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The tag was created and removed a few times in the past. And recently it was created again - it is still listed among the new tags.

  • Should there be a separate tag for on MathOverflow?
  • If yes, what should be the content of this tag.

You can see links to the previous occurrences in the MO editors' lounge. Specifically:

I decided to ask because on Mathematics Stack Exchange there are some problems around this tag - it is unclear whether should be a subset of or whether the latter should only be for more advanced questions.1 On MathOverflow it is unlikely that there would be a similar problem - since among the top-level tags2 there is , which should include , too. Still, since this tag was created and removed more than once, it seemed reasonable to bring it up on meta.

1Discussion on Mathematics Meta: There are 5,931 questions tagged both elementary-number-theory and number-theory and How to differentiate between (elementary-number-theory) and (number-theory).

2Why are MO tags formatted as they are? and Frequently asked questions about tagging on MathOverflow

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  • $\begingroup$ I don't understand the concern about "elementary number theory" being a subset of "number theory." "Analytic number theory" and "algebraic number theory" are subsets of "number theory," but of course it is totally appropriate for them to be tags too. $\endgroup$
    – Sam Hopkins
    Aug 10 at 14:56
  • $\begingroup$ @SamHopkins I mentioned this mainly because this is a problem on Mathematics, as mentioned in the post. (OTOH as you can see, the question where the tag was created does have any top-level tag.) $\endgroup$
    – Martin Sleziak
    Aug 10 at 17:24
  • $\begingroup$ Anyway, probably the fact that this tag was created and removed several times in the past is a sufficient reason to bring it up here on meta. $\endgroup$
    – Martin Sleziak
    Aug 10 at 19:30
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    $\begingroup$ I suspect that some of the angst over this tag stems from the fact that the word "elementary," especially in the context of number theory, is ambiguous. Does it mean "avoids complex analysis" or does it mean "can be stated using very little machinery"? Since mathematicians abhor ambiguity, we are tempted to get rid of ambiguous tags rather than live with them. $\endgroup$
    – Timothy Chow
    Aug 12 at 0:04
  • $\begingroup$ Related to Timothy Chow's comment: Why were proofs avoiding complex analysis preferred in number theory? Is this distinction still important? $\endgroup$
    – Martin Sleziak
    Aug 12 at 7:50
  • $\begingroup$ In the meantime, this occurrence of (elementary-number-theory) was removed. $\endgroup$
    – Martin Sleziak
    Aug 24 at 5:25

2 Answers 2

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Tags are useful, so should be allowed to let be and exist, unless there are overwhelming exceptional circumstances. elementary-number-theory is a perfectly cromulent tag.

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The elementary number theory tag should be attached to a number-theoretical question when the formulation of the question avoids complex variables, derivatives and integrals.

The above statement gives an early approximation of a solution to the problem of a MO-definition of the said tag. A perfect solution is perhaps not possible while the perfectness is not necessary anyway.

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