I am trying to get the Theorem. to line up with the bullet. I tried using \vspace{-\topsep}, but this moves the bullet up along with the Theorem.
\documentclass{article}
\usepackage{amsthm}
\newtheorem{theorem}{Theorem}
\begin{document}
\begin{itemize}
\item \begin{theorem}
$a^2 + b^2 = c^2$
\end{theorem}
\end{itemize}
\end{document}
As a theorem has a list structure, you just have to compensate for the corresponding vertical spacing:
\documentclass{article}
\usepackage{amsthm}
\newtheorem{theorem}{Theorem}
\begin{document}
\begin{itemize}
\item \leavevmode\vspace{-\dimexpr \baselineskip + \topsep}\begin{theorem}
$a^2 + b^2 = c^2$. Some text some text some text. Some text some text some text. Some text some text some text. Some text some text some text.
\end{theorem}
\end{itemize}
\end{document}
My suggestion:
\documentclass{article}
\usepackage{amsthm}
\newtheorem{theorem}{Theorem}
\newenvironment{ittheorem}[1]{\begin{minipage}[#1]{0.1\textwidth}\begin{itemize}\item \end{itemize}\end{minipage}\begin{minipage}{0.88\textwidth}\begin{theorem}}{\end{theorem}\end{minipage}}
\begin{document}
\begin{itemize}
\item
\begin{theorem}
$a^2 + b^2 = c^2$
\end{theorem}
\end{itemize}
\begin{ittheorem}[c]
$a^2+b^2=c^2$
you can include soome text and whatever accepted in a real theotem environment
\end{ittheorem}
\end{document}
Output:
\item\begin{minipage}[t]{\linewidth}{\begin{theorem...possibly with \ vspace correction inside the box to get whatever you need. – David Carlisle Jan 23 '18 at 23:56\newtheorem{theorem}{$\bullet$ Theorem}instead of usingitemize? – Cragfelt Jan 23 '18 at 23:58