TeX and LaTeX: Mathematics and Typesetting

15 Oct 2026

TeX is a text formatting and markup language developed by D. Knuth in the late 1970s and early 1980s, which has become the de facto standard for document preparation in mathematics and certain areas of the physical sciences because of its unsurpassed utility in typesetting mathematical formulae. LaTeX is an extension of TeX, which for purposes of discussion can be thought of as a third-party macro package for TeX to provide a logical system for document preparation, where the author does not have to give specific formatting instructions in order to achieve a particular look; the look is provided by an external document class description. [1] [2]

TeX is named after the Greek letters tau (τ), epsilon (ε), and chi (χ), reflecting the word τέχνη (téchnē), meaning "art," "craft," or "skill" in Greek. It is pronounced "tech" (as in technology), not "teks." LaTeX stands for Lamport TeX, named after its creator, Leslie Lamport. It is pronounced "LAY-tech" or "LAH-tech."

TeX Live is one of the major TeX systems (e.g., MiKTeX and TeX Live) that provides binaries for most flavors of Unix, including GNU/Linux and macOS, and also Windows. It includes the major TeX-related programs, macro packages, and fonts that are free software, including support for many languages around the world. Many Unix/GNU/Linux operating systems provide TeX Live through their own distributions and package managers. TeX Live is supported by the TeX Users Group and many other user groups around the world. [3 ]

MathJax is an open-source JavaScript display engine for LaTeX, MathML, and AsciiMath notation that works in modern browsers, with built-in support for assistive technology such as screen readers, including automatic speech generation and an expression explorer that can be used to investigate typeset mathematics at a more granular level than the complete expression. [4]

TeXLive.net is a powerful online site to edit TeX snippets, run LaTeX, and display PDF documents or error logs.

• 1. Mathematics
  • 1.1. Rules
  • 1.2. Superscripts and subscripts
  • 1.3. Fractions and binomials
  • 1.4. Greek letters
  • 1.5. Mathematical operators and symbols
  • 1.6. Summations, products, and integrals
  • 1.7. Brackets and parentheses
  • 1.8. Matrices and equations
  • 1.9. Functions and named operators
• 2. STEM in Asciidoctor
  • 2.1. Enabling STEM support
  • 2.2. Rendering mathematics with MathJax
  • 2.3. STEM macros versus MathJax delimiters
• Bibliography

1. Mathematics

LaTeX allows two writing modes for mathematical expressions: the inline math mode and display math mode: [5]

• inline math mode is used to write formulas that are part of a paragraph:

  The Pythagorean theorem is \(a^2 + b^2 = c^2\).

  The Pythagorean theorem is \(a^2 + b^2 = c^2\).

• display math mode is used to write expressions that are not part of a paragraph, and are therefore put on separate lines

  The quadratic formula is:
  
  \[
  x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
  \]

  The quadratic formula is:

  \[ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \]

1.1. Rules

• Use curly braces {} when an exponent contains more than one character.

  LaTeX	Result	LaTeX	Result
  x^{a+b}	\(x^{a+b}\)	x^a+b	\(x^a+b\)

• Use a backslash (\) followed by a command name to enter LaTeX symbols and expressions.

  LaTeX	Result	LaTeX	Result	LaTeX	Result
  \frac{a}{b}	\(\frac{a}{b}\)	\sqrt{x}	\(\sqrt{x}\)	x^2	\(x^2\)
  \alpha	\(\alpha\)	\infty	\(\infty\)	75\%	\(75\%\)
  \text{hello}	\(\text{hello}\)	\textit{hello}	\(\textit{hello}\)	\textbf{hello}	\(\textbf{hello}\)
  \underline{x}	\(\underline{x}\)	\overline{x}	\(\overline{x}\)	\vec{x}	\(\vec{x}\)
  \quad	\(a \quad b\)	\times	\(a \times b\)	\leq	\(a \leq b\)
  \text{for all } x>0	\(\text{for all } x>0\)	\neq	\(a \neq b\)	\pm	\(a \pm b\)

• Use spacing commands to control the horizontal space between mathematical symbols and expressions.

  LaTeX	Purpose	Example	Result	LaTeX	Purpose	Example	Result
  \!	Negative thin space	a\!b	\(a\!b\)	\	Normal space	a\ b	\(a\ b\)
  \,	Thin space	a\,b	\(a\,b\)	\:	Medium space	a\:b	\(a\:b\)
  \;	Thick space	a\;b	\(a\;b\)	\quad	Wide space	a\quad b	\(a\quad b\)
  \qquad	Extra-wide space	a\qquad b	\(a\qquad b\)	\hspace{1em}	Custom horizontal space	a\hspace{1em}b	\(a\hspace{1em}b\)
  \\	Line break	\a\\b	\(a\\b\)	\newline	Not generally supported as a math-mode line break

• Use environment that starts with \begin{...} and ends with \end{...} to format or arrange the content inside it.

  Environment	Purpose	LaTeX	Result
  equation	A single numbered equation	\begin{equation} E = mc^2 \end{equation}	\(E = mc^2\) (numbered)
  aligned	Multiple aligned equations	\begin{aligned} x + y &= 5 \\ x - y &= 1 \end{aligned}	\(\begin{aligned}x+y&=5\\x-y&=1\end{aligned}\)
  gather	Multiple centered equations	\begin{gather} x + y = 5 \\ x - y = 1 \end{gather}	\(\begin{gather}x+y=5\\x-y=1\end{gather}\)
  matrix	Matrix elements without surrounding brackets	\begin{matrix} a & b \\ c & d \end{matrix}	\(\begin{matrix}a&b\\c&d\end{matrix}\)
  pmatrix	Matrix elements surrounded by parentheses	\begin{pmatrix} a & b \\ c & d \end{pmatrix}	\(\begin{pmatrix}a&b\\c&d\end{pmatrix}\)
  bmatrix	Matrix elements surrounded by square brackets	\begin{bmatrix} a & b \\ c & d \end{bmatrix}	\(\begin{bmatrix}a&b\\c&d\end{bmatrix}\)
  cases	Piecewise-defined functions	f(x) = \begin{cases} x^2 & x \geq 0 \\ -x & x < 0 \end{cases}	\(f(x)=\begin{cases}x^2&x\geq0\\-x&x<0\end{cases}\)

1.2. Superscripts and subscripts

LaTeX	Result	Meaning
x^2	\(x^2\)	\(x\) squared
x^10	\(x^{10}\)	\(x\) to the tenth power
a_i	\(a_i\)	Subscript \(i\)
x_i^2	\(x_i^2\)	Subscript and superscript
x^{n+1}	\(x^{n+1}\)	A multi-character exponent
a_{i,j}	\(a_{i,j}\)	A multi-character subscript

1.3. Fractions and binomials

LaTeX	Result	LaTeX	Result	LaTeX	Result
\frac{a}{b}	\(\frac{a}{b}\)	\frac{x+1}{x-1}	\(\frac{x+1}{x-1}\)	\frac{1}{2}	\(\frac{1}{2}\)
\binom{n}{k}	\(\binom{n}{k}\)	\binom{n}{2}	\(\binom{n}{2}\)	\binom{n+1}{k-1}	\(\binom{n+1}{k-1}\)

1.4. Greek letters

LaTeX	Result	LaTeX	Result	LaTeX	Result
\alpha, A	\(\alpha, A\)	\beta, B	\(\beta, B\)	\gamma, \Gamma	\(\gamma, \Gamma\)
\delta, \Delta	\(\delta, \Delta\)	\epsilon, \varepsilon, E	\(\epsilon, \varepsilon, E\)	\zeta, Z	\(\zeta, Z\)
\eta, H	\(\eta, H\)	\theta, \vartheta, \Theta	\(\theta, \vartheta, \Theta\)	\iota, I	\(\iota, I\)
\kappa, K	\(\kappa, K\)	\lambda, \Lambda	\(\lambda, \Lambda\)	\mu, M	\(\mu, M\)
\nu, N	\(\nu, N\)	\xi, \Xi	\(\xi, \Xi\)	o, O	\(o, O\) (omicron)
\pi, \varpi, \Pi	\(\pi, \varpi, \Pi\)	\rho, \varrho, P	\(\rho, \varrho, P\)	\sigma, \varsigma, \Sigma	\(\sigma, \varsigma, \Sigma\)
\tau, T	\(\tau, T\)	\upsilon, \Upsilon	\(\upsilon, \Upsilon\)	\phi, \varphi, \Phi	\(\phi, \varphi, \Phi\)
\chi, X	\(\chi, X\)	\psi, \Psi	\(\psi, \Psi\)	\omega, \Omega	\(\omega, \Omega\)

1.5. Mathematical operators and symbols

LaTeX	Result	Meaning	LaTeX	Result	Meaning
+	\(+\)	Addition	-	\(-\)	Subtraction
\times	\(\times\)	Multiplication	\div	\(\div\)	Division
\pm	\(\pm\)	Plus or minus	\mp	\(\mp\)	Minus or plus
=	\(=\)	Equal to	\neq	\(\neq\)	Not equal to
<	\(<\)	Less than	>	\(>\)	Greater than
\leq	\(\leq\)	Less than or equal to	\geq	\(\geq\)	Greater than or equal to
\approx	\(\approx\)	Approximately equal to	\equiv	\(\equiv\)	Equivalent to; identically equal to
\propto	\(\propto\)	Proportional to	\infty	\(\infty\)	Infinity
\sqrt{x}	\(\sqrt{x}\)	Square root	\sum	\(\sum\)	Summation
\in	\(\in\)	Is an element of	\notin	\(\notin\)	Is not an element of
\subseteq	\(\subseteq\)	Is a subset of	\supseteq	\(\supseteq\)	Is a superset of
\cup	\(\cup\)	Union of sets	\cap	\(\cap\)	Intersection of sets
\emptyset	\(\emptyset\)	Empty set	\mathbb{R}	\(\mathbb{R}\)	Set of real numbers
\forall	\(\forall\)	For all	\exists	\(\exists\)	There exists
\land	\(\land\)	Logical AND	\lor	\(\lor\)	Logical OR
\neg	\(\neg\)	Logical NOT	\Rightarrow	\(\Rightarrow\)	Implies
\Leftrightarrow	\(\Leftrightarrow\)	If and only if	\partial	\(\partial\)	Partial derivative symbol

Use \mathbb{} (bb stands for blackboard bold) to typeset common number sets in blackboard bold. LaTeX Result Meaning LaTeX Result Meaning \mathbb{N} \(\mathbb{N}\) Natural numbers \mathbb{Z} \(\mathbb{Z}\) Integers \mathbb{Q} \(\mathbb{Q}\) Rational numbers \mathbb{R} \(\mathbb{R}\) Real numbers \mathbb{C} \(\mathbb{C}\) Complex numbers \mathbb{R}^n \(\mathbb{R}^n\) \(n\)-dimensional real coordinate space

1.6. Summations, products, and integrals

LaTeX	Result	Remark
\sum_{i=1}^{n} i	\(\sum_{i=1}^{n} i\)	Summation from \(i=1\) to \(i=n\).
\sum_{k=0}^{n} k^2	\(\sum_{k=0}^{n} k^2\)	Sum of the squares of the integers from \(0\) to \(n\).
\prod_{i=1}^{n} i	\(\prod_{i=1}^{n} i\)	Product of the integers from \(1\) to \(n\).
\lim_{n\to\infty} \sum_{i=1}^{n} \frac{1}{i}	\(\lim_{n\to\infty} \sum_{i=1}^{n} \frac{1}{i}\)	Limit of a sequence of partial sums.
\int x^2\,dx	\(\int x^2\,dx\)	Indefinite integral; \, adds a small space before the differential.
\int_0^1 x^2\,dx	\(\int_0^1 x^2\,dx\)	Definite integral from \(0\) to \(1\).
\iint_D f(x,y)\,dx\,dy	\(\iint_D f(x,y)\,dx\,dy\)	Double integral over a region \(D\).
\iiint_V f(x,y,z)\,dx\,dy\,dz	\(\iiint_V f(x,y,z)\,dx\,dy\,dz\)	Triple integral over a volume \(V\).
\oint_C F(z)\,dz	\(\oint_C F(z)\,dz\)	Contour integral over a closed curve \(C\).
\frac{1}{2\pi i}\oint_C \frac{f(z)}{z-a}\,dz	\(\frac{1}{2\pi i}\oint_C \frac{f(z)}{z-a}\,dz\)	Example of a contour integral from complex analysis.

1.7. Brackets and parentheses

Left delimiter	Right delimiter	LaTeX	Result
\left(	\right)	\left( x \right)	\(\left( x \right)\)
\left[	\right]	\left[ x \right]	\(\left[ x \right]\)
\left\{	\right\}	\left\{ x \right\}	\(\left\{ x \right\}\)
\left\lvert	\right\rvert	\left\lvert x \right\rvert	\(\left\lvert x \right\rvert\)
\left\lVert	\right\rVert	\left\lVert \mathbf{x} \right\rVert	\(\left\lVert \mathbf{x} \right\rVert\)
\left\langle	\right\rangle	\left\langle x \right\rangle	\(\left\langle x \right\rangle\)
\left.	\right|	\left. F(x) \right|_a^b	\(\left. F(x) \right| _a^b \)
\left|	\right.	\left| x \right.	\(\left| x \right.\)

Every \left must have a corresponding \right within the same mathematical expression. \left\{\frac{1}{n}:n\in\mathbb{N}\right\} \[ \left\{\frac{1}{n}:n\in\mathbb{N}\right\} \] To make one side invisible, use a dot (.) as the delimiter, which is useful for evaluating a function at a boundary. \[ \left. \text{expression} \right| \] \[ \left| \text{expression} \right. \] \[ \left. \text{expression} \right| \] \[ \left| \text{expression} \right. \]

1.8. Matrices and equations

LaTeX	Result	LaTeX	Result
\begin{matrix} a & b \\ c & d \end{matrix}	\[ \begin{matrix} a & b \\ c & d \end{matrix} \]	\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}	\[ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \]
\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}	\[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \]	\begin{vmatrix} a & b \\ c & d \end{vmatrix}	\[ \begin{vmatrix} a & b \\ c & d \end{vmatrix} \]
\begin{align*} x+y &= 10 \\ x-y &= 2 \end{align*}	\[ \begin{align*} x+y &= 10 \\ x-y &= 2 \end{align*} \]	\begin{split} A & = \frac{\pi r^2}{2} \\ & = \frac{1}{2} \pi r^2 \end{split}	\(\begin{split}A &= \frac{\pi r^2}{2} \\ &= \frac{1}{2} \pi r^2\end{split}\)

1.9. Functions and named operators

LaTeX	Result	LaTeX	Result	LaTeX	Result
\sin x	\(\sin x\)	\cos x	\(\cos x\)	\tan x	\(\tan x\)
\cot x	\(\cot x\)	\sec x	\(\sec x\)	\csc x	\(\csc x\)
\arcsin x	\(\arcsin x\)	\arccos x	\(\arccos x\)	\arctan x	\(\arctan x\)
\sinh x	\(\sinh x\)	\cosh x	\(\cosh x\)	\tanh x	\(\tanh x\)
\log x	\(\log x\)	\ln x	\(\ln x\)	\log_{a} x	\(\log_a x\)
\exp x	\(\exp x\)	\sqrt{x}	\(\sqrt{x}\)	\sqrt[n]{x}	\(\sqrt[n]{x}\)
\lim_{x\to 0}	\(\lim_{x\to 0}\)	\lim_{x\to\infty}	\(\lim_{x\to\infty}\)	\infty	\(\infty\)
\max(a,b)	\(\max(a,b)\)	\min(a,b)	\(\min(a,b)\)	\sup A	\(\sup A\)
\inf A	\(\inf A\)	\det A	\(\det A\)	\dim V	\(\dim V\)
\gcd(a,b)	\(\gcd(a,b)\)	\arg z	\(\arg z\)	\ker T	\(\ker T\)
\Pr(A)	\(\Pr(A)\)	\sin^2 x	\(\sin^2 x\)	\cos^2 x	\(\cos^2 x\)

2. STEM in Asciidoctor

Asciidoctor supports mathematical notation through STEM (Science, Technology, Engineering, and Mathematics) processing. It supports both AsciiMath and LaTeX-style mathematical expressions. When generating HTML, Asciidoctor can prepare STEM expressions for rendering by a JavaScript-based mathematics engine such as MathJax. [6]

2.1. Enabling STEM support

A document-level attribute can override the global setting when necessary.

To enable STEM processing, set the stem attribute in the document header or configure the stem attribute globally in the site’s _config.yml file for using the Jekyll Asciidoc plugin:

asciidoctor:
  attributes:
    stem: latexmath

The value latexmath selects LaTeX syntax as the default for STEM expressions. If no notation is specified, Asciidoctor defaults to AsciiMath.

2.2. Rendering mathematics with MathJax

Asciidoctor processes STEM macros during document conversion, but HTML output generally requires a mathematics renderer to display the expressions as formatted mathematics in the browser. MathJax is a JavaScript library that can render LaTeX mathematics in HTML.

<script>
  window.MathJax = { (1)
    options: {
      ignoreHtmlClass: 'nostem|nolatexmath' (2)
    },
    tex: {
      inlineMath: [['\\(', '\\)']], (3)
      displayMath: [['\\[', '\\]']], (4)
      tags: 'none' (5)
    },
  };
</script>
<script defer
    src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/4.1.3/tex-chtml.min.js" (6)
    integrity="sha512-kO24RkUwCpSCXtdV9p2FM/5isVLi06qQPGlE+AsOx8kN9MTc6Mk7qlZBSEh/b7bvCr2vEWlZLAdp20QLkB/qPg=="
    crossorigin="anonymous"
    referrerpolicy="no-referrer">
</script>

1	Defines the MathJax configuration before the library loads.
2	Excludes HTML elements whose class matches nostem or nolatexmath from MathJax processing.
3	Sets \(…​\) as the delimiters for inline mathematics.
4	Sets \[…​\] as the delimiters for display mathematics.
5	Disables automatic equation numbering.
6	Loads the MathJax TeX-to-Common-HTML component. The tex-chtml.min.js filename indicates TeX input processing, Common HTML output, and a minified JavaScript file.

2.3. STEM macros versus MathJax delimiters

There are two main ways to include mathematical expressions in an AsciiDoc document: using Asciidoctor’s STEM macros or writing LaTeX expressions directly between delimiters recognized by MathJax.

Method	Example	Processing
STEM macro	stem:[y = mx + c]	Asciidoctor recognizes the macro and processes the expression according to the configured STEM notation.
Explicit LaTeX macro	latexmath:[\frac{a}{b}]	Asciidoctor recognizes the macro and interprets its content as LaTeX notation.
Raw MathJax delimiters	\( \frac{a}{b} \)	MathJax processes the delimiters in the generated HTML, provided they are preserved and recognized by its configuration.

The distinction matters because Asciidoctor processes STEM macros during document conversion, whereas MathJax normally renders mathematical expressions in the browser after the HTML has been generated. The two approaches can coexist, but their processing pipelines should be configured consistently.

For a Jekyll site using Asciidoctor, prefer stem:[...] for inline mathematics and [stem] blocks for display mathematics to make the source more explicit and avoid relying on MathJax to recognize raw delimiters throughout the generated HTML.

• Use the stem inline macro to include a mathematical expression within a paragraph:

  The equation of a straight line is stem:[y = mx + c].

  The equation of a straight line is \(y = mx + c\).

  To specify LaTeX notation explicitly, use the latexmath macro:

  The quadratic equation is latexmath:[ax^2 + bx + c = 0].

  The square brackets delimit the macro’s content. Unlike raw MathJax delimiters, the Asciidoctor STEM macro does not require wrapping the expression in \(...\) or $...$.

• For a standalone equation, use a delimited STEM block:

  [stem]
  ++++
  x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
  ++++

  Because the document header specifies :stem: latexmath, the expression is interpreted as LaTeX and rendered as a display equation:

  \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

  Alternatively, explicitly specify the notation (e.g., LaTeX) on the block:

  [latexmath]
  ++++
  \int_0^1 x^2\,dx = \frac{1}{3}
  ++++

Bibliography

• [1] https://latex-project.org/

• [2] https://info.arxiv.org/help/tex.html

• [3 ] https://tug.org/texlive/

• [4] https://www.mathjax.org/

• [5] https://www.overleaf.com/learn/latex/Mathematics

• [6] https://docs.asciidoctor.org/asciidoc/latest/stem/

• [7] https://docs.asciidoctor.org/asciidoctor/latest/stem/mathjax/