Quotations in math mode using \enquote command from csquotes package

LaTeX issues one error and two warnings:

! Double superscript.
<recently read> ^

l.13 Quote by hand: $``a^2+b^2=c^2'
                                   '$
? 

LaTeX Warning: Command \textquotedblleft invalid in math mode on input line 15.

LaTeX Warning: Command \textquotedblright invalid in math mode on input line 15

Such errors and warnings should not be disregarded; it's a perhaps sad truth that \textquotedblleft in math mode produces a backslash, whereas \textquotedblright actually produces a closing double quote.

The error is because ' in math mode is interpreted as ^{\prime}, so c^2' indeed has a double superscript (the converse c'^2 is instead legal, as is c''^2).

If you want to quote something in math mode, you should use math symbols.

\documentclass{article}

\DeclareMathSymbol{\mlq}{\mathord}{operators}{'134}
\DeclareMathSymbol{\mrq}{\mathord}{operators}{'42}

\begin{document}

$\dots\mlq\dots\mrq\dots$

\end{document}