A mini rant about LaTeX
Thu Apr 29, 2010
Here is a comment I've just posted to a comment thread about LaTeX over here: http://blogs.nature.com/farhat/2010/04/16/collaborative-editing-with-latex. One of the commenters asked "Why not just use a word processor"
Just using a word processor simply does not cut it when it comes to expressing complex mathematical ideas. LaTeX, and it's precursor TeX, have evolved to be the only tools that can currently express the richness of the ideas within advanced mathematics. Whether this is a good thing or not is moot, it's simply the case, so that's one reason to use LaTeX.
A huge advantage of using a text only tool is keeping different versions of a document, and diffing between versions, is much easier than the horror that is "Track Changes" on most editors. Many groups I know keep their papers as LaTaX files in a code repository and use a system such as SVN for collaboration. This is not a benefit of LaTeX specifically, and is way beyond what most people would do with it, however the need for this kind of ability with the objects upon which we collaborate is painfully clear, and is only starting to be address in the "rich document" space with services such as Google Wave and Google Docs.
Ideally one would like to be able to write one's equations directly into the computer. For the time being LaTeX provides an expressive syntax from the keyboard that translates into mathematics on the screen. The iPad may well change this, but I suspect that any solution that takes handwriting and converts it to marked up mathematics will be built on top of the excellent codebase that is the LaTeX framework. This would be an excellent example of the DRY formalism (don't repeat yourself), build it on top of that which already works. For an example of a web app that does this already have a look at:
Richard is right that not separating the semantics from the presentation is a weakness. Sadly one issue is that a single equation or symbol can actually mean different things. The closest tool there is to encapsulate the semantics of mathematics is the semantic version of MathML. No one writes this by hand. The best tools for producing semantic MathML (as opposed to the presentation version of MathML), do so by translating from human input in the form of, yes you guessed it, LaTeX.
In spite of being semantically dumb there are a couple of interesting web services that build on top of the fact that there is a huge community of people out there who speak LaTeX. http://www.mathtran.org/formulas/ allows people to share formulas. http://www.latexsearch.com/ allows you to search through Springer's archive of mathematics. Springer has the most extensive archive of mathematical literature in the world, so that is no mean feat.
The last thing I will say is that LaTeX is just awesome. It produces beautiful documents. It is akin to learning a programming language, but then, if you are doing serious mathematics, it's just another symbol set, it's not that hard, really. I guess if you are doing something soft and not so well defined, then a word processor is going to be good enough for you.