\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts,amsthm} % some nice default packages

\begin{document}
\title{Example 1}
\author{Archer Me Dees}
\date{\today}   % the command \today inserts today's date
\maketitle      % if you omit this line, the title won't appear!

\section{First Section}
Let's talk about the quantity $c^2$. I'm pretty sure that
\begin{equation}
 c^2 \geq b^2 .   % equation and align environments automatically enter math mode
\end{equation}
In fact, my countryman showed that
\begin{align}
 c^2 &= a^2 + b^2  \\
     &= 3^2 + 4^2  \\
     &= 25
\end{align}
when $a = 3$ and $b = 4$.

\section{Second Section}
In this paragraph, we notice how $n^{a + b}$ differs from $n^a + b$.
And how $X_1$ is the same as $X_{1}$, but $X_{1 + 2}$ differs from $X_1 + 2$.
Also that, in tex files, line breaks between sentences or
even words
   or even weird whitespace don't matter.

A \emph{double} line break gives a \textbf{paragraph} break.

\end{document}
