On some other SE sites, code in between dollar signs gets rendered as mathematics (using MathJaX, I believe). This doesn't seem to work here? Why not? And how do I get round it?
On this site, we want to see the actual code far more often than we want to see the rendered output, so MathJaX is not enabled for this site. If you want to show the result of some input, you need to create an image of the output and upload it. One of the simplest methods of getting an image from your code is to use the standalone package (see Compile a LaTeX document into a PNG image that's as short as possible for more details). To upload it, click on the "add image" button at the top of the text box (the box symbol next to the one with the 1s and 0s) and, if you have at least 10 reputation points, you will be able to upload the image and have it embedded in your question/answer.
Math renderers such as 〈whatever〉TeX produce different results depending on tons of options. Moreover, the renderers have issues from times to times. We sometimes do wish to speak about these options and issues and even about versions of 〈whatever〉TeX and math-processing packages, but enabling MathJax would have made us less capable of doing so.
I do believe, however, that sometimes MathJax would help to make certain questions more easy to write and answer whereas all the other questions and answers would be more difficult to formulate.