For my two most recent questions, I used mathematics where I meant arithmetic as the latter doesn't exists.
The former says:
A simple test to apply is: would an amateur or professional mathematician take an interest in the question?
I guess a mathematician doesn't give a damn about something as "low and spiritless" as optimized integer multiplication. Should we create a tag arithmetic or should we edit mathematics to make it clearer that it includes computer arithmetic as well?
Code Review needs to strike a balance between tags that are specific enough to be useful, and specific tags that may be more precise, but too specific to be useful.
This requires grouping things together now, that at some point, if volumes increase, may need to be split again later.
In my mind, the mathematics tag is fine here, you are dealing with arithmetic, sure, but we don't need to compartmentalize the mathematics system just yet, the volumes are not there, yet.
In this case, for both your questions, the mathematics is fine. Should the wiki be udpated? Perhaps, but I think the description covers the important part... that someone interested in mathematics would be interested in both long-form multiplication, and Big Rational numbers
I'm not convinced that arithmetic is a desirable tag to have, nor do I think that mathematics is a useful tag for that class of arithmetic problems.
The problem with arithmetic is that it's hard for people to tell when to apply the tag. After all, we use arithmetic all the time. Even if we came up with specific guidelines, the name of the tag is still so broad that the guidelines would likely be ignored, and the tag would end up being meaningless.
I suggest using the bitwise and algorithm tags in conjunction with a tag for the kind of number ― something like integer, rational-numbers, floating-point. Those tags deal with issues of number representation, manipulation, and situations such as overflow. You could still apply the mathematics tag at your discretion, but only if the code has something interesting about the mathematics that might be worth discussing (such as arithmetic operations modulo a prime number).
