\[ …\] in place of $$ …$$?\( ... \), has precisely the same effect as the
TeX primitive version $ ... $. (Except that
the LaTeX version checks to ensure you don’t put \( and
\) the wrong way round; this does occasionally detect errors….)
Since this is the case, one often finds LaTeX users, who have some
experience of using Plain TeX, merely assuming that LaTeX’s
display maths grouping \[ ... \] may be replaced by
the TeX primitive display maths $$ ... $$. Some
people “go the whole hog” and use \begin{displaymath}
… \end{displaymath} (which “looks nicer”, in some
sense, and actually describes what’s being done.
Unfortunately, they are wrong: if LaTeX code is going to patch display
maths, it can only do so by patching \[ and \]. The most
obvious way this turns up, is that the class option fleqn
simply does not work for equations coded using
$$ ... $$, whether you’re using the standard classes
alone, or using package amsmath. Also, the \[ and
\] construct has code for rationalising vertical spacing in some extreme
cases; that code is not provided $$ ... $$, so if you
use the non-standard version, you may occasionally observe
inconsistent vertical spacing. Similar behaviour can bite if you are
writing a proof; placing the “QED symbol” doesn’t work
if it is in $$-displayed maths.
There are more subtle effects (especially with package
amsmath), and the simple rule is “use
\[ ... \] (at least) whenever displayed maths is
needed in LaTeX”.
This answer last edited: 2013-02-20
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