Capitalizing mathematical parts in section mark

Question

In book documentclass, the section marks in the header are put in all caps. For normal text, that is okay.

However, I've just noticed that the same happens to letters in math mode, which is obviously bad, as the meaning of the letter may change depending on the capitalization. Is there a simple way to fix it? (Hopefully without having to rewrite all headers via fancyhdr or something.)

MWE:

\documentclass{book}
\begin{document}
    \section{$n+2=N$}
\end{document}

Answer 1

You can switch out \MakeUppercase for \MakeTextUppecase which skips math mode:

\documentclass{book}
\usepackage[overload]{textcase}
\begin{document}
    \section{$n+2=N$}
\end{document}

Answer 2

You can manually protect single characters (or a range in which everything is lowercase) by using \lowercase:

\documentclass{book}
\begin{document}
  \section{$\lowercase{n+n-n}+2=N$}
\end{document}