\documentclass[11pt]{article}
\usepackage[margin=0.8in]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{lmodern}
\pagestyle{empty}

\title{A little mathematics,\ a terminal}
\author{ghostty-tex}
\date{}

\begin{document}
\maketitle

\section*{Source on the right. PDF on the left.}
Write LaTeX in Emacs, press \texttt{C-c C-c},
and keep the compiled page beside your source.
The image travels through the Kitty graphics
protocol, inside the same terminal window.

\section*{The Gaussian integral}
One familiar result is worth typesetting well:
\[
  \int_{-\infty}^{\infty} e^{-x^2}\,dx
  = \sqrt{\pi}.
\]
Squaring it lets us work in polar coordinates:
\begin{align*}
  I^2 &= \int_{\mathbb R^2}
          e^{-(x^2+y^2)}\,dx\,dy \\
      &= \int_0^{2\pi}\int_0^\infty
          e^{-r^2}r\,dr\,d\theta = \pi.
\end{align*}

\section*{Keep writing}
Recompile to refresh the preview. Turn PDF
pages from the source buffer with
\texttt{M-n} and \texttt{M-p}.
\end{document}