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I came across this umlauts in math mode question today. However I still do not understand the underlying mechanic why we need to use manual umlauts and do not have enough reputation to comment on the answer.

I have a possible explanations but do not know if it is correct:

  • There are no code points for umlaut characters in math fonts (at least there is not block for them in unicode). Therefore we need to typeset them manually using the appropriate macros like \ddot{a} etc as it is not possible to convert the normal serif fonts to math style.

    If this is the case why would packages like unicode-math not just apply said macro automatically?

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In math accents like the diaresis have a mathematical meaning and \ddot{a} is "a with the ddot accent" and not "ä" (U+00E4).

Umlauts and other chars with accents are not used in math as it would be confusing: one couldn't see if "ä" or "\ddot{a}" is meant.

So use \ddot{a} in math and never ä.

There is small exception: Sometimes words are used e.g. in superscripts, and such words can contain accents depending on the language. In such cases a sensible input is to switch to a text font.

\documentclass{article}
\usepackage{unicode-math}
\begin{document}
$\ddot{a} \neq T_{\mathrm{Wärme}}$
\end{document}

enter image description here

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