Formulas on this site are typeset by MathJax. You write them in TeX, and the browser turns them into crisp vector graphics that scale with the text and follow the light/dark theme. The library is served by this application itself, so no third-party host is involved, and it is only loaded on posts that contain formulas.
Inline math Link to heading
Wrap a formula in single dollar signs to put it in a sentence: the area of a circle is \(A = \pi r^2\), and Euler's identity \(e^{i\pi} + 1 = 0\) ties five constants together. The alternative delimiters \(\alpha + \beta = \gamma\) work as well.
The area of a circle is $A = \pi r^2$ and \(\alpha + \beta = \gamma\).
Display math Link to heading
Double dollar signs (or \[ ... \]) give a centered formula on its own line. The quadratic formula:
\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]
The Gaussian integral, which is a good test for integrals and limits:
\[\int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}\]
A sum, which also shows how limits move above and below the operator in display mode:
\[\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}\]
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
$$\int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}$$
$$\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$$
Aligned equations Link to heading
Use the aligned environment to line up several steps at the = sign:
\[\begin{aligned} (a + b)^2 &= (a + b)(a + b) \\ &= a^2 + ab + ba + b^2 \\ &= a^2 + 2ab + b^2 \end{aligned}\]
Environments such as equation and align are numbered automatically, and \label with \eqref lets you refer
back to them, like \eqref{eq:maxwell} below:
\begin{align} \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \label{eq:maxwell} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{align}
Matrices and cases Link to heading
\[A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}, \qquad \det A = ad - bc\]
\[|x| = \begin{cases} x & \text{if } x \ge 0, \\ -x & \text{if } x < 0. \end{cases}\]
Fourier transform and Bayes' theorem, for good measure:
\[\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\, e^{-2\pi i x \xi}\, dx\]
\[P(A \mid B) = \frac{P(B \mid A)\, P(A)}{P(B)}\]
Writing math in your own posts Link to heading
Every post is a Markdown file, and any post that contains a formula loads MathJax automatically: there is nothing to
switch on. You do not need to escape <, &, _ or * inside formulas, and a plain dollar sign such as in
"costs $5 and $10" stays text. To show a literal dollar sign right next to a formula, write \$. Code is skipped,
which is why the TeX source above is displayed as written. See
Writing posts in Markdown, with LaTeX for the full rules, and the
list of supported TeX commands for everything else.