Math on the Web

Andrej Bauer has setup a Mathematics and Computation Blog. As a first step he has tried to address the persistent and annoying problem of math on the web. As a basic tool for precisely stating and transfering understanding of technical subjects, mathematics is very necessary. Despite this necessity, every mechanism for expressing mathematics on the web seems unnaturally clumsy. Here are some of the methods and their drawbacks:

1. MathML This was supposed to be the answer, but it has two severe drawbacks: “Internet Explorer” doesn’t read it and the language is an example of push-XML-to-the-limit which no one would ever consider writing in. (In contrast, html is easy to write in.) It’s also very annoying that math fonts must be installed independent of the browser, even for mozilla based browsers.
2. Create inline images. This has several big drawbacks: font size is fixed for all viewers, you can’t cut & paste inside the images, and you can’t hyperlink from (say) symbol to definition. Math World is a good example using this approach.
3. Html Extensions. For example, y_i = x². The drawback here is that the available language is very limited (no square roots, integrals, sums, etc…). This is what I have been using for posts.
4. Raw latex. Researchers are used to writing math in latex and compile into postscript or pdf. It is possible to simply communicate in that language. Unfortunately, the language can make simple things like fractions appear (syntactically) much more complicated. More importantly, latex is not nearly as universally known as the mathematics layed out in math books.
5. Translation. An obvious trick is to translate this human-editable syntax into something. There are two difficulties here:
   1. What do you translate to? None of the presentations mechanisms above are fully satisfying.
   2. Lost in translation. For example in latex, it’s hard to make a hyperlink from a variable in one formula to an anchor in the variable definition of another formula and have that translated correctly into (say) MathML.

Approach (4) is what Andrej’s blog is using, with a javascript translator that changes output depending on the destination browser. Ideally, the ‘smart translator’ would use whichever of {MathML, image, html extensions, human-edit format} was best and supported by the destination browser, but that is not yet the case. Nevertheless, it is a good start.