How to write good tag wikis?

Question

I occasionally find that important tags are missing tag wikis or have only very rudimentary information in them. At the same time, I often find it hard to write good tag wikis.

The challenge-type tag wikis don't seem to have that problem - I think they are all fairly decent:

code-golfcode-challengepopularity-contestfastest-codefastest-algorithmmetagolfatomic-code-golfcops-and-robbers

However, the thematic tags are often quite useless. From Jeff Atwood's post about tag wikis:

Avoid generically defining the concept behind a tag, unless it is highly specialized. [...]

Concentrate on what a tag means to your community. [...]

Provide basic guidance on when to use the tag. [...]

A lot of our tag wikis don't follow these guidelines. Have a look at these:

stringnumberarithmeticsequencegeometrygraphssortinggriddatechessfractal...

Many of these simply boil down to "challenges related to X", sometimes with some encyclopaedic information about the concept which you might as well look up on Wikipedia.

So my question is, can we do something about this? Is there some useful information, for this community, to put into these tag wikis? Some wikis, like math and game for instance, reference other tags which might be more appropriate. What else could be useful in the wikis?

Or should we just follow Jeff's advice in point 5, and just dispense these tag wikis altogether?

But if the tag is common knowledge — that is, if you walked up to any random person on the street and said the tag word to them, and they would know what you were talking about — then don’t bother explaining the tag at all. Stick to usage of the tag within your community in the excerpt.

Even so, I think an excerpt like "for challenges involving some sort of sequence." for sequence is still completely useless and tautological. Note that we even have the following rejection reason for tag excerpt edits:

Circular tag definition. Tag excerpts amounting to, "[tag] is for questions about [tag]" are pointless and usually rejected. Excerpts should describe why and when a tag would be used.

Answer 1

In my opinion, the most useful piece of information in a PPCG tag wiki is Jeff's point 4: what kinds of questions should be tagged with it, and what kinds of questions shouldn't. The sequence tag is a good example of one that I'm not sure when to use (so I don't, unless I'll do a challenge straight from the OEIS).

A good course of action for the current low-quality tag wikis, at least for the thematic ones, could be to take a look at the questions that are currently tagged with them, and try to find some common ways in which the tag relates to the challenges. For example, I suspect that most questions tagged with primes are about generating prime numbers (or some variants of them) or testing primality under various restrictions, with a couple of more exotic cases thrown in, so the wiki should reflect that. On the other hand, something like grid is less clear. Some challenges have a 2D grid of numbers or characters as input and/or output, and others specify that the input or output should be interpreted as the coordinates of a grid. The wiki could list these "use cases" as examples.