Math and Hypertext

Hypertext is appealing because it offers a way of organizing information so that the interconnections between ideas can be laid bare. A mathematics text is often internally cross-referenced to a great extent. Is paper still the best medium for presenting ideas?

HTML 3.0 was a proposed hypertext specification of the World-Wide-Web Consortium (W3C) which included mathematical capabilities. It resembled TeX in syntax, with modifications to make it compatible with HTML syntax. You can try it out if you are using an older version of the Arena browser. Unfortunately the HTML 3.0 specification was abandoned, and its successor, HTML 3.2 has dropped the math part of the specification. Current versions of the Arena browser don't even display the math part of the HTML 3.0 demonstration document correctly.

A currently developing attempt at a standard is MathML, another project of W3C. Much has changed since the failure of the HTML 3.0 specification, and MathML may well succeed.

The Arena browser, which was the testbed of math support in HTML 3.0 is no longer supported by W3C (it is currently in the hands of Yggdrasil). The newer Amaya browser is the W3C organization's current testbed for MathML. We will be able to say that MathML has arrived when it is supported by Microsoft and Netscape. These companies are not represented on the MathML task force. However, both companies are involved in the XML specification, and XML support is promised or already implemented for both Netscape Navigator and Microsoft Explorer. Since, according to W3C ``MathML is cast as an application of XML. As such, with adequate style sheet support, it will ultimately be possible for browsers to natively render mathematical expressions,'' this means that Netscape and MS Explorer should eventually support MathML.

Unfortunately MathML appears unnecessarily complex and, unlike TeX can't be easily written by hand. Is there no better way? A fairly obvious idea is that html could have a ``tex'' tag. You'd write:

<tex> \int_{-\infty}^\infty e^{-\pi x^2}\,dx=1 </tex>

Or if you wanted a displayed formula, you'd type <tex align="center">. Between the tags, < and > would be escaped: <tex> x^2+y^2 \< 1 </tex> . This scheme can be criticised on grounds of purity---we are mixing two markup languages, HTML and TeX. This is only an aesthetic consideration---it would be easy for a preprocessor to take the document and run a Pidgin TeX to MathML preprocessor on any text between and tags.

Meanwhile, alternatives exist:

• In the preprint server, documents are stored as dvi, postscript or PDF to be retrieved using a browser. This is an informal method of publications. Electronic Journals such as those published by the American Mathematical Society resemble the preprint server in technology but serve the more traditional goals of formally refereed publication.
• An entire page of text can be represented by a gif. A .dvi file is much smaller but a gif will be accessible from any graphical browser, so if bandwidth is subordinate to convenience, this may be a valid solution. If you want to create a gif containing the content of a page or more from a postscript file, here is the process. Assuming that you have ghostscript and the netpbm utilities installed, run gs with the option -sDEVICE=ppmraw -r100x100. Then pipe the output to ppmtogif. If you prefer, you may run pnmcrop before ppmtogif to crop the gif. Suggested shell scripts to carry out this task may be found at Luc Levroye's Postscript Page, or here is one I wrote myself.
• First, there is HyperTeX, which adds hyptertext capabilities to a TeX document. To preview Hypertex you need a HyperTeX previewer, such as xhdvi (a modification of xdvi). To write your own HyperTeX, you need the hyperbasics.tex macros. There are no modifications needed to the TeX program---everything is done with macros and \special commands. The principal problem that I see with HyperTeX as it currently exists is that the previewers are still in the beta stage. In September 1996, Kasper Peters posted to comp.text.tex that he's rewriting xhdvi as a netscape plugin.
• IBM's TechExplorer version 1.2 here is a netscape plugin. Their literature states ``IBM's techexplorer Hypermedia Browser Version 1.0 formats and displays expressions and documents containing mathematical and scientific markup. It is a Netscape Navigator plug-in for readers and publishers of scientific documents coded with the popular TeX and LaTeX markup languages.'' This sounds like the right sort of thing ... if you're running Windows 95, NT, Solaris 2.5, AIX or IRIX.
• Project MINSE is another scheme for putting mathematics on the web.
• Java offers another possibility. Here and here and here are applets which suggests some approaches, and here is IDVI, a dvi previewer written in Java!
• LaTeX2HTML, works very well, though I personally found the process of preparing documents this way confusing. For a good example of what can be done with this program, see the Proceedings of the Organic Mathematics Workshop. LaTeX2HTML is a large and complex perl script, authored by Nikos Drakos. In its conception and execution, it is a brilliant piece of work. It produces html documents from latex source, and rendering mathematics is only a small part of this objective. To render mathematics, first latex then dvips is run, then various filters (from standard image-processing packages such as pbmplus or netpbm) which produce gifs out of the postscript. In the end, the formulas are turned into bitmapped graphics. This is a somewhat slow way of putting mathematics on the web, because of the large bandwidth requirements for all those gifs. But it works, and it may be ideal for some purposes, such as putting math on a local network, or for documents where the formula density is low.
• Hyperlatex is another latex to html scheme. The method of treating formulas in Hyperlatex is discussed here.
• Webify is another scheme for converting postscript documents to HTML, which like LaTeX2HTML relies on the netpbm filters to create graphics files.

Links

Here is Paul Pollock's useful page on this topic.

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