The asterisk was used in the 80s as a 'jolly' character for Operating System maintenance and procedures. I used the asterisk a lot when, under MS-DOS, I had to copy files or folders in particular ways. If I needed to copy only the .EXE files to a floppy disk, I'd write:
copy *.exe a:
The asterisk meant that 'all' files with an .exe extension had to be copied.
The asterisk was quite versatile! Say, for example, you wanted to copy to a floppy disk (or move, or delete) a group of files, but only those which name started with 1989_04, you could write:
copy 1989_04*.* a:
Meaning that any file starting with 1989_04 was going to be copied, and also with any extension
(.*). So, if there were some .doc and some .xls, they'd be copied. If you wanted to specify only one type of extension, say .doc, then you'd write:
copy 1989_04*.doc a:
The asterisk was a much more powerful tool, these are just a few examples. Let me show you something that I still remember. Say you wanted to 'type' (list the file content on the screen) many files instead of only one at a time, you could write:
for %f in (*.*) do type %f
In this case,
*.* means any file with any name
(*) and any extension
(.*). You could obviously replace partially or totally those 2 asterisks based on your needs.
If you open the old issues of PC Magazine that you have at home, some of which I'd love to buy, and you browse through the technical pages (usually located toward the end of the magazine and having paragraphs or tables with pink or green background), you'll find tons of other examples of commands, instructions, and codes using the asterisk. Sometimes you'll find them also in the section where the magazine staff answered readers' questions. I also added some additional examples of the use of the asterisk under MS-DOS and various info in the 'about me' section of my profile. I am basing my answer on MS-DOS because I know it, but I'm sure similar uses of the asterisk were occurring for other 80s operating systems.
In conclusion, in the 80s there were already countless uses for the asterisk in a large variety of contexts and situations, therefore, we should not be surprised if we found it on all types of keyboards.
⋅which I think is much more common than
×in higher mathematics