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+
+\MakeShortVerb{\|}
+\def\cmd#1{\texttt{\char'134#1}}
+\title{How does \acro{HTML} handle mathematics?}
+\author{Malcolm Clark}
+\begin{Article}
+\section{Introduction}
+There is a very short answer to the question posed in
+the title: not at all. However, as an instantiation of
+SGML (see, for example, \cite{EvH}, \cite{Goossens} and \cite{Bryan}),
+we can look first at how mathematics is handled in other
+\acro{SGML} \acro{DTD}s; and then examine how the expired \acro{HTML}3 draft
+proposed to include mathematics.
+
+The \acro{DTD}s already available which are designed to
+handle mathematics include \acro{ISO}\,9573 (\cite{ISO9573})
+(confusingly, also known as \acro{ISO}\,12083),
+which is part of \acro{CALS}, \acro{AAP} (Association of
+American Publishers) (\cite{AAP}), and the \acro{HTML}3 draft (\cite{math}).
+The Euromath \acro{DTD} might also be relevant (\cite{Euromath}),
+but since its status is closer to that
+of proprietary it is too awkward to consider here.
+Van Herwijnen (\cite{EvH}) comments on the first two,
+comparing them to \TeX\ and |eqn|.
+A longer and more detailed examination of the \acro{AAP}, Euromath and
+\acro{ISO}\,12083\slash \acro{ISO}\,9573 is given in Poppelier, van
+Herwijnen and Rowley (\cite{PvHR}).
+
+Van Herwijnen provides an example from physics for the decay of a particle
+ together with representations in
+\TeX, |eqn|, \acro{ISO}\,9573 and \acro{AAP}.
+The equation is:
+\begin{displaymath}
+\Gamma(J/\psi\rightarrow\eta_c\gamma)
+= \frac{\alpha Q_c^2}{24}
+\left\vert A(J/\psi\rightarrow\eta_c\gamma)\right\vert^2
+\frac{m_\psi^2}{m_{\eta_c}^2}
+\left(1-\frac{m_{\eta_c}^2}{m_\psi^2}\right)^3
+\end{displaymath}
+The entire expression is too extensive to compare here, but
+the left hand side of the equation in \acro{ISO}\,9573 may be
+given as
+\begin{Verbatim}
+<mfn> <fname> &Gamma; <of>J/&psi; &rarr; &eta;
+<sub> c</sub> &gamma;
+\end{Verbatim}
+while using the AAP dtd, it could be
+\begin{Verbatim}
+<g>G</g>(<fr sol>J</><g>y</g> &ar; <g>h</g>
+<inf>c</inf><g>g</g>)
+\end{Verbatim}
+For the sake of completeness, the |eqn| alternative is
+\begin{Verbatim}
+Gamma(J/psi rarrow eta sub c gamma)
+\end{Verbatim}
+Eric's comments are interesting.
+He comments that the two \acro{SGML} representations are cumbersome
+and difficult to read, especially when contrasted to \TeX\ and |eqn|.
+He also rails against the obsession with representation.
+For example $\Gamma$ `means' decay width, but as far as the \acro{DTD}s are
+concerned we have \texttt{\&Gamma;} and \texttt{<g>G</g>}.
+To be fair, \TeX\ and |eqn| hardly
+fare better, but at least we do know that we could have
+provided a more meaningful command. The second representation (\acro{AAP}) is
+particularly unfortunate, since instead of treating the symbol
+as a symbol, it treats it as a Greek letter. Of course, Eric is deeply
+imbued with the basic notions of \acro{SGML}, and would be very
+sensitive to this.
+
+His contention is that someone who already knew \TeX\ or |eqn| would
+have no motivation for learning or using these rather baroque alternatives.
+
+There is a point to be made about the rather cumbersome nature of
+the \acro{SGML}. Writing it by hand will be cumbersome, but surely no-one
+ever wants to write in this way. Structure editors are available.
+ In the \TeX\ world, Scientific Word gives a structure editor
+for \LaTeX. This can be done since it is possible
+to hold an equation as elements in a tree structure, so that modification
+or correction to an element can be managed quite simply, and changes can
+propagate down the tree. The same sort of thing exists within the \acro{SGML}
+world. Euromath uses the Grif (\cite{Grif} and \cite{GrifSA})
+ editor for just this, and it would
+be easy to see other similar editors, like Chamberlin's
+Quill (\cite{Chamberlin})
+maintaining the information. There is a question lurking whether
+mathematicians would actually like to input in this way.
+Just as experienced keyboarders find
+\acro{GUI}s very difficult and slow to use, perhaps the same sort of
+resistance would
+be found. However, the real point is that humans should not be expected
+to write \acro{SGML}. If they really must write \LaTeX, then an approach
+like Scientific Word, which could be coerced into generating a tree structure
+which could be mapped onto a \acro{DTD}, is potentially more valuable.
+
+A general issue, which Eric raises implicitly, is that none of the \acro{DTD}s
+offer a way of encoding meaning in a flexible way. Either the
+element is present already, or it is not. There appears
+to be no straightforward way of extending the range of elements. In the world
+of high energy physics and mathematics this must be something
+of a straightjacket. On the other hand, the bane of many editors'
+lives is the ease with which individual authors
+can `extend' \TeX\ or \LaTeX\ by adding a few new definitions.
+
+\subsection{SGML Notations}
+If we really did have existing equations, then one way to
+handle them within \acro{SGML} is through a Notation (see also \cite{Bryan}).
+A Notation permits
+a document to include data which is not to be parsed. It is
+therefore possible to include \TeX\ or \LaTeX\ and assume that
+at that point a convenient processor will be magicked to deal with
+it. He gives the example of the definition in a \acro{DTD}:
+\begin{Verbatim}
+<!NOTATION TeX SYSTEM "">
+<!NOTATION LaTeX SYSTEM "">
+<!ELEMENT Formula - 0 CDATA>
+<!ATTLIST Formula #NOTATION (TeX|LaTeX|eqn)
+ #CURRENT>
+\end{Verbatim}
+which may then be used later with the |Formula| element as
+\begin{Verbatim}
+<FORMULA NOTATION=TeX>
+...
+</FORMULA>
+\end{Verbatim}
+
+A scheme which already maps \acro{SGML} to \LaTeX\ (e.g.~\cite{Flynn} or
+ \cite{Goossens2}) would
+find this a very easy way to absorb maths, provided all the
+equations were in the same notation. The prospect of a
+\cmd{newcommand} or \cmd{def} within the Notation could be
+worrying.
+
+Although this sort of expedient is plausible, it is not entirely
+successful. One of the arguments behind the use of \acro{SGML} is that it codes
+structure or meaning, rather than appearance (to echo one of Eric's points).
+\TeX\ and \LaTeX\ sometimes code meaning,
+but not in a consistent and reliable way.
+How do we extract information? If we have \acro{SGML}, it is relatively
+easy to find corresponding structural elements, which may then be extracted.
+Once we start including a Notation, this chance is all but gone;
+and if we include alternative Notations (say \TeX, \LaTeX\ \emph{and} |eqn|)
+it becomes even more problematic.
+
+It is not clear to me how these Notations, or even the \acro{DTD}s
+differentiate between in-line and displayed equations. I assume
+that an attribute could be included which specified the style.
+On the other hand \acro{ISO}\,12083 distinguishes between
+in line, displayed and `display formula groups' styles, through the
+use of different elements.
+
+There is perhaps a deeper question here,
+which is this, should it be at all relevant?
+Should the author be able to specify that
+some equations are in-line and others are to be displayed?
+It should make no difference at all to the content, although
+it would make great changes to the appearance. But to deal with maths
+is to deal with appearance, to a large extent. The display seems
+to be a key issue. Since many equations are strongly two dimensional
+(as opposed to the one dimensional nature of most text), it is a key question
+whether it is reasonable to expect this aspect to be reflected in
+any linearisation.
+
+To give \acro{ISO}\,12083 its due, it says ``Since there is no consensus
+on how to describe the semantics of formulas, it only describes
+the presentational or visual structure.''
+
+\section{\acro{HTML}3 (expired draft)}
+\acro{HTML}3 supports a |<math>| element which provides some
+capability for the inclusion
+of maths expressions. The draft (\cite{math})
+ does indicate that this capability is limited.
+It describes the functionality as similar to that found in ``common word
+processing packages''. In itself this may be seen as a hint of one of
+the driving
+forces within \acro{HTML}3 -- a desire to emulate word processor
+functionality. For a language which derives initially from a high
+energy physics community, this is a modest aim. The other design aim
+of |<math>| in \acro{HTML}3 is to be ``concise and comparatively easy
+to read''. As a rider, it is suggested that this will make formulae
+longer than \LaTeX, but shorter than Euromath or \acro{ISO}\,12083.
+
+It is stated that the maths owes ``a lot to \LaTeX's math mode''. In some cases
+it uses names for elements which are derived from \TeX/\LaTeX. Immediately a
+misconception springs up. The second paragraph of the section on maths gives
+examples of \LaTeX\ commands: namely \cmd{atop}, \cmd{choose} and \cmd{sqrt}.
+Only \cmd{sqrt} is a \LaTeX\ command. The \cmd{atop} and \cmd{choose}
+ are unrepentant \TeX. Ignoring
+for a moment the fact that there is a clear confusion between \LaTeX\ and \TeX\
+in the mind of the author of the draft (Dave Raggett),\footnote{I suspect
+this is quite a widespread misunderstanding.} there is actually a deeper problem.
+The use of an operator like \cmd{over} requires much more work on the part of a
+processor, since it is often not until the whole expression has been parsed that
+sense can be made of what is actually \cmd{over} what (see \cite{seb}).
+From years of teaching
+\TeX, I can confirm that the \cmd{over} command (and its buddies, \cmd{above},
+\cmd{atop}, \cmd{choose}, \cmd{brack} and \cmd{brace}) can lead to immense
+frustration and confusion.
+
+\acro{HTML}3 also has an |<above>| token, but this is quite different from
+\TeX's \cmd{above}. Since
+the \TeX\ command is quite typographic, specifying the width of the line
+separating numerator and denominator, this is probably not too ambiguous. The
+function of the \acro{HTML}3 tag is to allow something to be drawn above an
+expression. There is a similar |<below>| tag.
+|<above>| is a sort of numerator operator:
+\begin{Verbatim}
+<math>
+<above>x+y</above>
+</math>
+\end{Verbatim}
+gives something like
+\begin{displaymath}
+\overline{x+y}
+\end{displaymath}
+with the nuance that the element takes an attribute |sym| which can specify
+other symbols: |line| (the default), |cub|, |larr|, |rarr|, |hat| and |tilde| (in
+a sense |hat| and |tilde| correspond to \cmd{widehat} and \cmd{widetilde}).
+For example,
+\begin{displaymath}
+\overbrace{a+b+c}
+\end{displaymath}
+would be
+\begin{Verbatim}
+<math>
+<above sym=cub>a+b+c</above>
+</math>
+\end{Verbatim}
+the corresponding |<below>| has the same list of possible |sym| attributes,
+though I don't immediately understand what |hat| and |tilde| would do.
+
+There are also some terminological surprises. |<math>| almost borrows
+the use of underscore and carat/circumflex for sub-scripts and
+super-scripts, except that they are referred to as index and exponent.
+The |^| and |_| are actually |shortref|s for |<sup>| and
+|<sub>|.\footnote{The notion of exponent and index may be welcome,
+since we would expect \acro{HTML} to be concerned with the underlying
+content. Perhaps \TeX\ does tend to overload the idea, since a superscript may
+signify more things than just an exponent. A semantic separation
+might be a very good
+idea, but this is unlikely to be the intention, since they are
+|shortref| characters for |<sub>| and |<sup>|.
+Poppelier \textsl{et al.}\ put this very succinctly:
+``What is the function of the 2 in SU$_2$, $\log_2x$, $x_2$, $x^2$ $T_2^2$?
+In SU$_2$ it is the number of dimensions in the Lie group; in $\log_2x$ it is
+the base of the logarithm; if $x$ is a vector, the ${}_2$ in $x_2$ is an index;
+the ${}^2$ in $x^2$ could be a power, but if $T$ is a tensor, the ${}^2$ in
+$T_2^2$ is a contrainvariant tensor index.''
+} Since \acro{HTML} syntax and \LaTeX\
+syntax are rather different, the ease of \LaTeX's sub- and super-scripting has
+to be abandoned. The \acro{HTML} tag has to be terminated. It is
+unfortunate that there
+was not a way of employing an implied end tag.
+For example
+\begin{small}
+\begin{displaymath}
+a^{23}_n
+\end{displaymath}
+\end{small}
+is given from
+\begin{Verbatim}
+<math>
+a^23^_n_
+</math>
+\end{Verbatim}
+
+Should you need to subscript a
+subscript, the |shortref| form cannot be used. Although |<math>| does support a
+grouping operator,
+\begin{displaymath}
+a_{b_c}
+\end{displaymath}
+is obtained from
+\begin{Verbatim}
+<math>
+a<sub>b<sub>c</sub></sub>
+</math>
+\end{Verbatim}
+Perhaps cleverly, superscripting an expression with a binary operator results
+in the expression being placed over the operator, like \cmd{stackrel}.
+For example
+\begin{displaymath}
+A \stackrel{\alpha'}{\longrightarrow} B \stackrel{\beta'}{\longleftarrow} C
+\end{displaymath}
+would be
+\begin{Verbatim}
+<math>
+A &rarr;^&alpha;&prime;^
+ B &larr;^&beta;&prime;^ C
+</math>
+\end{Verbatim}
+In passing note that the use of the `prime' operator is different from
+\TeX\slash \LaTeX\ use, and the use of space. I am not entirely clear about the
+use of space in |<math>|. It is certainly not ignored, as in \TeX, and
+the draft does comment on the use of different horizontal white space
+within the equation. The draft runs
+\begin{quote}
+Spacing between constants, variables and operators is determined
+automatically. Additional spacing can be inserted with entities such as
+|&thinsp;|, |&sp;| and |&quadsp;|. White space in the markup
+is used only to delimit adjacent variables or constants. You don't need
+spaces before or after binary operators or other special symbols as these
+are recognised by the \acro{HTML} math tokeniser. White space can be
+useful, though, for increased legibility while authoring.
+\end{quote}
+This does imply a rather different use of space.
+This use of space does have the effect that a `prescript' can be made
+quite unambiguously simply by ensuring it is preceded by a space.
+It would imply
+a string |sin| is recognised as `some sort of function'. The string |xyz|,
+would also presumably imply `function', while in \LaTeX\ it would imply
+the three variables $x$, $y$ and $z$.
+It does leave unclear how
+\(\sin^2\theta \) and
+\begin{displaymath}
+\max_{i=1}^n x_i
+\end{displaymath}
+would be handled with ease. If the $\sin^2\theta$ uses |<sup>|
+but the
+\begin{displaymath}
+\max_{i=1}^n x_i
+\end{displaymath}
+requires |<above>| and |<below>| then
+we have an interesting inconsistency.
+
+|<math>| does adopt \TeX/\LaTeX's notion of binary operators,
+and in general claims
+to reflect the assumptions of \TeX/\LaTeX. It does not however provide support
+for multi-line equations, stating that `this can be effectively handled by
+combining math with the |TABLE| element'. To me this wanders far from the basic
+concepts of \acro{SGML}. However, what it appears to mean is that
+the |<array>| tag uses the same sort of syntax as |<table>|, not that
+an array uses the table tags.
+
+
+From the draft, it is anticipated that chemistry could be set from within
+the |<math>| tag. I would view this as a mistake. It may be (almost) defensible
+from within \LaTeX\ to use math structures, although the various chemistry
+packages at least try to separate the notions. It seems unfortunate that HTML3
+should not attempt something similar.\footnote{And of course this
+emphasises the
+inadequacy of referring to a subscript as an index and a superscript as an
+exponent. The terms are pretty meaningless for chemical notation.} An example
+might be
+\begin{Verbatim}
+<math class=chem>
+Fe_2_^2+^+Cr_2_O_4_
+<math>
+\end{Verbatim}
+for
+\begin{displaymath}
+\mathrm{Fe}_2^{2+}+\mathrm{Cr}^{}_2\mathrm{O}^{}_4
+\end{displaymath}
+where the different notational style of chemistry is tackled, notably
+its use of an upright font and consistent baselines for subscripts.
+
+
+Some hints on appearance are provided: it is expected that functions
+(operators), numbers and other constants are portrayed in an upright font, and
+variables are italic. Unlike \TeX/\LaTeX, limits for integrals and summation
+signs are said to be placed directly above or below, or to the immediate right
+(depending on the symbol). Unfortunately, the draft does not indicate quite
+what this ambiguous term means. I suppose it does not mean `emulate' the
+\TeX/\LaTeX\ mode, though that is obviously plausible, and from the point of view
+of a browser author could be a reasonable path.
+
+What does it look like?
+\begin{Verbatim}
+<math>
+&int;_a_^b^{f(x)<over>1+x} d x
+</math>
+\end{Verbatim}
+for
+\begin{displaymath}
+\int_a^b\frac{f(x)}{1+x}dx
+\end{displaymath}
+Note that the sub- and
+super-scripts, like \TeX/\LaTeX\ also denote limits.
+
+
+Some maths accents are available: |<vec>|, |<bar>|, |<dot>|, |<ddot>|, |<hat>|
+and |<tilde>|. There are no explicit equivalents for \cmd{check}, \cmd{breve},
+\cmd{acute} and \cmd{grave}, although they could be created with |<above>|.
+
+Another borrowing from \TeX/\LaTeX\ is the notion of grouping:
+\acro{HTML}3 uses a |<box>| element where \TeX/\LaTeX\ would use parentheses.
+|<box>| can be replaced by a |shortref| form of |{|
+and |}|, which greatly aids brevity and comprehension.\footnote{Should
+you need the symbols themselves, they are obtained by
+the entities \texttt{\&lcub;} and \texttt{\&rcub;}.}
+Although \TeX nically a braced group is a sort of `box',
+perhaps |<group>| might have
+been a better, though less concise term, in the context.
+It is perhaps an unfortunate choice, since `box' carries overtones for
+many \TeX\
+users. Still, it does ensure that all the power of grouping is present (fairly
+essential in view of the |<over>| element). To overload slightly, one of the
+attributes of the |<math>| element is |box|, which causes a box to be drawn
+around the formulae. The |<box>| element is used in a number of ways; it is
+used, for example with the |<left>| and |<right>| commands for delimiters which
+grow. This leads to a rather strange construction:
+\begin{Verbatim}
+<math>
+f(x)=<box>
+ (<left> 1+x <over> sin x <right>)
+ <\box>
+</math>
+\end{Verbatim}
+where |(<left>| gives a left parenthesis of appropriate size and |<right>)|
+gives the corresponding right parenthesis.
+As with \TeX, it is recognised that sometimes it
+may be necessary to have a delimiter larger than `default'. |<box>| therefore
+has a |size| attribute to enable this to happen. The permitted values are
+|normal|, |medium|, |large| and |huge|. The |shortref| form cannot
+take attributes.
+
+Integrals (and other large operands which are stretchy) also need the use of
+|<left>|, without any corresponding |<right>|. For example
+\begin{Verbatim}
+<math>
+<box>&int;_-&inf;_^&inf;^
+ <left> f(x,y) <over> x^2^+y^2^
+ </box> d x&thinsp;d y
+</math>
+\end{Verbatim}
+should give
+\begin{displaymath}
+\int_{-\infty}^\infty\frac{f(x,y)}{x^2+y^2}dx\,dy
+\end{displaymath}
+
+Although |<math>| is said to recognise functions as maths entities, there is no
+list of all the entities given in the draft. However, straightforward elements
+like |<sqrt>| and |<root>| exist which work the same as their \TeX\ counterparts.
+The \LaTeX\ notation for $\root n \of x$ however is \cmd{sqrt} with an
+optional argument: |\sqrt[n]{x}|, not as HTML3:
+\begin{Verbatim}
+<math>
+<root>n<of>x</root>
+</math>
+\end{Verbatim}
+which is rather closer to \TeX.
+
+ What the draft terms `Greek letters' are available in a similar way to
+\TeX/\LaTeX\ as entity references (and includes omicron).
+Some control over font styles is available through |<b>| and |<t>|. The first
+emboldens, while the latter makes upright (Times?). You may even combine
+the two as |<bt>|. Note that these changes apply to variables and constants,
+and not to numbers, delimiters, operators and other symbols. An interesting
+attribute is |class|, so that we could identify a vector as
+\begin{Verbatim}
+<math>
+<b class=vector>a</b>=A&prime;
+</math>
+\end{Verbatim}
+
+Arrays or matrices are quite verbose, but broadly similar to \LaTeX. They are
+introduced by |<array>|, while each row starts with |<row>| and each cell with
+an |<item>|. This is in line with HTML's |<table>| model. Adapting some aspects
+of \LaTeX, column definitions can be added, for example
+|coldef="CCCC"|, the default, where columns are centred. The alternatives are
+|R| and |L|. This is one of the few instances in HTML where case is vital. If the
+attributes are separated by |+|, |-| or |=| this will propagate down the array
+as a separator. For example
+\begin{Verbatim}
+<array coldef="R=C+C+C">
+\end{Verbatim}
+Other attributes include |ldelim| and |rdelim| to specify the right and left
+delimiters of the array or matrix. Unlike other instances where a name is used,
+the symbol itself appears to be used in this context.
+
+
+\subsection{Summary}
+I tend to think that this makes it more difficult for someone with a \LaTeX\
+background to interpret |<math>|. When two languages are quite different, there
+is rarely confusion in flipping from one to the other, but when they share
+many similarities it can be frustratingly simple to converge at all the wrong
+times. Note also that |<math>| uses the ISO entity names for
+symbols (\cite{SandS}) rather than
+the \TeX\ names. In a few cases this sows potential confusion.
+The confusion which exists within the draft between \TeX\ and \LaTeX\
+is not of itself a problem, except that people coming to HTML3, being told
+it is `like \LaTeX', would find some key differences.
+
+The main divergences are
+\begin{enumerate}
+\item the interpretation of space\label{space}
+\item need to close most \acro{SGML} elements (e.g.\ |^| and |_|)
+\item |<over>|
+\item interpretation of functions (a consequence of \ref{space})
+\item entity names similar but not identical to corresponding commands
+\item use of |&prime;|
+\item missing commands
+\item poor support for cross-referencing
+\end{enumerate}
+
+
+\section{Future of maths in HTML}
+At this point, it may be worth considering the extent to which any maths
+expression can divorce the semantic component from the form on the page. Often
+the way equations are portrayed can assist in their interpretation. Both tables
+and maths seem to be examples where the meaning and the appearance are very
+closely intertwined. There are instances where an author changes notation in
+order to pursue an argument. One assumes that the essential meaning does not
+change between changes in notation, and that perhaps a markup system might not
+even note the change, except perhaps as an attribute.
+
+The draft document which forms the basis of this discussion
+expired in September, 1995. Some of the new structures which
+it introduced, notably tables, form part of most browsers now,
+but mathematics didn't make it (although |<sub>| and |<sup>|, without
+|<math>| did) (see \cite{html32}). An email from Dave Raggett
+(to David Carlisle), who wrote the draft, notes that \acro{W}3\acro{C}
+\begin{quote}
+has set up a small working party on math, and we expect
+to publish a detailed proposal by early Summer. The March'95 spec
+will provide a starting point, but we may end up with something
+rather different.
+\end{quote}
+
+\noindent He goes on to state:
+\begin{quotation}
+\noindent The \acro{W}3\acro{C} math group has the goal to develop an
+open specification
+for \acro{HTML} math that:
+\begin{itemize}
+\item[]Is suitable for teaching, and scientific publishing.
+\item[]Works with symbolic and numerical math applications
+\item[]Supports filters to/from other math formats, e.g.\ \TeX
+\item[]Is easy to learn and to edit by hand
+\item[]Is well suited to template and other math editing techniques
+\item[]Can be rendered to:
+\begin{itemize}
+\item[]graphical displays
+\item[]speech synthesisers
+\item[]plain text displays e.g.\ \acro{VT}100 emulators
+\item[]print media, including braille
+\end{itemize}
+\item[]Supports lengthy expressions via fold\slash unfold and
+line breaking with author control.
+\end{itemize}
+This is shaping up as the need for simple macros and declarations
+that define terms etc. for use across multiple |<math>| elements,
+and parsing of |PCDATA| using ``models'' referenced by |<math>| elements.
+These models define how to interpret stuff at a level sufficient to
+support symbolic manipulation without having to make all these
+distinctions explicit in the markup itself.
+\end{quotation}
+
+This is quite a bold extrapolation from the original specification.
+Some of the suggestions seem to me to be incompatible. The inclusion of
+symbolic and numerical applications is interesting and goes far
+beyond the existing maths \acro{DTD}s.
+
+The relevant \acro{W}3\acro{C} web page (\cite{W3C}) contains a
+reference to \acro{QED}, an ambitious
+programme to build a `single, distributed, computerized
+repository that rigorously represents all important, established
+mathematical knowledge'. If this genuinely represents part of
+\acro{HTML}'s solution to maths, we will have some time to wait before
+a system is available.
+
+\section{Conclusion}
+It is not clear to me at present whether \acro{HTML} will ever be rich enough
+to do the sorts of things which mathematicians and physicists want to do
+with maths. Of course, it could be that these are not the market at all.
+I have long argued that one of \TeX's (and \LaTeX's) major problems is
+that the population of users who benefit by it is small -- very much
+a minority. And the expansion of the use of computers has made them
+an even smaller minority. At best we are a niche market. Some of the
+simpler problems are already tackled quite conveniently by word processors,
+further eroding the niche. Why bother with mathematics at all? Is it
+really worth the effort, compared with something sexy like |<frame>|s?
+
+Having said that, it appears that Public Entities in \acro{ISO}\,8879
+(\cite{SandS})
+are sufficient
+to encompass most of the symbols I have seen in \LaTeX\ and \AmSTeX. The
+potential is there. What makes this especially intriguing is that there
+is software around like Panorama from SoftQuad which is designed to
+enable any \acro{SGML} document whose \acro{DTD} is known to be
+rendered on the screen.
+Therefore for truly `heavy' applications, this seems a much better
+way to go. In fact, I would see it as an altogether better way to go.
+Browsers which could examine the |Doctype|, find it on an appropriate
+server and then render it would be much more flexible, and enable us to use
+existing \acro{SGML} documents easily on the Web. \acro{HTML} would
+simply be a lightweight
+\acro{DTD} used because it had a lower overhead.
+
+On the other hand, browsers like Netscape Navigator
+are becoming larger, are starting
+to include `plug-ins' and be Acrobat-aware.
+If \acro{HTML}3 version 2, as outlined by Raggett does support filters
+(hopefully to \LaTeX\ rather than \TeX), as well as symbolic
+manipulation (Mathematica, Maple, etc.), it could be a very powerful
+tool.
+However, the latest information available through the World Wide Web Consortium
+does not encourage belief that this is much more than a dream.
+
+\begin{thebibliography}{}
+
+\bibitem[ANSI, 1994]{AAP}
+\acro{ANSI}/\acro{NISO}, (1994).
+\newblock Information and documentation -- Electronic
+manuscript preparation and markup.
+\newblock Technical Report, ISO 12083:1994 {\acro{ANSI}/\acro{NISO}}.
+
+\bibitem[Bryan, 1988]{Bryan}
+Bryan, M. (1988).
+\newblock {\em {SGML} an author's guide}.
+\newblock Addison-Wesley.
+
+\bibitem[Chamberlin, 1988]{Chamberlin}
+Chamberlin, D.~D. (1988).
+\newblock An adaptation of dataflow methods for \acro{WYSIWYG}
+document processing.
+\newblock In {\em ACM Conference on Document Processing Systems}.
+
+\bibitem[Euromath consortium, 1996a]{Euromath}
+Euromath consortium (1996a).
+\newblock Euromath system.
+\newblock \url{www.math.ethz.ch/~shared/emb/GeneralFiles/Euromath.html}
+
+\bibitem[Flynn, 1995]{Flynn}
+Flynn, P. (1995).
+\newblock \acro{HTML} and {\TeX}: making them sweat.
+\newblock {\em {\BV}}, 5(2):7--11.
+
+\bibitem[Goossens and Saarela, 1995a]{Goossens2}
+Goossens, M. and Saarela, J. (1995a).
+\newblock {\TeX}\ to \acro{HTML} and back.
+\newblock {\em {\TUB}}, 16(2):174--214.
+
+\bibitem[Goossens and Saarela, 1995b]{Goossens}
+Goossens, M. and Saarela, J. (1995b).
+\newblock A practical introduction to \acro{SGML}.
+\newblock {\em {\TUB}}, 16(2):103--150.
+
+\bibitem[Grif, 1996]{GrifSA}
+Grif (1996).
+\newblock {GRIF} {S}. {A}. -- \acro{SGML} and \acro{HTML} solutions.
+\newblock \url{www.grif.fr}
+
+\bibitem[\acro{ISO}, 1988]{ISO9573}
+\acro{ISO} (1988).
+\newblock Information processing -- \acro{SGML} support
+facilities -- Techniques for using \acro{SGML}.
+\newblock Technical Report, \acro{ISO}/\acro{IEC} \acro{TR} 9573:1988,
+\acro{ISO}.
+
+\bibitem[Poppelier et al., 1992]{PvHR}
+Poppelier, N.~A.~F.~M., van~Herwijnen, E. and Rowley, C.~A. (1992).
+\newblock Standard \acro{DTD}s and scientific publishing.
+\newblock {\em {EPSIG} {N}ews}, (3):10--19.
+
+\bibitem[Quint and Vatton, 1986]{Grif}
+Quint, V. and Vatton, I. (1986).
+\newblock Grif: an interactive system for structured document manipulation.
+\newblock In van Vliet, J.~C., editor, {\em Text processing and Document
+ Manipulation}, pages 200--213. Cambridge {U}niversity {P}ress.
+
+\bibitem[Raggett, 1995]{math}
+Raggett, D. (1995).
+\newblock \url{www.w3.org/pub/WWW/MarkUp/html3/}
+\newblock Expired \acro{HTML3} draft.
+
+\bibitem[Rahtz, 1995]{seb}
+Rahtz, S. P.~Q. (1995).
+\newblock Another look at {\LaTeX}\ to \acro{SGML} conversion.
+\newblock {\em {\TUB}}, 16(3):315--324.
+
+\bibitem[Smith and Stutely, 1988]{SandS}
+Smith, J. and Stutely, R. (1988).
+\newblock {\em {SGML} the user's guide to {ISO}\,8879}.
+\newblock Ellis Horwood.
+
+\bibitem[van Herwijnen, 1990]{EvH}
+van Herwijnen, E. (1990).
+\newblock {\em Practical {SGML}}.
+\newblock Kluwer Academic Publishers.
+
+\bibitem[\acro{W}3\acro{C}, 1996b]{html32}
+\acro{W}3\acro{C} (1996b).
+\newblock \acro{HTML} 3.2 specification.
+\newblock \url{www.w3.org/pub/WWW/MarkUp/Wilbur/}
+
+\bibitem[\acro{W}3\acro{C}, 1996c]{W3C}
+\acro{W}3\acro{C} (1996c).
+\newblock Math markup in \acro{HTML}.
+\newblock \url{www.w3.org/hypertext/WWW/MarkUp/Math/}
+
+\end{thebibliography}
+\end{Article}
+