I know that this question was asked almost 80 times and that the best solution is probably to use \texorpdfstring{...}{...} but I don't want to a mess inside the document so I was thinking of this solution.
\pdfstringdefDisableCommands{%
\def\${}%
\def\alpha{alpha}%
}
But this doesn't change the fact that
\section{$\alpha$}
gives the warning
Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' [...]
So the question is: Can I use \pdfstringdefDisableCommands{...} to avoid using \texorpdfstring{...}{...} when handling math in sections?


\alphais supported by optionpsdextraand the bookmark needs to be in Unicode:\usepackage[pdfencoding=auto, psdextra]{hyperref}. Without optionpsdextrathe macro\textalphacan be used (optionunicodeorpdfencoding=autois still needed). – Heiko Oberdiek May 09 '18 at 20:20