﻿---
title: Math
description: The math directive renders mathematical expressions using LaTeX syntax. Mathematical expressions are rendered client-side using KaTeX for fast, accurate...
url: https://docs-v3-preview.elastic.dev/elastic/docs-builder/pull/2842/syntax/math
---

# Math
The `math` directive renders mathematical expressions using LaTeX syntax. Mathematical expressions are rendered client-side using KaTeX for fast, accurate display.

## Basic usage

<tab-set>
  <tab-item title="Preview">
    `S(doc) = exp(\lambda \cdot max(0, |fieldvalue_{doc} - origin| - offset))`
  </tab-item>

  <tab-item title="Markdown">
    ```markdown
    :::{math}
    S(doc) = exp(\lambda \cdot max(0, |fieldvalue_{doc} - origin| - offset))
    :::
    ```
  </tab-item>
</tab-set>


## Display math

For block-level mathematical expressions, use display math syntax:
<tab-set>
  <tab-item title="Preview">
    ```math
    \[
    \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}
    \]
    ```
  </tab-item>

  <tab-item title="Markdown">
    ```markdown
    :::{math}
    \[
    \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}
    \]
    :::
    ```
  </tab-item>
</tab-set>

The directive automatically detects display math based on:
- LaTeX display delimiters: `\[` and `\]`
- TeX display delimiters: `$$` and `$$`
- LaTeX environments: `\begin{...}` and `\end{...}`
- Multi-line expressions
- Complex expressions containing `\frac`, `\sum`, `\int`, `\lim`, etc.


## Adding labels

Label mathematical expressions for cross-referencing:
<tab-set>
  <tab-item title="Preview">
    `E = mc^2`
  </tab-item>

  <tab-item title="Markdown">
    ```markdown
    :::{math}
    :label: einstein-equation
    E = mc^2
    :::
    ```
  </tab-item>
</tab-set>

This creates an element with `id="einstein-equation"` that can be referenced elsewhere in the document.

## Complex expressions

The math directive supports complex LaTeX expressions:
<tab-set>
  <tab-item title="Preview">
    ```math
    \begin{align}
    \frac{\partial f}{\partial x} &= \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \\
    \nabla \cdot \vec{E} &= \frac{\rho}{\epsilon_0}
    \end{align}
    ```
  </tab-item>

  <tab-item title="Markdown">
    ```markdown
    :::{math}
    \begin{align}
    \frac{\partial f}{\partial x} &= \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \\
    \nabla \cdot \vec{E} &= \frac{\rho}{\epsilon_0}
    \end{align}
    :::
    ```
  </tab-item>
</tab-set>


## Supported LaTeX features

The math directive supports most common LaTeX mathematical notation:
- **Fractions**: `\frac{numerator}{denominator}`
- **Superscripts and subscripts**: `x^2`, `x_i`
- **Integrals**: `\int`, `\iint`, `\iiint`
- **Sums and products**: `\sum`, `\prod`
- **Limits**: `\lim`, `\limsup`, `\liminf`
- **Greek letters**: `\alpha`, `\beta`, `\gamma`, etc.
- **Matrices**: `\begin{matrix}`, `\begin{pmatrix}`, etc.
- **Aligned equations**: `\begin{align}`, `\begin{eqnarray}`
- **Roots**: `\sqrt{x}`, `\sqrt[n]{x}`
- **Operators**: `\sin`, `\cos`, `\log`, `\exp`, etc.