\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}