Why is LaTeX giving all of my theorems the same number?

Question

Whenever I try to number my theorems according to the section they are in, they all end up having the same number. I tried the other numbering schemes to see what they do, and the only one that gives different numbers is when I point back to the theorem before it.

Here is my code for all three numbering schemes:

\documentclass{article}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}

\begin{document}

\section{numbered by section}
\theoremstyle{plain}\newtheorem{fst}{Theorem}[section]
\begin{fst}\end{fst}
\theoremstyle{plain}\newtheorem{snd}{Theorem}[section]
\begin{snd}\end{snd}

\section{counted}
\theoremstyle{plain}\newtheorem{athm}{Theorem}
\begin{athm}\end{athm}
\theoremstyle{plain}\newtheorem{bthm}{Theorem}
\begin{bthm}\end{bthm}

\section{numbered by name of first theorem}
\theoremstyle{plain}\newtheorem{thma}{Theorem}[section]
\begin{thma}\end{thma}
\theoremstyle{plain}\newtheorem{thmb}[thma]{Theorem}
\begin{thmb}\end{thmb}

\end{document}

This is what that gives me:

As you can see, in the first two sections, the theorems did not count properly. What should I be doing differently? While the last version works, I would really like to be able to use the other two. Everything I look up says this is how to do it, so I'm not sure what else to try.

Answer 1

So, you found the solution already. If you want different theorem environments to share a counter, use the third numbering scheme. However, why do you define a new theoremstyle for each of your theorems? It suffices to define one for each kind of "theorem-like" environment and use it throughout. For example,

\theoremstyle{plain}
\newtheorem{definition}{Definition}[section]
\newtheorem{theorem}{Theorem}[section]

\begin{definition}
A definition.
\end{definition}

\begin{theorem}
The first theorem.
\end{theorem}

\begin{theorem}
The second theorem.
\end{theorem}

If you want to use the same counter for definitions and theorems, use \newtheorem{theorem}[definition]{Theorem} instead.