when teaching arithmetic × was typical, but when teaching elementary
algebra or higher math · was used
I would agree with this. Essentially, it seems like "real" math – to
the extent that it uses numbers beyond {0, 1, 2} in the first place
:-) – uses ·
Oh, now I understand your comment. Matrix multiplication has no dot (and
uses juxtaposition); the inner ("scalar") product uses · , and the cross
product uses × . I don't remember deviating usage or any variation of
that pattern, though I wouldn't be surprised if non-math disciplines in
the US have looser conventions for the inner vector product.
For ordinary clusters of numbers and variable names (where German usage
knows no × ), juxtaposition of numbers without some explicitly printed
operator naturally doesn't occur. In the US, × in place of · is like I
described – for my generation of people being educated.
Stephan