Re: Goals verses syntax in MathML


Andrew Mathas wrote:

> I have just been reading about the proposed MathML solution to
> displaying mathematics on the web. 

First of all, MathML is not a proposed solution, but an adopted
Recommendation of the W3C which has been implemented in a number of
software packages, and is in the process of being implemented in many

> I would like to echo the
> comments of others that the proposed solution is absurdly
> complicated.
> For example, the present syntax appears to require that the font of 
> pevery symbol be explicitly declared; would it not be more sensible 
> to have a default font for every symbol inside a mathematics mode? 
> Common features of mathematics, like subscripting and superscripting,
> plus (+) and minus signs (-), etc. should also have reasonable shorthands.

Second, it is not the case that you must specify a font for every symbol.
Renderers provide a default font, and beyond that, the <mstyle>
elements provided a mechanism for scoped font changes.

Now for the main point from Mathas posting -- that MathML is too

In my view, the main problem with MathML is one of public image.  I
think that many people think of MathML as something which should be
roughly comparable to TeX or HTML.  When the Math working group began
working on MathML, this was was we had in mind too -- in fact it was
called "HTML Math" when the design objectives Mathas quotes were

However, this turned out to be unrealistic for a number of reasons.  

  1) W3C is a _Consortium_ and therefore, working coming out of W3C must
  be not only technically competant, but economically and politically
  viable too, form the point of view of the member organizations.
  This point cannot be stressed enough.   

  2) If there is any hope at all of getting math into mainstream Web
  browsers, math markup must be compatible with mainstream extension
  mechanisms.  In practical terms, this means MathML needed to
  to be an XML application, which also unfortunately means it is

  3) The simpler the language, the more complicated the processing.
  A simple language for computer algebra means complicated processing
  for high quality publishing and vice verse.  The closer to TeX a
  language is, the more irrate organizations committed to SGML become
  and vice versa. Once again, a solution which is deemed unacceptible
  by a substantial sector of the W3C membership is simply not viable
  within the context of the consortium.

Given these technical, political and ecomonic constraints, the working
group therefore was obliged to redirect its efforts toward something
which WAS achievable -- namely MathML.  

As I have written before, MathML is a low-level markup and should be
viewed as roughly comparable to PostScript or DVI, and not as a
competitor of TeX.  As such it has the strengths and weaknesses of a
low-level format.  On the positive side, it is powerful.  On the
negative, it requires application software to be useful,
i.e. converters, authoring tools, renderers -- a situation very
closely analogous to that of PostScript and PDF.

In my view, the most significant thing about MathML is that it
actually exists.  It may not be perfect, but just exactly as it was
supposed to, it is facilitating the development of a wide variety of
math savvy web applications.  Some software is already available, and
much more is coming.  If it weren't for MathML, either that software
development would not be taking place, or software would all be merely
generating GIFs, with no hope for interoperability, searching, or
high-quality rendering in the future.  

It regret that in the end, meeting the original goals for HTML-Math
has required a communication layer/application layer solution,
primarily because of the time lag for implementation.  In my view,
this evolution has caused a lot of confusion and discontentment on the
part of thoughtful observers such as Mathas, and I wish economic and
political realities had been otherwise.

However, I am unapologetic about the facts.  I may be proven wrong by
events, but at the moment, I remain unshakable in my opinion that
MathML is a significant step forward toward putting mathematics on the
Web, and that it is vastly preferable to nothing.  

Robert Miner

Robert Miner                               http://www.geom.umn.edu
The Geometry Center                        phone: (612) 626-8313
HTML-Math WG co-chair                      fax:   (612) 625-8083