematics
For the first time MathML 3 specifies control over automatic linebreaking and provides improved features for manual forced linebreaking and alignment of expressions.
Officially registered MIME Types
The mime type application/mathml+xml has been unofficially used for some time, but it is now officially registered (along with two more mime types specific to Presentation and Content MathML). These Mime types might prove particularly useful in systems that use MIME to label clipboard fragments.
Closer alignment between Content MathML and OpenMath
Chapter 4, describing Content MathML has been totally rewritten to provide a direct, explicit alignment with OpenMath. This alignment was always in the background (the two languages being developed at roughly the same time, by overlapping groups of people) but making the alignment explicit, and making small changes on both the MathML and OpenMath side has allowed many rough edges to be removed, and I think gives a much clearer presentation of the “semantics” underlying the Content MathML elements.
The normative DTD used for MathML 1 and 2 is replaced in MathML 3 by a Relax NG schema. this is much more expressive than a DTD, and allows many of the constraints that previously could only be expressed in words to be built in to the grammar. A DTD (and XSD schema) are still provided in the Math Working Group pages, as a convenience.
Many clarifications and improvements throughout the spec
If you stare at the MathML2 spec for 7 years you may notice that some parts are clearer than others.
Integration with HTML5
This is briefly mentioned in Chapter 6, but mainly specified in the HTML 5 draft specification. One of the main difficulties of using MathML on the web has always been that it was designed as an XML application to fit with XHTML, and using XHTML has proved to be far more difficult than envisaged in 1998 when XML started. Some notable browsers are only now starting to support XHTML in beta releases, and even in browsers with good XML/XHTML support, it is difficult to integrate XHTML with HTML based document systems (such as the blogger system hosting this blog). HTML5, allowing MathML (and SVG) in text/html systems will be a massive boost to getting Mathematics into web based systems.