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As the previous discussion on displaying mathematics on the web has become quite lengthy, I am opening a fresh post to continue the topic.  I’m leaving the previous thread open for those who wish to respond directly to some specific comments in that thread, but otherwise it would be preferable to start afresh on this thread to make it easier to follow the discussion.

It’s not easy to summarise the discussion so far, but the comments have identified several existing formats for displaying (and marking up) mathematics on the web (mathMLjsMath, MathJaxOpenMath), as well as a surprisingly large number of tools for converting mathematics into web friendly formats (e.g.  LaTeX2HTMLLaTeXMathML, LaTeX2WPWindows 7 Math Inputitex2MMLRitexGellmumathTeXWP-LaTeXTeX4htblahtexplastexTtHWebEQtechexplorer, etc.).  Some of the formats are not widely supported by current software, and by current browsers in particular, but it seems that the situation will improve with the next generation of these browsers.

It seems that the tools that already exist are enough to improvise a passable way of displaying mathematics in various formats online, though there are still significant issues with accessibility, browser support, and ease of use.  Even if all these issues are resolved, though, I still feel that something is still missing.    Currently, if I want to transfer some mathematical content from one location to another (e.g. from a LaTeX file to a blog, or from a wiki to a PDF, or from email to an online document, or whatever), or to input some new piece of mathematics, I have to think about exactly what format I need for the task at hand, and what conversion tool may be needed.  In contrast, if one looks at non-mathematical content such as text, links, fonts, non-Latin alphabets, colours, tables, images, or even video, the formats here have been standardised, and one can manipulate this type of content in both online and offline formats more or less seamlessly (in principle, at least – there is still room for improvement), without the need for any particularly advanced technical expertise.  It doesn’t look like we’re anywhere near that level currently with regards to mathematical content, though presumably things will improve when a single mathematics presentation standard, such as mathML, becomes universally adopted and supported in browsers, in operating systems, and in other various pieces of auxiliary software.

Anyway, it has been a very interesting and educational discussion for me, and hopefully for others also; I look forward to any further thoughts that readers have on these topics.  (Also, feel free to recapitulate some of the points from the previous thread; the discussion has been far too multifaceted for me to attempt a coherent summary by myself.)

The various languages and formats that make up modern web pages (HTML, XHTML, CSS, etc.) work wonderfully for most purposes, but there is one place where they are still somewhat clunky, namely in the presentation of mathematical equations and diagrams on web pages. While web formats do support very simple mathematical typesetting (such as the usage of basic symbols such as π, or superscripts such as x2), it is difficult to create more sophisticated (and non-ugly) mathematical displays, such as

$\displaystyle \hbox{det} \begin{pmatrix} 1 & x_1 & \ldots & x_1^{n-1} \\ 1 & x_2 & \ldots & x_2^{n-1} \\ \vdots & \vdots & \ddots & \vdots \\ 1 & x_n & \ldots & x_n^{n-1} \end{pmatrix} = \prod_{1 \leq i < j \leq n} (x_j - x_i)$

without some additional layer of software (in this case, WordPress’s LaTeX renderer). These type of ad hoc fixes work, up to a point, but several difficulties still remain. For instance:

1. There is no standardisation with regard to mathematics displays. For instance, WordPress uses $latex and$ to indicate a mathematics display, Wikipedia uses $and$, the current experimental Google Wave plugins use $$and$$, and so forth.
2. Mathematical formulae need to be compiled from a plain text language (much as with LaTeX), rather than edited directly on a visual editor. This is in contrast to other HTML elements, such as links, boldface, colors, etc.
3. One cannot easily cut and paste a portion of a web page containing maths displays into another page or file (although with WordPress’s format, things are not so bad as the raw LaTeX code will be captured as plain text). Again, this is in contrast to other HTML elements, which can be cut and pasted quite easily.
4. Currently, mathematical displays are usually rendered as static images and thus cannot be easily edited without recompiling the source code for that display. A related issue is that the images do not automatically resize when the browser scale changes; also, in some cases they do not blend well with the background colour scheme for the page.
5. It is difficult to take an extended portion of LaTeX and convert it into a web page or vice versa, although tools such as Luca Trevisan’s LaTeX to WordPress converter achieve a heroic (and very useful) level of partial success in this regard.

There are a number of extensions to the existing web languages that have been proposed to address some of these difficulties, the most well known of which is probably MathML, which is used for instance in the n-Category Café. So far, though, adoption of the MathML standard (and development of editors and other tools to take advantage of this standard) seems to not be too widespread at present.

I’d like to open a discussion, then, about what kinds of changes to the current web standards could help facilitate the easier use of mathematical displays on web pages. (I’m indirectly in contact with some people involved in these standards, so if some interesting discussions arise here, I can try to pass them on.)

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