Mathematics on the Web

This page recreates a few of the links found on the more comprehensive page http://www.cecm.sfu.ca/~jalester/MOTWsites.html. That page includes links used in a talk by June Lester about what does and does not work when attempting to communicate mathematics on the web. On this page we illustrate some of what doesn't work.

Note: our focus here is on the presentation of the web pages, rather than the creation of them. There are many products which, for example, will create in-line GIFs to display formulae; some may create these GIFs with much less effort on the part of the page designer, but that's not what we wish to critique here. Our criteria only concern the final product -- how will your web page look on my screen?

More precisely, I show here the effect of visiting some of the sample pages which were evidently intended by the designers of these products to illustrate how well (or how easily) mathematics can be communicated across the web. The methods might fail for a number of reasons. To begin with, it is difficult enough to describe mathematical layout in a "linear" format, although we know this is possible and done regularly with TeX. Setting math onto the Web adds the frustration that it is difficult to predict the combination of hardware and software which will be available at the user's end. Indeed, it is supposed to be a feature of HTML that the presentation of the pages will reflect the preferences of the viewer of the web page as well as those of the creator of that page; each can control font choices, colors, viewing area, and so on.

When fetching these pages I made absolutely no effort to accomodate the page designers -- I just clicked from my default set-up, which is, admittedly, a bit out of the ordinary. (But this is my point: that page designers cannot tell in advance how my system will be configured.) In my case I use no Microsoft products and (except at home) no Intel products; I have many "features" turned off for security or speed of loading (java, cookies, etc.) I use large fonts and a large viewing area to help me see detail more easily. My only obvious concession was not to try to load these pages with Lynx (a text-only viewer which is the fastest tool I have). This is not (only) curmudgeonry on my part; some limitations are dictated by those who provide my hardware and internet connections. I do, in fact, take the trouble to switch settings when there is something I really want to read (I'll even check a half-dozen very different machines to find one which works right.) Again, let me emphasize that my purpose here is to illustrate the limitations which some users of the Web will encounter when trying to read mathematical pages.

Apparently all this wreaks havoc with web pages (even pages by people who usually know what they're doing). Here's what I see when I try these:

• LaTeX2HTML, math --> GIFs (e.g.The Defect of a Triangle) (Note in particular the failure to align GIFs with the text baseline)
  
• TtH math --> symbol font + tables (e.g. Electric Probes in Magnetized and Flowing Plasmas) (The page designer must have assumed I had some font installed.)
  
  I don't know what products were used to create http://www.rsasecurity.com/rsalabs/bulletins/twinkle.html and http://www1.shore.net/~ndm/java/mmexplorer/ax-ext.html but they suffer the same deficiency:
  
  I recently found that StarOffice could be used as a browser; interestingly, it gets this set of pages "right" (they are readable as intended, if not exactly elegant).
• Stef's HTML Equation Generator, math --> GIFs + symbol font (e.g. The Riemann Curvature Tensor) (Symbol fonts are completely out of proportion. Use of ordinary font, not even italicized, makes equations look terrible)
  
• WebEq math --> applet (e.g. Brouwer's Theorem) (Not bad appearance: except for font-size disparities, the only problems are a couple of missing symbols and slightly truncated images such as the \emptyset. This page takes rather a long time to load.)
  
  (On another machine I have java turned off completely and, predictably, the output is terrible:)
  
• MathType math --> Tex or MathML or GIFs (e.g. Mean, Variance, and Standard Deviation) (Also not bad except for use of (in my case non-existent) symbol fonts. Also some font-size disparaties. Second illustration shows the same document in PDF format. Note that a font is missing. Also note size of default font.)
  
  
• TrueDoc uses javascript to load fonts on the fly; indeed you can design your own fonts. Supposedly. Here's MATH EQUATIONS supposedly with 11 fonts and no GIFs at all. Images show results in my Netscape, Amaya, and StarOffice browsers.
  
  
  
• ASCII-art is limited and ungraceful, but often serviceable. A sample from my own pages:
  
  But when that same page is viewed through Deja.com, it's HTML-ized, and so my browser uses a proportional-width font, making a mess (and the mess would be worse if the re-transmitter chose not to respect line-breaks at all!)
  

So what does work? Well, there are a few options you might want to consider, but each has pros and cons like the examples above.

• Writing TeX source directly into the human-readable display (e.g. writing out "a_n" and "\alpha") is comprehensible to mathematicians but not to most novices. Likewise one can communicate in a quasi-computer-language fashion. These are the kinds of methods prefered for email communication; details.
• It is possible to create a page of mathematics by any other means, then scan in (or use screen capture) whole pages as .GIF or .JPEG images. (The former is probably better for text.) Viewers for these image formats are included in most browsers. Unfortunately these tend to be large files, are not searchable documents, and cannot be modified by the page author without recreating the entire document.
• HTML now has a few "official" standard versions as well as proprietary "improvements" incorporated by some browser producers (but not necessarily supported by other vendors. Check out the Best Viewed With Any Browser campaign.) HTML mathematics primitives e.g. for subscripts and math-italics E_n(f) are clumsy and rendered improperly by text-only browsers such as Lynx.

  The base alphabet for HTML is supposed to be ISO8859 or UNICODE (depending on which HTML standard version you wish to consider) which allows for the direct embedding of various accented characters, but of course these may or may not be supported by your browser: e.g. an "o" with an umlaut over it should be representable by either an HTML-recognized ASCII string or a single ISO character; do these both work for you? (ö and �� ) With the full 16-bit character set, nearly all mathematical symbols would be directly available in HTML (but not the spacing and two-dimensional layout which can be fine-tuned in TeX, say). For information on proposed standards for math symbols, try AMS or unicode.

  The next generation(s) of HTML are under development; presumably future browsers will accomodate MathML documents; see http://www.w3.org/TR/REC-MathML/. These developments are thankfully being guided by parties such as the American Mathematical Society. Expect to see a healthy market in enhanced browsers for the webpage reader (see below) and editors for the webpage producer (e.g. MathType, above); for MathML is designed to be very detailed and much too cumbersome for humans to read and write directly. (examples)

• If the person on the viewing side can be assumed to have a plug-in, one can use the web to distribute files of various filetypes, including several popular types of files which render mathematics essentially perfectly: DVI, PostScript, PDF, Mathematica, and even Microsoft Word files can be read this way. IBM's Techexplorer is a plugin which can read TeX and MathML directly. Mnemonic is a new stand-alone browser designed to support the newer standards for HTML, and XML (and some TeX). Other browsers are likely to support some of these formats in time (I believe Amaya can already).

  Besides the installation of the plug-in (a one-time chore), these formats require transmitting rather large files -- often for no particular purpose, since simple text is sufficient for many messages. Also note that not all these formats can render complicated mathematics, included graphics, and hypertext links with equal ease for the page designer and the person viewing them. I don't know if they are all supported by printer software, either.

Sadly, I don't have a final recommendation. My own choice is

• For informal material, I just use flat text with ASCII-art and TeX-like syntax used as appropriate
• For simple formal documents I use HTML with minimal markup (e.g. math symbols in italics). I prefer single, small, searchable, scalable documents whose appearance is a little poor, rather than large binaries, multiple inline GIFS, whole page images, assumed symbol fonts, and assumed browser.
• For complex formal documents I will go whole hog to PDF. My main concerns here (time to launch the viewer and size of transmitted file) are gradually being addressed by protocol and hardware improvements.
• For complex sets of documents, I would recommend an off-line master copy of files in some universal format (TeX is probably OK), from which ASCII, HTML, PDF, and maybe DVI files can be generated and offered as user options.

This web page is merely an attempt to highlight some of the ongoing trends. For further information, consult:

• Math Typesetting for the Internet (Math Forum, Swarthmore)
• Some other pages with many links: tex4ht, acrotex, tth, rsc, Gellmu, Calculus@Internet Websurfing tips
• the newsgroups comp.text.tex, comp.text.sgml, comp.text.xml, comp.infosystems.www.authoring.html. There are mailing lists for MathML (www-math@w3.org), WebMath (http://www.camel.math.ca/cgi-bin/wcms/webmath.pl) and electronic math journals (emj@cnsibm.albany.edu).
• You might want to contemplate the methods used at some sites to distribute mathematics articles in a variety of formats, the reformatting (apparently) done on the fly! Visit the Zentralblatt, Math Reviews, ArXiv preprint server, or JFM sites.