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Math on the Web: A Status Report
Focus: Standards-based Math on the Web
by Robert Miner and Paul Topping, Design Science, Inc.
The Web Revolution
The World Wide Web is nearly a decade old now and its effect on math and science communication has
already been amazing. An enormous amount of information has been made available on the Web.
Increasingly, cross-referenced research articles and abstracts are available in
searchable online archives. In education, engaging interactive materials are
widespread, and Web-based course management tools are becoming frequent virtual
companions to traditional pedagogical tools. A quick glance at a few innovative sites, many of them long-established,
gives an idea of the advances that have been made in the communication of
mathematics on the Web:
New resources for students
- The Math Forum maintains
extensive archives of math resources and provides the tremendously popular
Ask Dr. Math service where students can get personal answers to questions
from a staff of volunteer "math doctors." Math
Goodies takes a different approach, offering lessons, puzzles and
worksheets with interactive drill problems that give students immediate
feedback. The Index
of Famous Curves at St. Andrews University represents yet a third
kind of resource for students, the multimedia math and science encyclopedia,
describing curves with images, equations, and interactive applets.
New ways for teachers and students to interact
- Many, many course homepages show that teachers are using email, discussion
boards, and courseware systems to augment more traditional pedagogical
tools. Some commercial courseware systems such as Prometheus
offer "complete solutions" including math-enabled tools for
posting messages. Other sites offer course management services a la carte,
such as the math-capable message board hosting available at LiveMathBoard
and math-capable online testing from Wiley
New ways of presenting math
- The ability to present multimedia information in an interactive way is one
of the most enticing aspects of the Web. Many superlative math sites
demonstrate how these techniques can be used to make traditional topics come
alive, and make advanced topics more accessible. The Knot
a Braid of Links has been collecting examples of such sites since
1996, from Euclid's
Elements presented via dynamic geometry applets, to simulations of
phenomena in wavelet theory such as the Twin
New tools for research
- Researchers in academia and industry have also reaped benefits from the Web.
Preprint servers such as the arXiv
and online journals speed the dissemination of current information, and make
articles available for online cross-referencing. Searchable online
abstracting services, such as MathSciNet,
have revolutionized literature searches. And a few innovative sites such as
On-Line Encyclopedia of Integer Sequences are beginning to offer
specialized searching and indexing on mathematical content, pointing the way
toward a future where researchers in widely differing specialties can find
connections between each other's work.
Sites such as these demonstrate that the Web can be a powerful vehicle for
communicating mathematics and science in general, just as it is revolutionizing
communication in other disciplines and fields of endeavor. In spite of this, it
is nonetheless true that there are still significant obstacles to publishing
mathematics on the Web that other disciplines do not face. As has long been the
case in print, authoring and publishing mathematical notation can be a
Many Technologies, None Perfect
There are many exciting and innovative math and science Web sites.
Their developers are to be applauded, since the technology landscape
for Math on the Web is complex. Currently, if you are planning a new
Math on the Web project, you must choose from a dazzling array of
technologies, each of which has its own advantages and
HTML pages with GIF images for equations:
- Because the format is HTML-based, math can more easily be combined
with other media such as movies, sounds, interactivity, data access,
- Doesn't require server-side support.
- No need for fonts to be installed (important for cross-platform
- Interaction with math is limited to scripts selecting among
pre-composed equation images.
- Ugly printing because GIFs are low-res screen images.
Adobe Acrobat (PDF):
- Good for online delivery of documents whose primary publishing
medium is paper.
- Good quality formatting and printing that is faithful to the
designer's original intent.
- Doesn't require server-side support.
- If math fonts are embedded in the document, math symbol display is
guaranteed to work.
- Because the format is not HTML-based, math can't be combined easily
with other media such as movies, sounds, interactivity, data access,
- The Web browser is merely hosting the PDF viewer application which
must integrate its own user interface with that of the
browser. This can be more cumbersome or confusing
for the user and limits interaction. Changes made using the
browser's interface (e.g. Text Smaller or Larger) have no effect on the
IBM Techexplorer pages (see the comments about Techexplorer components under
HTML + Components):
- Uses TeX, a language used by legacy documents and understood by many
- Doesn't require server-side support.
- Prints with TeX quality.
- Requires the Techexplorer plug-in which is not free, except for its
trial version which doesn't allow documents to be printed..
- Although Techexplorer does allow inclusion of basic media formats,
math can't be combined with the full range of media available in HTML
- The Web browser is merely hosting the viewer application (similar to
the PDF Viewer) which must
integrate its own user interface with that of the browser. This can
confuse the user and limits interaction. Changes made using the
browser's interface (e.g. Text Smaller or Larger) have no effect on the
Server-side programming (CGI, Perl, Java, ASP scripts, etc.):
- Can produce pages as in HTML + Components but avoid the image size
- Can produce pages with the widest range of browser compatibility
(although this requires some challenging programming).
- Minimal load on the client (browser) as all scripts are executed on
- Scripting needs only to target the server platform, not all the
- Works well for accessing specialized software such as a
computer algebra system.
- Server-side scripting is difficult to write and debug because (a) it
is running on a different computer from the browser, (b) must serve
multiple clients simultaneously, (c) it runs the risk of making a
production server unstable or requires setting up an identical, parallel
server for testing.
- Unlike other solutions, all load is concentrated on the server.
- User interaction requires a round-trip to the server making
interaction sluggish and unpredictable.
HTML + Components (Design Science WebEQ, IBM Techexplorer components):
- The page is HTML-based, making it easy to integrate with other Web
- Interaction is snappy as it occurs on the client and doesn't require
- Interaction is powerful as scripts can generate math to be displayed
on the fly.
- Interface between math rendering component and page requires that
the width and height of each equation be known in advance. This is
difficult to do if the math is generated by scripting.
- Math pages containing hundreds of individual equations can cause
performance problems due to the inability of browsers to handle that
many component instances. This issue can be minimized by
using components in conjunction with GIFs for non-interactive equations.
Standards are Paving the Way to Better Solutions
Though there are many technologies available for Math on the Web
projects, none of them is ideal.
Many who consider Math on the Web projects for the first time are surprised
that there is no direct support for math in HTML. After all, what is math but
fancy text? In fact, this has been proposed and attempts to get it to happen are
part of a history almost as long as that of the Web in general.
Efforts to get math into HTML ultimately evolved into the creation of the
Math Working Group at the World Wide Web Consortium (W3C), the body responsible for
Web standards. The efforts of the Math Working Group ultimately led
to the development of MathML, a powerful new language for encoding
math expressions for the Web. MathML is now part of an extremely powerful, standardized
component-based architecture for the Web, capable of accommodating the
requirements of math communication.
The HTML Platform
Each of the many technologies for putting math on the Web has its merits. However, in the long term there can
doubt that, taken together, the collection of HTML-centric technologies
that have taken shape through years of industry collaboration at the
W3C represent the future of the Web. We're calling this collection of Web standards
The problem with current technologies for putting math on the Web
is that they are too complicated and ad hoc. It often takes expert
knowledge and programming skill to get different math software
packages to work together, but no single approach provides a complete
answer. The remedy is obviously standards. And although they take
time to evolve (through organizations like W3C), once they take hold,
their benefits are enormous.
As a consequence, the HTML Platform is the safest bet in the long
run for lowest cost of authoring, highest level of capability,
reduced vendor lock-in, and the most secure future. To get a better idea
of what the HTML Platform consists of, we now take a look at the
individual standards of which it is comprised.
For the question, "What language are Web pages written in?", the short answer
is, "HTML, of course!". The long answer is, well, longer. Although very simple Web
pages can be written in HTML alone, most pages are constructed from a
conglomeration of computer languages and mechanisms working together. They go by
acronyms like HTML, CSS, XSL, DOM, and MathML. These languages are defined by
standards published by the W3C. (They actually call them "recommendations"
rather than "standards" but they work the same way.)
Here is a list of the standards that Math on the Web developers should be
concerned with, along with the role each plays in The HTML Platform:
||HyperText Markup Language
||Defines the document structure and acts as the glue that holds all the
other pieces together.|
||Cascading Style Sheets
||Associates formatting information (font, size, style, color, etc.)
with HTML structural elements (headings, paragraphs, tables, etc.).|
||Extensible Markup Language
||The universal format for structured documents and data on the Web.
Based on the earlier, more complex, SGML standard. XML is not itself a
language but a meta-language used to create other languages, such as XSL,
XHTML, MathML, ChemML, etc.|
||Extensible Stylesheet Language
||Consists of two parts:
- XSL Transformations  (XSLT):
a language for transforming XML documents
- An XML vocabulary for specifying formatting semantics (XSL
||Document Object Model
||The Document Object Model is a platform- and language-neutral
interface that will allow programs and scripts to dynamically access and
update the content, structure and style of documents.|
||Simple scripting language used to make Web pages react to user input.
Typically, scripts use the DOM to modify the Web page within the browser.
All execution occurs on the "client" (Web browser) as opposed to the
"server" (Web server).|
||HTML plus the ability to include scripts within a Web page to accept
user input, perform computations, and modify the Web page within the
browser using the DOM interface in order to effect user feedback.|
||An XML-based version of HTML.|
||Mathematical Markup Language
||An XML-based language for describing mathematics for both presentation
 and other MLs
||Chemistry Markup Language, etc.
||Other domain-specific markup languages may be used in a Web page to
describe structured text and/or data.|
|Applets and Plug-ins
||Separately downloadable mini-applications that extend the capabilities
of the browser. These may be written in Java for cross-platform
compatibility or in C++ for performance. The WebEQTM Equation Input Control
is a good example, providing a way for users to enter math notation and
send it to the Web page as MathML.|
You can find out more about most of these pieces of the HTML Platform by
visiting the W3C's Web site at http://www.w3.org/. Links to specific standards
are also listed in References.
All modern Web browser makers have committed to supporting the standards of
the HTML Platform.
For the Math on the Web author, it is largely a matter of when, not if, a
browser implements a particular HTML Platform standard. Like all new technology,
the HTML Platform is not standing still. The W3C and its member organizations
are constantly pushing the HTML Platform forward. Although the Math on the Web
author must still be concerned with questions about whether this technology is
supported in that browser, this is inevitably the case with leading-edge
The role of MathML in a dynamic math page
MathML support is already widespread enough that it has begun to
play a pivotal role for dynamic math in Web pages. Part of
the appeal of the Web as a medium is that it is interactive.
Information is presented in an active environment with many kinds of
interactive controls. In the case of math content, MathML-capable
components can be "wired together" to create dynamic math and science
The most basic situation are MathML "islands" in the Web page,
which display as traditional mathematical notation. In some browsers
like Amaya and Mozilla, display of MathML islands is now built-in.
With Netscape and Internet Explorer, MathML can be rendered via
plug-ins or applets.
The role of MathML islands in an HTML document is similar to the role of TeX's
math mode within a TeX document. However, MathML has the potential to go much farther than
styled using CSS. Equations can be hooked up
to HTML controls like buttons and pulldown menus.
Applets and plug-ins can send MathML-encoded equations to server-side
software such as computer algebra systems or scientific visualization
The combination of MathML and scripting facilitate an enormous range
of dynamic math applications. Here are some
- When the user clicks on a button in the page, a script is invoked that
modifies a MathML island using DOM access. The user sees the math change based
on the click. A typical use might be to display a hint to a student
in a lesson.
- An interactive assessment page allows the student to invoke an equation
editor applet. When the user closes the editor window, the MathML for the
equation is sent as input to a script that sends it back to the Web server.
Software on the Web server checks the student's answer and sends the result
back to the script running in the page which informs the user of his/her
- A Web page that works as a special-purpose calculator and grapher allows
the user to make radio-button and checkbox choices and enter numerical
coefficients. A script invoked by a "Compute" button generates MathML that
will be sent to a Computer Algebra System or other computational component
running on the client or server computer. The results are shown to the user
both as a graph (using a graphing applet) and in standard mathematical
Much as HTML is the glue that binds the various parts of the Web page
together, MathML is the glue that binds the mathematical and computational
elements together. MathML is the language with which the equation editor applet,
the Computer Algebra System, and the graphing applet communicate.
The HTML Platform vs. proprietary, single-vendor platforms
The biggest choice facing the Math on the Web author is whether to
go with a proprietary, single-vendor platform, or to stick with a open
standards-based, multi-vendor platform. The standards-based platform
is the better choice in the long run, but the case isn't so clear when
you have to do something today. This is a very common dilemma
for technology adopters. The proprietary, single-vendor solution has
some advantages, especially in the short term:
- Available sooner;
- Easier to evaluate for possible adoption;
- Once adopted, easier to learn as there is a single source for all
documentation, knowledge, and support.
The proprietary, single-vendor solution has some big disadvantages which grow
as time passes:
- The vendor is slow to implement new technologies as it has to do all the
- The customer gets locked in to the proprietary solution as there are no
- Switching to the open standards-based, multi-vendor solution can be
difficult and costly as the customer has a huge investment in training,
expertise, and experience in dealing with the single vendor's system, much of
which may have to be discarded.
- It is usually more difficult for a proprietary system to interoperate with
standards-based systems. This is what occurs when Adobe Acrobat, IBM
Techexplorer, and other
viewers take over the browser. The viewer's user interface must be
overlaid on top of the browser's, thereby confusing the user.
- The proprietary vendor can charge higher prices, especially after the
initial purchase (e.g. support, upgrades, etc.) because of the customer's
difficulty in switching vendors.
In the long term, the open standards-based, multi-vendor solution
has big advantages that grow even larger as time passes:
- Multiple, competing vendors for each component of the solution (authoring
systems, in-page editors, applets, browsers, etc.) mean more customer choice
of product and vendor, lower prices, and more features. This is capitalism at
- There is much less vendor lock-in. Switching vendors is easier for a
single part of your solution than for the whole thing.
- It will be easier to find training, support, contract help, etc. as the
technologies you are dealing with will be mainstream, often not specific to
Math on the Web.
- Similarly, trained and experienced personnel will be easier to find and
train as the skills you will be looking for will be common.
What's Available Now
There are already a number of software packages that have some level of
MathML support. In particular, Design Science is one of the oldest and most
respected vendors of MathML software. Our WebEQ software was the first
commercially available software with MathML support, MathTypeTM was the second.
The following list touches on some of the highlights:
- MathType -- DSI's premiere equation editor can export equations as MathML.
MathType gives an easy way of authoring MathML expressions.
- WebEQ Math Viewer -- this scriptable Java applet displays math expressions
in Web pages, and can dynamically update the display in response to mouse
gestures or other controls, such as buttons, in a Web page.
- WebEQ Equation Input Control -- The Equation Input Control (or EIC) is a
Java equation editor applet. The EIC gives readers a way to enter math on a
Web page, in addition to the other standard HTML input controls like text
areas and radio buttons. The EIC is configurable to meet a range of
- tex4ht 
-- this free Perl program is a very powerful HTML translator,
generating HTML + MathML from LaTeX.
- PassiveTeX  and
-- these free macro packages facilitate using TeX to
directly typeset MathML.
- Mathematica 4.x -- this powerful scientific computation platform can
import, export, and evaluate MathML.
- IBM Techexplorer
 -- the IBM Techexplorer plug-in takes over the browser window to
display TeX documents by default. However, with some effort, Techexplorer can also be used as a component within the HTML platform to display and
manipulate MathML expressions in a way similar to the WebEQ Math Viewer.
- Amaya  -- the demonstration and test-bed browser from W3C supports both
display and editing of MathML.
- Mozilla  -- the open source version of the Netscape browser currently
implements most of MathML. There is a strong likelihood MathML support will
appear in the Netscape-branded version of the browser before long.
- Internet Explorer  -- Microsoft has introduced a new plug-in technology
 that allows much better integration into a Web
page than other plug-in technologies. More on this below.
For a more comprehensive list of MathML-enabled software, consult the W3C
Math home page.
What's in the Works
Design Science  will be introducing a
number of products supporting MathML and the HTML Platform in early 2001:
MathType 5 with MathPage technology
- The next version of Design Science's premiere MathType equation editor
will revolutionize the process of exporting a Word document with math to the
Web. DSI's MathPageTM technology augments Word's "Save As HTML"
feature in powerful ways.
MathPage uses the full power of the
HTML platform to create HTML pages with math as MathML islands for display
in MathML-capable browsers, such as IE with MathPlayer, Mozilla, and Amaya. For maximum backward compatibility,
MathPage can also produce math as GIF images, with high resolution images for printing,
all perfectly aligned with the surrounding text.
A great math site is great because of its content, not its
technology, and that will never change. But the technology is
important too, and the many choices between solutions, none of which
are ideal, have posed a real obstacle to would-be Web authors and readers. Standards have been developed at
the W3C to address the problems, and
the HTML Platform that has emerged from these efforts is a very powerful
and flexible architecture for math and science publishing on the Web.
But as always, for authors making choices today, the
paramount question is "What works now, and when's the next release?"
On that point, the current picture is quite positive. As we have
seen, MathML is becoming widely supported. The First International
MathML Conference  was held this fall, and the amount and quality of
MathML implementation work on display was impressive. By the end of
next year, excellent MathML support will be freely available in most
major browsers. Several computer algebra systems currently support
MathML, and more are on the way. Excellent authoring tools are
available for developers. And much, much more is on the way, from
Design Science and others.
Math on the Web has come a long way, and has a bright future.
Design Science believes the coming year is going to be a very big one
for Math on the Web. The HTML Platform has matured over the last two
years, and Math on the Web is well on the way toward claiming the
 The Math Forum, http://www.mathforum.com/
 Math Goodies, http://www.mathgoodies.com
 Index of Famous Curves, http://www-groups.dcs.st-and.ac.uk/~history/Curves/Curves.html
 Prometheus, http://www.prometheus.com
 LiveMathBoard, http://www.livemath.com/livemathboard
 Wiley e-Grade,
 Knot a Braid of Links, http://west.camel.math.ca/Kabol/index.html
 Euclid's Elements, http://aleph0.clarku.edu/~djoyce/java/elements/elements.html
 Twin Dragon, (originally at http://cm.bell-labs.com/who/jelena/TwinDragon/)
 arXiv, http://www.arxiv.org
 MathSciNet, http://www.ams.org/mathscinet/
On-Line Encyclopedia of Integer Sequences, http://www.research.att.com/~njas/sequences/
 HTML and XHTML, http://www.w3.org/MarkUp/
 CSS, http://www.w3.org/Style/CSS/
 XML, http://www.w3.org/XML/
 XSL, http://www.w3.org/Style/XSL/
 XSLT, http://www.w3.org/TR/xslt
 DOM, http://www.w3.org/DOM/
 MathML, http://www.w3.org/Math/
 CML, (originally at http://www.vsms.nottingham.ac.uk/vsms/talks/chemweb.html)
 Design Science, Inc. (MathType, WebEQ, MathPlayer), http://www.dessci.com
 TeX (TUG: TeX Users Group), http://www.tug.org
 PassiveTeX, http://www.tei-c.org.uk/Software/passivetex/
 xmltex, http://www.dcarlisle.demon.co.uk/xmltex/manual.html
 Wolfram Research (Mathematica), http://www.wolfram.com/
 IBM Techexplorer, http://www-4.ibm.com/software/network/techexplorer/
 Amaya, http://www.w3.org/Amaya/
 Mozilla, http://www.mozilla.org
 Microsoft Internet Explorer, http://www.microsoft.com/windows/IE/
 Element Behaviors in Internet Explorer 5.5, http://msdn.microsoft.com/en-us/magazine/cc301531.aspx
 The First International
MathML Conference, http://www.mathmlconference.org/
We plan on updating this report as the world of Math on the Web changes.
If you would like us to let you know, join our Math on the Web mailing
MathType, WebEQ, MathPage, and MathPlayer are trademarks of Design Science,
Inc. All other company and product names are trademarks and/or registered
trademarks of their respective owners.