In the documentation of amsart. AMS Author Handbook: Journal Classes, it is said that
\specialsectiondiffers from\sectionmainly in the formatting of the heading.
It is listed between \part and \section.
Grätzer said in his More Math into LaTeX (4ed and 5ed) that:
There is also the seldom used top level
\specialsectioncommand. Articles do not have parts and chapters, but sometimes a long article may require further division using the\specialsectioncommand.
However, \part is defined in the amsart.cls, as other document classes (such as article.cls) do. And I notice that \specialsection shares the same counter with \section, and the typesetting formats of the two commands are rather similar (a little difference in fonts and spacing).
\def\specialsection{\@startsection{section}{1}%
\z@{\linespacing\@plus\linespacing}{.5\linespacing}%
{\normalfont\centering}}
\def\section{\@startsection{section}{1}%
\z@{.7\linespacing\@plus\linespacing}{.5\linespacing}%
{\normalfont\scshape\centering}}
So I wonder how it is used.
BTW, the commented source code of AMS classes (amsclass.pdf) says that
Specialsection correlates to our inhouse Z-head.
And I think it is also difficult to understand.
\specialsection, possibly not to have a number, but, indeed, the documentation is not very clear. – egreg Sep 26 '16 at 10:19\part. i shall investigate, but may not be able to find anything definitive, the perpetrators being either deceased or long gone from ams. – barbara beeton Sep 26 '16 at 14:04