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?