I had a look at KaTeX and I'm convinced that it is *plenty* powerful for our needs. The improved rendering speed is nice too.

I tried out some math expressions from my own SE posts. It looks like ~~some of the features are not correctly working,~~ and some are visually not pleasing to read.

* ~~`\begin{gathered} ... \end{gathered}` isn't working~~ (using `aligned` instead makes all lines aligned to the right.)

$$
\begin{gathered}
  \text{byte count before zilde} + \text{byte count of single zilde} \times \text{length of zilde chain} \\
  = 52 + 3 \times (72x^{12} + 101x^{11} + 108x^{10} + 108x^9 + 111x^8 + \\ 44x^7 + 32x^6 + 87x^5 + 111x^4 + 114x^3 + 108x^2 + 100x + 33)
\end{gathered}
$$

$$
\begin{aligned}
  \text{byte count before zilde} + \text{byte count of single zilde} \times \text{length of zilde chain} \\
  = 52 + 3 \times (72x^{12} + 101x^{11} + 108x^{10} + 108x^9 + 111x^8 + \\ 44x^7 + 32x^6 + 87x^5 + 111x^4 + 114x^3 + 108x^2 + 100x + 33)
\end{aligned}
$$

* Using lots of fractions/binomials inside a container (cases or matrix) makes them look cramped. **Edit:** Changed `\tfrac` and `\tbinom` to plain `\frac` and `\binom`. Looks like they're now correctly rendered small inside containers, but the cramped issue is still there.
  
  $$
  \begin{aligned}
  X & = \text{uniform random value in } (0,1) \\
  Y & = \begin{cases} X + \frac12, \quad X < \frac12 \\
  X - \frac12, \quad X \geq \frac12 \end{cases} \\
  Z & = \frac32 - (X + Y)
  \end{aligned}
  $$

  $$
  \begin{bmatrix}
  \binom{1}{1} & \binom{1}{2} & \cdots & \binom{1}{n+m} \\
  \binom{2}{1} & \binom{2}{2} & \cdots & \binom{2}{n+m} \\
  \vdots       & \vdots       & \ddots & \vdots         \\
  \binom{n+m}{1} & \binom{n+m}{2} & \cdots & \binom{n+m}{n+m}
  \end{bmatrix}
  \begin{bmatrix}
  a_1 \\ a_2 \\ \vdots \\ a_{n+m}
  \end{bmatrix}
  =
  \begin{bmatrix}
  \binom{1}{n} \binom{1}{m} \\
  \binom{2}{n} \binom{2}{m} \\
  \vdots \\
  \binom{n+m}{n} \binom{n+m}{m}
  \end{bmatrix}
  \Leftrightarrow Ba = v
  $$
  
  **Edit:** The KaTeX [Commen Issues](https://katex.org/docs/issues.html) page says:
  
  > When displaying fractions one above another in these vertical layouts there may not be enough space between rows for people who are used to MathJax's rendering.

  Their recommended solution is:

  > The distance between rows can be adjusted by using `\\[0.1em]` instead of the standard line separator distance.
  
  The math below uses `\\[0.2em]` instead to emphasise the difference:
  
  $$
  \begin{bmatrix}
  \binom{1}{1} & \binom{1}{2} & \cdots & \binom{1}{n+m} \\[0.2em]
  \binom{2}{1} & \binom{2}{2} & \cdots & \binom{2}{n+m} \\[0.2em]
  \vdots       & \vdots       & \ddots & \vdots         \\[0.2em]
  \binom{n+m}{1} & \binom{n+m}{2} & \cdots & \binom{n+m}{n+m}
  \end{bmatrix}
  \begin{bmatrix}
  a_1 \\ a_2 \\ \vdots \\ a_{n+m}
  \end{bmatrix}
  =
  \begin{bmatrix}
  \binom{1}{n} \binom{1}{m} \\[0.2em]
  \binom{2}{n} \binom{2}{m} \\[0.2em]
  \vdots \\
  \binom{n+m}{n} \binom{n+m}{m}
  \end{bmatrix}
  \Leftrightarrow Ba = v
  $$



* ~~`\implies` symbol isn't working.~~

$$
M = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \implies
S^{-1}M = \begin{pmatrix} c & d \\ -a & -b \end{pmatrix},
T^{-1}M = \begin{pmatrix} a-c & b-d \\ c & d \end{pmatrix}
$$

$$
M = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \Rightarrow
S^{-1}M = \begin{pmatrix} c & d \\ -a & -b \end{pmatrix},
T^{-1}M = \begin{pmatrix} a-c & b-d \\ c & d \end{pmatrix}
$$