I want to write a short note using amsart and I wish that the numbering of formulas should be (1), (2) and so on (not (0.1)...) and also that Theorems should get the numbers 1,2, (not (0.1)...).
What should I do to avoid the proliferation of 0. ?
Use this in your preamble:
\usepackage{chngcntr}
\counterwithout{equation}{section}
You should do nothing special:
\documentclass{amsart}
\newtheorem{thm}{Theorem}
\begin{document}
\begin{thm}
This states an important fact.
\end{thm}
And we follow with a very important equation
\begin{equation}
1=1
\end{equation}
\end{document}
You probably have something like
\newtheorem{thm}{Theorem}[section]
and
\numberwithin{equation}{section}
otherwise, as you see, the section number is not added.