PDF version (388 KB)
Math on the Web: A Status Report
Focus: Interactive Math
by Robert Miner and Paul Topping, Design Science, Inc.
A bias toward future trends is hard to avoid in a periodic status
report. Reading and writing about how things will be better tomorrow
is more appealing than the difficulties of today. Past issues of this
report have doubtless been guilty of "future bias" by focusing mostly
on emerging technologies and new products. As a counterweight, in this
report, we will look at some empirical evidence about the math actually
on the web today.
The methodology is simple. We take a look at the first 50 hits in
the search engine Google for four topics: finding a common
denominator, factoring polynomials, Taylor series, and beam bending.
These 200 pages form a cumulative record of evolving web technology
and practice. Categorizing the resulting collection according to
technology and mode of presentation reveals some interesting
results. For example, interactivity is present in around 20% of the
pages. This is quite a high figure considering that it is mostly
older pages that rank highly in search engines.
Another theme we will examine is the progress of MathML, the
standard XML encoding for mathematics developed through the World Wide
Web Consortium in 1998. XML is a generic set of rules for specifying
markup languages. Markup languages defined in terms of XML cover a
huge range of applications from web pages to database records. By
using a common XML format for diverse kinds of data, managing data
using generic tools becomes easier and cheaper. That is the theory
anyway, and even if a footnote or two might be required to qualify
that statement in practice, there is no real question that the
movement toward XML today is broad and deep.
Consequently, trend watchers have long predicted that MathML will
become increasingly important as XML does. This is already happening
number of concrete ways which we identify below. However, the trend toward MathML in the
future must be tempered by the fact that it does not yet appear in the
200 Google pages in our study. We will explore some of the reasons
why MathML technology doesn't appear to have percolated down to the
authors in the trenches yet, and what software vendors can do to
help end-users take advantage of the benefits of MathML as part of the
larger XML world.
MathML Consolidates Gains as XML Data Format
Archival Data vs. Content Delivery
MathML, as an encoding of math notation, is seldom useful in
isolation. MathML is almost always used in combination with other
markup languages, such as HTML. MathML only describes the math within the
document, while some other markup language is necessary to describe the text and
high-level document structure, such as section headings and so on.
When MathML was originally developed at the World Wide Web Consortium (W3C),
the expectation was that it would mostly be used together with HTML, the markup
language for web pages. In fact, MathML was developed as only one of a
collection of standards meant to create a rich, interactive medium for content
delivery which in past issues of this report we have called the MathML+HTML Platform. The MathML+HTML platform
includes style languages (CSS and XSL), a programming model for
conventions detailing how to use multiple XML languages together
(namespaces, schemas, XHTML modules, etc.).
The effectiveness of the
web as a means of delivering content depends not only on standards, but also on
browsers. Though the standards of the MathML+HTML platform are quite stable
and mature, implementation in browsers has lagged behind. There has been
significant progress, especially in the last year. However, interoperability
problems remain an issue, especially in contexts such as education where many older browsers
are still in use. Inertia is also a major culprit. As the wave front of web
innovation has slowed and broadened, the introduction of new browser technology
has become proportionally more difficult. While new sites can take
advantage of new technologies relatively easily, retrofitting a pre-existing
site is often not a priority unless there are other reasons justifying a
re-design of the site as well. Consequently, adoption of MathML as a means of
content delivery is proceeding slowly.
In sharp contrast, MathML as an archival
data format is enjoying great success. Unlike the web, which arose
from nothing in the mid-90's, publishers of technical documents have long been
dealing with older formats and workflows for math and other technical
data. In large part, XML was developed specifically to address problems
evident in these older formats. However, because content providers had
workable solutions in place and a level of quality they needed to maintain,
their migration to XML workflows has been slower and more deliberate than the
unconstrained rush to the web of the mid-90's.
MathML as a data format is on the right side of the XML technology adoption
curve. MathML, as a relatively mature standard with no real competitors, is the
obvious choice for math in XML. Because it is the obvious choice, that is
where software development and workflow integration resources are going. This in turn makes MathML even more attractive, and so on, thereby effectively
"locking in" MathML as the solution of choice for math in XML. Significant new
MathML adoption activity in the last six months on the
part of organizations such as Elsevier, Wiley, the American Institute
of Physics and Marcel Dekker suggests MathML lock-in is underway, just as
trend watchers have long predicted. Another indicator of MathML's
success in this arena is its inclusion in new document formats[8,9] for the
archival holdings of the National Library of Medicine and PubMed
Cost savings are one obvious motivation behind the move by content producers
to XML and, by extension, MathML. The ability to store and process math
markup inline with the rest of a document simplifies maintenance and increases
reuse, thereby reducing costs. The alternatives of storing math as images
or in formats such as TeX which require external processing are widely regarded
as error prone, inflexible, and difficult to maintain in the context of a
publishing workflow. Beyond cost savings, however, MathML is an information-rich
encoding which creates many opportunities to add value. MathML enforces a structured
approach to encoding mathematics notation, and can contain semantic
hints about the meaning of a formula as well. As a result, MathML
holds promise for facilitating a variety of "smart" services for
mathematics. Examples include making math accessible to the visually
impaired, making math available for calculation, better searching of
mathematics, and of course, interactivity. There are a variety of
research and development projects underway in all of these areas, and as more
content producers shift to using MathML, it will be interesting to see what
value-added services emerge as content producers seek to differentiate their
The MathML Software Landscape
The adoption of MathML by large content producers is fueling the development of
high-end, MathML-aware software. However, progress
in software aimed at supporting individual authors is more mixed. In
particular, MathML support in browsers has suffered some recent
setbacks, as well as some substantial advances.
On the positive side, browser support for MathML in Internet
Explorer under Microsoft Windows has become much more widely available. Design
Science's MathPlayer extension, which adds MathML support to IE, has
over 100,000 downloads. In another significant development, Microsoft has licensed MathPlayer for use with MSN. MathPlayer will be distributed with the MSN client software, bringing MathML browser support to many millions of desktops over the coming months.
MSN subscribers will use MathPlayer to view content in their Math Homework Help feature, part of
an MSN offering for students and parents.
MathML support also continues to
improve in recent releases of the Mozilla/Netscape[13,14] browser. However,
in May, AOL Time Warner and Microsoft announced they had reached an
agreement which will make Internet Explorer the default browser for
AOL users. While it is not yet clear what impact this will have on
future development of Netscape or Mozilla, its open source twin, it
seems unlikely to be good. At the same time, Apple announced a switch to the Safari browser as the default browser for OS X. Safari at present
offers no math support, though MathML ranks high in informal polls of
requested features. It is to be hoped that the Safari team listens to
its users. With the Netscape/Mozilla browser under siege, and a Microsoft announcement that it will no longer be developing Internet
Explorer for the Mac, Apple users' prospects for robust math support
are once again lagging behind other platforms.
Turning from browsers to
authoring tools, there are several significant new developments. Design
Science introduced MathFlow, a suite of MathML tools for use with
Editor. Arbortext Editor is a high-end XML editor, and MathFlow aims at
supporting content producers using MathML within XML workflows. One can
expect to see further activity in the area of MathML+XML editing tool
integration in coming months. A more end-user oriented tool is SciWriter,
recently introduced by Soft4Science. SciWriter is a dedicated XHTML+MathML editor. New releases of MathType and
WebEQ from Design Science, and
Scientific Word from MacKichan Software also add new features for MathML
Two areas that have not seen much progress are TeX translation
software, and support for MathML in page layout programs such as Quark XPress
InDesign. As we will see in our analysis of math currently on
the web in the next section, TeX translation software remains an important means
of putting math on the web for a significant class of academic authors. The continued lack of good TeX-to-MathML conversion software is therefore an
obstacle to MathML adoption by academic authors which should be removed as soon as possible. Similarly, the adoption of MathML by publishers is increasing pressure for
MathML support in page layout software. While several groups are exploring
solutions, this remains a significant gap in the MathML software landscape.
Focus on Interactive Math
Debate on Technology in Education
Interactive, multimedia documents are frequently touted as one of
the great appeals of the web, and that is unquestionably true at some
level. Of course there are many cases where interactivity is
not appropriate. Few people want to study their bank
statements amidst a multimedia swirl of sound, animation and imagery.
However, the debate over when interactivity and multimedia are
effective for instructional purposes is not always so clear cut. This
is particularly true in the area of online learning.
The debate runs that while engaging students' interest is good,
replacing substance with glitz is bad. Finding the proper balance is
difficult, though one suspects that using technology to enhance
learning is probably no more difficult to do well than it is to use
any other educational methodology well. Further, only some topics are
well-suited to the use of web technology, and even in those cases,
using technology to good effect is apt to require a good deal of
creativity, energy and persistence on both the part of the instructor
and the students.
Nonetheless, using the web in math and science education has many
proponents. In part, this is also a form of future bias. A certain
fraction of teachers and students always will be caught up in using
the latest technology simply because it is new and exciting. In a
kind of placebo effect, teaching and learning benefits simply because
learning benefits whenever teachers and students are energized for any
reason. Because of the need to constantly re-energize teachers and
students, there is a long and venerable tradition of new initiatives
in teaching methodology, and that is a good thing.
The appeal of the new, however, is too short lived and too tied to
individual personalities to have lasting impact. The long term
impact of the web on math and science education will depend largely on
the extent to which it can move out of the province of enthusiasts and
into the mainstream. An obvious point of comparison is use of
graphing calculators, which has become entrenched over the last
decade. The argument for graphing calculators originally ran much the
same as that for the web today. They were a means of engaging
students by presenting material in graphical and computational ways.
While graphing calculators also had an early cadre of enthusiasts, a
key factor in their success was that they could be used by average
teachers in mainstream settings. The learning curve was not too
steep; textbooks could be written that incorporated calculator
investigations within the capabilities of average students. And as
calculators only cost a bit more than a textbook, and any classroom
with an overhead projector could become a calculator lab, the
financial burden of incorporating calculators into the curriculum was
The possibilities that the web offers obviously far exceed the
capabilities of a graphing calculator. However, the challenges of
making web-based instruction work for the mainstream are also proportionally greater. Problems of hardware and software
compatibility, and network and computer access remain significant for web-based education on a large scale.
Because of the huge range of possibilities, integration of web-based
materials into mainstream curricula largely remains ad hoc and
proprietary. Obtaining the necessary software tools and the
technical skills to use them also remains difficult for both students and
Though these challenges are substantial, the appeal of the web is
sufficiently great that they have not deterred people from taking them
on. One approach that has gained momentum over the last several
years is the widespread use of learning management systems (LMS) such
as WebCT, Blackboard, and
eCollege. Such systems provide a generic
framework for web-based courses, and even some functionality aimed
specifically at math and science, such as math-enabled message boards.
However, LMS's are generally agnostic when it comes to the actual
course materials instructors manage with them. Typically, an
instructor uses the LMS to create a course web site, and then uploads
instructional materials to that site. If the 200 documents we survey
in the next section are any indication, there is little
convergence in approaches used for math content on the web.
The Google 200
To find out how math on the web, particularly interactive
math, is really being used, we examine the first 50 hits in
the search engine Google for each of the following topics:
- finding a common denominator
- factoring polynomials
- Taylor series
- beam bending
These topics were selected with several objectives in mind. The level
of the topics ranges from basic to advanced. They also span several
disciplines, with beam bending being a standard topic in engineering, and Taylor
series figuring prominently in a number of disciplines. Finally, an
attempt was made to choose topics where interactivity might reasonably be
employed to good effect.
The resulting collection of 200 documents is scarcely a scientific
sample of math on the web, but it is informative nonetheless. Many of the pages appear to be quite old, but no
attempt was made to quantify this impression. In most cases,
duplicate hits to the same site have been counted as a single item.
Pages that are too broken or unfinished were eliminated from
The general profile of the collection is as follows:
|completely off topic
||38 - coincidence, advertisements, software manuals, etc.
||12 - mostly homework help
|professional or research related
||19 - lesson plans, research articles, etc.
||81 - 23 commercial, 58 academic
||50 - broken, unfinished, duplicate, etc.
The incidence of off-topic pages was highest in the "beam bending"
and "finding a common denominator" searches. For beam bending, this
is most due to coincidental hits on beam bending equipment and
engineering company web sites. In the case of common denominators,
most of the irrelevant hits were coincidental, where the phrase was
being used as a figure of speech. Similarly, the density of research-related pages was predictably highest in the Taylor series and beam
bending searching, while lesson plans and other pages aimed at
teaching professionals were denser in the other searches.
Of the Google 200, 81 pages are instructional materials. The
following table summarizes the wide range of technologies employed for
the math in these pages. HTML pages in the table are described as
plain, fancy and latex2html. The categories are
purely subjective. Plain pages look as though they were probably
created by hand-editing HTML code, while fancy pages exhibit more
graphic design and were likely created using dedicated web authoring
tools. Pages generated by the converter program latex2html are fairly
plain, but they have a unique look and feel, and they are the only
group of documents produced with a single tool large enough to be
worth noting. The rows of the table shaded blue are formats for static math. Those shaded pink are approaches for interactive math.
||#81 was scanned handwriting!
||#101 was HTML output from PowerPoint
||#62 is a former project of the authors
||1 plug in
Nearly a quarter of the 81 instructional pages were on
apparently commercial or non-academic, non-profit sites. Such sites
were more prevalent at lower levels, often aimed at parents looking
for math help for their children, or parents home schooling children.
The 12 newsgroup threads in the collection should probably be counted
along with the commercial content pages, since the majority of the newsgroup threads were
moderated homework-help message boards on
commercial or non-profit sites.
Some notable sites from the collection are:
- ExploreMath is an
innovative new site offering a large archive of Flash "gizmos", lesson
plans, and hosted course pages.
- eFunda is a engineering
resource site making extensive use of webMathematica.
- The Math Forum-Ask Dr. Math
is in a
class by itself in the category of moderated homework help sites. Having
practically invented the genre, the depth of their moderated forums is
While about 20% of the 81 instructional pages had some form of interactive
math on them, proprietary commercial technology did not
figure prominently. With the exception of some Maple worksheets,
some webMathematica sites, and a custom plug-in, all interactivity was
time, there were also a number of abandoned pages with custom applets
or scripts now broken and in disrepair. Such pages, often the work of
students, frequently have the air of having been a great learning
experience for the author, which were abandoned as soon as the project
There were no pages using LiveMath,
Maplet.NET, MathWright, or
Techexplorer to mention a few of the better known commercial vendors
of interactive math solutions. There was a single page using WebEQ,
but it was broken. There are, of course, many pages on the web using
all of these technologies, but they didn't make the Google 200.
Freely available toolkits for interactive math faired no better. Two
excellent examples of this genre are Configurable Java applets at
Hobart and William Smith Colleges, and Manipula Math. This reinforces the impression that historically interactive math pages have
often been more for the author than the reader.
The Absence of MathML
MathML makes no appearance at all in the Google 200. However,
there are several factors one needs to take into account when
interpreting this statistic. First, pages using MathML are likely too
new to rank highly at Google. Rankings at Google depend on other
sites referencing a page, as well as the content of the page itself.
Secondly, much of the MathML-based content of which we are aware is in
professionally developed content to which access is controlled. For
example, MSN Math Homework Help uses MathML, but it is only available to
premium subscribers and, therefore, does not usually register in
Another likely place one might find MathML is in course web sites
in university learning management systems. However, pages within LMS's are access controlled and, therefore, they do not typically
register with search engines either. As many of the web-savvy authors
that a few years ago were developing the pages that currently appear in the Google 200 are likely the same people who now use LMS software, this
is a potentially significant factor.
The Need for Authoring Tools
Over half the pages in the Google 200 use HTML with bitmapped equation images. More than
half of those have been prepared with the assistance of mainstream
HTML editing software. However, in very few pages did the mathematics match
the production values of the rest of the document. In most cases, the
math was badly aligned and often poorly typeset. Clearly, there is a
need for better math support in mainstream HTML editors, such as those
that made many of the pages in the collection.
In the area of interactivity, most of the pages in the collection
were developed either by professionals or by individual enthusiasts.
The techniques employed are ad hoc and idiosyncratic. Consequently,
the material in the collection doesn't point a clear direction for
authoring tools. However, one thing is clear. Unless authoring
becomes easy and robust enough that non-programmers are comfortable
with it, significant use of interactivity will largely remain
restricted to professionally created sites.
The recent 3.5 release of the WebEQ Developers Suite takes a
tentative step in the direction of reducing the need for programming
in authoring interactive math. The new release includes a Solutions
categories of objects that can be used in a page:
- Equations, which give authors an easy way to insert equations into
MathML equations across browser platforms. Equation objects also
provide an easy way to manipulate equations in response to user actions
- Controls, which insert applets into the page for
displaying, editing, graphing, evaluating and comparing MathML
equations. The Control objects provide a simple way to incorporate the
- Logic Modules, which implement a number of standard
interactive math tasks in a configurable way: quizzes, step-by-step
exposition, and animations.
contains several dozen HTML templates and sample pages. The templates
illustrate a variety of interactive math activities, and can be easily
While the Developers Suite is still a collection of tools for
programmers, Design Science has announced plans for an authoring tool
for non-programmers, building on the Solutions Library and integrating
with the Dreamweaver HTML
This section spotlights important developments that have been announced since
the most recent
edition of the Status Report was published in January, 2003 . The list may
not be complete, and the authors apologize in advance for any omissions.
- Microsoft and Design Science announce MathPlayer for MSN. Microsoft
and Design Science announced a licensing arrangement that will provide
MathPlayer™ to users of MSN's Math Homework Help content. Math Homework Help
gives students step-by-step guidance with problems in commonly used textbooks,
and MathPlayer is software that enables high-quality display, print and
interaction of mathematics within Microsoft's Internet Explorer for Windows web
- Microsoft and AOL Time Warner strike a deal. CNN/Money reports
that Microsoft agreed to pay AOL Time Warner $750M to settle an anti-trust
lawsuit filed by AOL on behalf of its Netscape subsidiary. The companies
also agreed to a seven-year licensing deal that allows AOL to use Microsoft's
Internet Explorer web browsing technology.
- National Library of Medicine announces archival formats using
Library of Medicine (NLM) announces the creation and free availability of a
standard model for archiving and exchanging electronically journal articles.
- WebEQ 3.5 Developers Suite released.
Design Science announced the release of WebEQ™ 3.5, a developer's toolkit for
building web pages which include interactive math. The new version includes new
web-based controls for graphing and evaluating equations, and a Solutions
Library to reduce the development time in creating interactive pages.
- SciWriter 1.0 released. Soft4science, a Germany-based software
developer, released SciWriter 1.0, an XML based "WYSIWYG style" word processor
that integrates writing mathematics and text in the same environment.
SciWriter's document format is a subset of
XHTML 1.1 and MathML 2.0
- Integre Technical Publishing acquires
Techexplorer. Integre Technical Publishing has acquired the Techexplorer
Hypermedia Browser plug-in and related technologies from IBM Research.
Techexplorer is a cross-platform, cross-browser plug-in that supports rendering
and dynamic scripting of TeX and MathML markup.
- MathPlayer available for 3rd party redistribution.
Design Science announced that MathPlayer™ is now available to anyone who wants
to distribute MathPlayer on networks, intranets and on physical media, such as
- Scientific Word 5 released.
MacKichan Software announced the release of Scientific Word 5.0, a word
processor that enables a user to export as MathML+HTML.
- MathType 5 for Macintosh in beta testing.
Design Science announced the beta release of MathType™ 5 for Macintosh, a native
OS X application that also works on OS 9, that matches MathType for Windows
- MathType 5.2 for Windows in beta testing.
Design Science announced the beta release of MathType™ 5.2 for Windows, an upgrade
that is fully compatible with Microsoft Office 2003 (Office 11).
 Google, http://www.google.com;
 MathML, http://www.w3.org/Math;
World Wide Web Consortium (W3C), http://www.w3.org/;
 Cascading Style Sheets (CSS), http://www.w3.org/Style/CSS;
 Extensible Stylesheet Language (XSL), http://www.w3.org/Style/XSL;
 Document Object Model (DOM), http://www.w3.org/DOM;
Extensible Hypertext Markup Language (XHTML), http://www.w3.org/MarkUp/Overview.html;
 National Library of Medicine Journal Archiving and
Interchange DTD, http://dtd.nlm.nih.gov/tag-library;
National Library of Medicine Journal Publishing DTD, http://dtd.nlm.nih.gov/publishing/;
 PubMed Central, http://www.pubmedcentral.gov;
 Microsoft Internet Explorer, http://www.microsoft.com/windows/ie/default.asp;
 MathPlayer, http://www.dessci.com/en/products/mathplayer/;
Netscape 7.0, http://channels.netscape.com/ns/browsers;
Mozilla 1.1, http://www.mozilla.org/;
 Safari 1.0, http://www.apple.com/safari/;
 MathFlow 1.0, http://www.dessci.com/en/products/mathflow;
PTC Arbortext Editor,
SciWriter 1.0, http://www.soft4science.com/;
 MathType, http://www.dessci.com/en/products/mathtype/;
 WebEQ, (formerly http://www.dessci.com/en/products/webeq/ since replaced by
 Scientific Word, http://www.mackichan.com;
 Quark XPress 6.0, http://www.quark.com;
 Adobe InDesign 2, http://www.adobe.com/products/indesign/main.html;
 WebCT, http://www.webct.com/;
 eCollege, http://www.eCollege.com;
 latex2html, http://www.latex2html.org/;
 ExploreMath, http://www.exploremath.com;
 eFunda, http://www.efunda.com/
 Wolfram Research (Mathematica), http://www.wolfram.com/;
 Ask Dr. Math, http://mathforum.org/dr.math/;
 LiveMath, http://www.livemath.com;
 Maplesoft (Maple.NET), http://www.maplesoft.com;
 MathWright, http://www.mathwright.com;
 Techexplorer, http://www.integretechpub.com/products/techexplorer
(was formerly http://www.integretechpub.com/webmath/techexplorer.html);
 Configurable Java applets, http://math.hws.edu/javamath/;
 Manipula Math, http://www.ies.co.jp/math/java/comp/index.html;
Math on the Web Status Report (all editions), http://www.dessci.com/en/reference/webmath/status/;