Am 16.01.2017 um 11:41 schrieb David Carlisle:
>
> Any apparent correspondence between inner and outer math and
> displaystyle and textstyle is more or less accidental.
\ifinner is described in the TeXbook simply as
True if \TeX\ is in internal vertical mode, or restricted
horizontal mode, or (nondisplay) math mode (see Chapter~13).
which is unfortunately an oversimplification as the "style" can be
explicitly set via \displaystyle and \textstyle and that is not
reflected by the \ifinner test.
Most math environment do exactly this, ie typesetting the formulas using
$...$ = \ifinner=true but changing the style to \displaystyle when
needed (with still \ifinner=true) which makes \ifinner pretty useless
inside math
As Joseph said, that is really only reflected when you look at \mathchoice
