Choice of font size in part name and numbering

Question

I would like to use bigger fonts (14pt) for the name and the numbering of the parts, except in the TOC. I know that I must use the package titlesec but I do not understand how. There is a similar question for a different class here : Control font size \part. The package sectsty does not work with amsart.

\documentclass[12pt]{amsart}
\newtheorem{thm}{Theorem}[section]
\renewcommand{\thethm}{\Roman{part}.\arabic{section}.\arabic{thm}}
\renewcommand{\thepart}{\Roman{part}}
\begin{document}
\setcounter{tocdepth}{1}
\tableofcontents
\part{blabla}
\section{blablabla}
\begin{thm}
    The integer $1+1$ is finite.
\end{thm}
\begin{thm}
    The integer $1+1$ is less than $1000$.
\end{thm}
\end{document}

Answer 1

With amsart you cannot use titlesec.

Just find the definition of \part and add

1. \large
2. \let\@secnumfont\relax

(the latter in order to use boldface for the part number in the title).

\documentclass[12pt]{amsart}
\makeatletter
\def\part{%
  @startsection{part}
  {0}
  {\z@}
  {\linespacing@plus\linespacing}
  {.5\linespacing}
  {\let@secnumfont\relax\normalfont\large\bfseries\raggedright}%
}
\show@seccntformat
\makeatother
\newtheorem{thm}{Theorem}[section]
\renewcommand{\thethm}{\Roman{part}.\arabic{section}.\arabic{thm}}
\renewcommand{\thepart}{\Roman{part}}
\begin{document}
\setcounter{tocdepth}{1}
\tableofcontents
\part{blabla}
\section{blablabla}
\begin{thm}
    The integer $1+1$ is finite.
\end{thm}
\begin{thm}
    The integer $1+1$ is less than $1000$.
\end{thm}
\end{document}