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MWE

\documentclass{article}
\usepackage[utf8]{inputenc}

\usepackage{amsmath}

\usepackage[thmmarks]{ntheorem}
% proof
\theoremstyle{plain}
\theoremheaderfont{\normalfont\bfseries} 
\theoremprework{\medbreak}
\theorempostwork{\medbreak}
\theoremindent0mm
\theoremsymbol{\ensuremath{\Box}}
\theoremseparator{}
\theorembodyfont{\normalfont}
\newtheorem*{beweis}{Beweis.}

\begin{document}

\section{Introduction}

\begin{beweis}
    This is really just a formula
    \begin{equation*}
        a^2 + b^2 = c^2
    \end{equation*}
\end{beweis}
\end{document}

Because the proof ends with a formula, I don't get the endmarks, any suggestions?

1

Two items:

  1. ntheorem does not hook into amsmath envs unless you tell it to, add the amsmath option to ntheorem

  2. You \Box command is not defined by default, remember to add the amssymb package.

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