Best way to set up a wiki for maintaining a structured math journal

Does anyone know of a tool which

1. Can display formulas neatly, preferably like this website without hassle. (Unlike wikipedia with :<math>)
2. Has a wiki like structure: i.e categories of pages, individual articles with hyperlinked sections, subsections etc.
3. Preferrably can be used online and does not require installation of some software.
4. Comes with a free host, i.e for people with little money and no university server.

So basically I need a notebook on steroids :)

Update: Edited this question to remove the essay I wrote on blogs. You may refer to the revision history if you're interested. I am keeping it open in case anyone knows of further alternatives than have already been mentioned. At present I have settled on and am fairly content with Drupal.

This site uses MathJax, which has pretty much become the web standard Latex tool, because it's so easy to use.

You can get a free account at the Tumblr blogging site, and link MathJax in to it.

AFAIK, you can't incorporate MathJax into freely-hosted Wordpress.com sites. You can incorporate it into Wordpress if it's self-hosted. There may be other free Wordpress hosting sites where you could do it.

And apparently you can incorporate Mathjax into Blogger.

You can also link Mathjax to your own installation of various content management systems: Movable Type, Joomla, Drupal, MediaWiki, TiddlyWiki, and Moodle.

And just in case this question does get closed, similar questions could be asked and answered over on the WebApps StackExchange.

Edit: so, if it's a wiki you want, search for "free mediawiki hosting" or "free tiddlywiki hosting", and then look for one which will allow MathJax too.

After spending a lot of time searching I have finally set it up. The answer is Drupal 7. It redresses all complaints except one (it requires an offline installation). I am currently maintaining it locally (with remote desktop) but I will probably get one of the free hosts when I choose to upload it.

1. The equations look georgeous (easy install for Mathjax module). For example:

2 It is possible to have a blog + a wiki

3.The Learning curve is not so steep.

I had actually installed mediawiki and converted many of my latex files to wikitext, but this was so good I abandoned the mediawiki project. I post this here if someone else finds it useful.

It looks like the polymath wiki you mention is just a plain old no-frills MediaWiki installation. Getting MediaWiki installed on a webhost isn't actually very hard, although admittedly getting the LaTeX support working and customizing the wiki to your needs may take some effort. (If you don't like the standard texvc based LaTeX renderer, you could also install the MathJax extension for MediaWiki.)

If you want a free wiki host, try Googling for one, or start here. However, keep in mind that there ain't no such thing as a free lunch. At best, you'll probably have to live with third-party ads on your wiki; at worst, you may find that the fine print says that your wiki doesn't really belong to you, and that the host can just take it over and do what they want with it if you try to do something they don't like (like, say, closing it or moving it to another host).

Most MediaWiki hosts will probably support the standard texvc based <math> syntax, but I doubt they'll have the MathJax extension installed out of the box. However, even if you can't install the extension, you might still be able to add rudimentary MathJax support to your wiki via custom site JS.