\documentclass{article}
\begin{document}

\hbox{text $math$ text}

\hbox{text $$alsotext$$ text}

Footnote\footnote{text $math$ text}
Another\footnote{text $$displayedmath$$ text}

Note that dollar inside equation, etc.~fails.
% \[ math {\rm $text$ } math \]

% \[ math $$math$$ math \]

\mbox{text $math$ text}

\mbox{text $$alsotext$$ text}

\[ a + \mbox{text $math$ text}  + c \]

\[ a + \mbox{text $$alsotext$$ text}  + c \]

\[ a + \makebox{text $math$ text}  + c \]

\[ a + \makebox{text $$alsotext$$ text}  + c \]

Base\raisebox{1em}{text $math$ text}

Base\raisebox{1em}{text $$alsotext$$ text}

Base\shortstack{text\\ $math$\\ text}

Base\shortstack{text\\$$alsotext$$\\ text}


\end{document}