Personal wiki-hosting with LaTeX-like equations

Question

I really like how Wikipedia works. But you cannot write original research nor beletry on Wikipedia :-( … nor use it as you personal blog ;-) So I would like to find some wiki-hosting as similar to Wikipedia as possible.

I know there is quite a lot of wiki hostings, I tried a few (namely Wikispaces, Wikia, and Wikidot) but I was not satisfied. None of them provide all features which I want:

• LaTeX-like syntax for writing math equations.
• Preferably standard MediaWiki syntax and interface. I'm used to it from Wikipedia but it is not absolutely necessary.
• Page editing can be restricted just to some users (e.g. me and my friends).
• Not too much limited space for images (at least like 100 MB?).
• Free of charge.

What I want to use it for?

I'm a physicist and sci-fi fan. I often dream about some scientific concepts which are too frivolous and flippant to produce a scientific publication, but it is also not really a story to write a sci-fi novel. I find the wiki format ideal for noting down such ideas, to collaborate on it with friends, and to present it to others. Because I'm a physicist, even though the ideas are frivolous, I would still prefer to use maths (LaTeX equations) for the description of some aspects.

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EDIT - currentrly I'm using wikidot, it is not MediaWiki, but syntax is easy, it has LaTeX math equation and otherwise quite pleasing.

Answer 1

I've recently (today) started using Tiddlywiki, and I'm considering moving some of my shorter notes there from Git because of its interesting format. I think it fits your requirements, particularly because you could either host it on your Dropbox or Drive accounts, or on their service, and edit it using any browser. It's disadvantage, in my opinion, is that it doesn't have version control. So the user has to perform regular backups.(*)

Features:

• LaTeX-like syntax for math equations through the KaTeX plug-in
• Uses WikiTex markup. It also has a plug-in for Markdown support
• Page editing is restricted to yourself, but you could add collaborators by creating a shared Dropbox folder, for example. There is also the option of hosting the wiki on TiddlySpot, which stores it using an unencrypted password that you could then share with your friends.
• The space for image storage would be limited to the space in your Dropbox or Drive accounts. Or you could use an image hosting service, like imgur, Photobucket, or flickr and link the images from there.
• It's free of charge

Although it's different than the traditional wiki style, I believe the "tiddlers" format it utilizes is good for short notes and to keep track of brain droppings.

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(*) Edit:

The desktop app TiddlyDesktop does automatic backups. Quote:

Backups

Backups are automatically made every time saving changes results in a file being overwritten. The previous content of the file is copied to a backup file with a filename such as \MyData\index.html_backup\index.20150107172517000.html.

The path of the backup file can be an absolute path or a relative path to the directory containing the TiddlyWiki file. The backup path can contain the following special tokens:

$filename$ to stand for the filename portion of the URL of the TiddlyWiki file

$filepath$ to stand for the entire filepath of the URL of the TiddlyWiki file