I suggest we take a look at some of the actual tags currently created and see what we like and what we'd do differently (we need an overarching tagging approach too, but why not start with what's here). Others should edit this to flesh it out, but some immediate things I see are:

• We have [nt.number-theory] and [number-theory], with the same number of questions in each at the moment. On reflection, the arXiv prefixes don't seem helpful, because although they might theoretically help people who are familiar with the tags discern which questions they'd be interested in, the majority of people using the tags will be new users who see no difference in the two.

*General point: It is likely that at any given time, the majority of the people interacting with the tagging system will be new users who have not read and are not interested in the FAQ.

• Some tags seem to me clearly useless: [learning], or [intro], for example. (intro could mean anything from kindergarten to graduate school).

• We currently have [summation], [series], [radius of convergence]. I'd suggest a [sequences-and-series] tag, which will pop up for anyone asking a question about either sequences or series, and separate out this (common) problem type from more general calculus or real-analysis questions.

• We need a way to distinguish abstract algebra questions from solving simultaneous equations or the quadratic formula. This way needs to be as transparent as possible for both types of users asking an "algebra" question. Some of the more common dichotomies here should probably be explained in the FAQ.

• Some tags are ambiguous, or simultaneously too general and too specific: [gradient], for example, or [recursive]. We want to avoid things like [normal], etc.

• I'd make the same argument about the [infinity] tag: It's appealing to new users not particularly familiar with mathematics, maybe, but the concept of infinity pervades all of mathematics; the tag is too broad to anyone who is more versed in pure mathematics. This is not a "that's dumb" accusation. But if we have an [infinity] tag, it wouldn't be a tag you'd want to ignore - almost anything related to math could pop up there - but at the same time most of the questions would likely be ill-formed, and people might block the tag with that expectation.

• I kind of like the tag [pi]. There are going to be a few recurring questions about ideas people have gotten in their heads from pop math and other curiosities, and I think having a few such localized tags solves this classification problem neatly. People who have more mathematical or historical questions about computing pi, history, etc, will probably know how to tag accordingly, or can have questions retagged at worst.

• I like tags like [group] for this reason: lots of people will come with questions about such ubiquitous objects, and not enough familiarity with the jargon and theory to label it abstract-algebra or something else that unifies it. However, I don't like the tag [natural-number], so I'm particularly open to being wrong on this one. The two strike me differently, but I don't actually know how to distinguish between them as a matter of policy.