It seems that preview has problems with backslash in several instances.
For example, if I try this text:
$\{x\}=\{y\}$
$r(ξ, \bar{ξ}) = \frac{1}{\#𝒢} \sum_{g ∈ 𝒢} r_0 (g(ξ), g(\bar{ξ}))$
$\begin{pmatrix}
x_1 \\ x_3 \\ x_3 \\ x_4
\end{pmatrix}$
It either renders incorrectly or not at all in the preview after entering the question:
However, after the question is posted, everything looks fine - the screenshot is below and people with 10k+ reputation points on Mathematics can see the question here:
Once the question was posted, after clicking on edit, the preview behaves correctly:
The examples used above are based on various bug reports, such as:
Missing brackets in ${x}$ in drafts, not missing in the final question/product and
Including a hash character (#) in a math equation causes it to not render (in new-question page). Problem with \\
- which is used as a newline in various matrix-like environments - was mentioned here: MathJax preview renders slowly and improperly. At some point in the distant past it was recommended to use \\\\
instead - but as you can see, \\
clearly works now in the final post; the problem is only in the preview before posting. See here: Using the align environment?