\documentclass{amsart}
\usepackage{hfont}
\makeatletter
\def\markboth#1#2{%
 \begingroup
   \@temptokena{{#1}{#2}}\xdef\@themark{\the\@temptokena}%
   \mark{\the\@temptokena}%
 \endgroup
 \if@nobreak\ifvmode\nobreak\fi\fi}
\def\thanks#1{\g@addto@macro\thankses{\thanks{#1}}%
}
\makeatother
\begin{document}
\title{Title}
\author{Author1}
\thanks{Thanks1}
\author{Author2}
\thanks{Thanks2}
\maketitle

\section{Section1}
This is a test.

\newpage
\section{Section2}
This is a test.

\newpage
\section{Section3}
This is a test.
\end{document}