Displaying Math on the Web -- Further Information

hand-drawn equation: the integral from zero to infinity of e to the (minus x squared) dx equals (the square root of pi) over 2

Displaying Math on the Web: Samples and Tools | Comparison of Approaches | Further Information

History and the horizon
Alternate viewers and tools
Math software integration
Accessibility for the visually impaired
Resources and further reading

History and the horizon

There have been various efforts to incorporate mathematics into HTML, but aside from the addition of tags for simple subscripts and superscripts, little concrete change has been visible in final specifications. However, larger changes under way bode well for the future, in particular the current draft specification to redefine HTML as an application of XML (eXtensible Markup Language) and public statements of support for XML from both Microsoft and Netscape.

In the spring of 1998, the W3C Math Working Group produced an initial recommendation for MathML, an XML-based format for marking up equations both in terms of presentation and structure. It is intended not only to encode mathematical notation for visual display, but also to capture semantics in a way that lets other tools process the content of equations. MathML basically consists of a set of HTML-like tags used hierarchically to represent the structural relationships between elements in a mathematical expression. It can be read by humans, but is extremely verbose and is intended not for direct editing but rather for machine-to-machine communication, including authoring tools or syntax converters.

Ultimately, the hope is that browsers will be able to render MathML directly. It is already being incorporated into authoring tools, applets, and plug-ins aimed at the scientific community. While it is too early to predict the outcome of this approach, the progress of MathML and the general move toward support of XML and associated standards for structural markup hold out distinct hope for mathematics on the Web.

Alternate viewers, plug-ins, and tools

The Amaya test-bed browser/editor from the W3C renders MathML and includes a WYSIWYG editor; playing with it or just looking at screen shots on the Web page gives a good idea of how browser integration of MathML might eventually work. At this writing, only an early beta version (0.95) of Amaya is available on Athena. Version 2.0 has recently been released and should be installed before long, but in the meantime the early version can be run by typing:

     athena% add outland; amaya

The e-Lite browser from ICESOft uses the WebEQ rendering engine to render MathML; it is written in Java, and is thus available cross-platform.

The EzMath editor can convert a notation inspired by spoken mathematics to either MathML or markup which can be rendered by the EZMath plug-in. At this writing, EZMath is available only for Windows.

The IBM techexplorer Hypermedia Browser is a plug-in for Netscape and Internet Explorer which renders at least "basic" TeX/LaTeX markup directly; at this writing it is available for several varities of Unix and Windows, but not the Mac. Support for MathML has recently been announced.

The TeX Users Group maintains a list of software related to TeX on the web, including many converters and a few browser plug-ins.

The producers of MathType, a commercial equation editor widely used with MS Word and other packages will include a MathML export feature in their next release.

Math software integration

Various vendors of math package including notebook-like front ends inlcuding Maple and Mathematica continue to introduce features to make their programs more interoperable with the web. For example, Maple users can now:

export worksheets to HTML (equations are converted to GIF images)
open worksheets in Maple directly from web URLs
export worksheets to a format usable with their new Maple Explorer interactive browser (Windows only at this writing)

Generally, such features are either one-way, platform-restricted, or reliant on proprietary formats, but do provide convenient tools for users of the package. Support for MathML is increasigly being promised

On a related note, vendors also recognize that web browsers can be used to provide an interface to some portion of their computational engines. Matlab Release 11 introduces the Matlab Web Server and Wolfram Research has an interactive Mathematica demo on the web called The Integrator. Each of these is intended to allow a user to perform computations without access to the full software package.

Accessibility for the visually impaired

Making mathematics notation accessible to the visually impaired is an important goal, and there are numerous centers around the country working in this and related areas of web accessibility. Computer-based approaches include audio screen readers and braille converters (using Nemeth Code, the standard North American braille code for mathematics and science notation). Two projects funded by the NSF include the following (each has links to other sites):

MAVIS (Mathematics Accessible To Visually Impaired Students) at New Mexico State University
The Science Access Project at Oregon State University

For general information about making web materials accessible to those with disabilities, see:

Web Accessibility Initiative (W3C)
Designing More Usable Web Sites (Trace Center)
MIT's ATIC lab (Adaptive Technology for Information and Computing)

Resources and further reading

There is a wealth of information and opinion on the web about math on the web:

For official details on MathML, see the W3C Math pages; for general information on web standards and working groups, start at the top level of the W3C (World Wide Web Consortium).
The WebEQ MathML Information Center includes a resource list, sample documents, and a WebEQ-based service for rendering and validating MathML.
Brian Hayes' Bit Rot article in American Scientist discusses the general evolution of data formats and provides good context for thinking about the spectrum from paper to TeX to XML.
Robert Miner's HTML Math Implementation Goals dates from a couple of years ago, but provides illuminating examples to motivate requirements for supporting math notation in browsers.
Ian Hutchinson's Comparative Review of World-Wide-Web Mathematics Renderers compares Amaya, e-Lite, and Netscape; he also has a useful overview of Approaches to WWW Mathematics Documents.
Richard Fateman's More Versatile Scientific Documents provides a through collection of references related to electronic representation of mathematics, interspersed with sound editorial comments.
The April 1999 issue of IEEE Spectrum (members only) included an article on "Math on the Internet" which discusses both web-publishing and web-interactive computational features from software vendors.

...and there are numerous projects to keep an eye on, whether directly devoted to math on the web or to related developments:

The MathML in Mozilla project may ultimately lead to MathML rendering in Netscape.
The SGML and XML News page is a good place to keep abreast of implementations, adoption of standards, and general announcements.