Question: We currently have a good 5 pages or so of tags at this time. It would help if users were proactive in trying to edit tag Wikis so we can build up quality in our tags. 

This serves out as a reminder to the community.

You do not have to go into too much detail about the subject. Even an excerpt is fine. This will also help us differentiate between useful and useless tags.

Finally it should be noted that Wikis discussing the *history* of such concepts are proffered.

Answer: 
One thing I'd caution against is just copying tag wikis verbatim from other sources. Tag wikis should be written to be directly applicable to this site. Copying the text from another source constitutes plagiarism if you don't cite the source appropriately. Specifically, many users try to copy summaries from Wikipedia, sometimes attributing it to Wikipedia (usually not), but it's impossible for a tag wiki excerpt to satisfy Wikipedia's citation requirements since it is shown truncated and with hyperlinks removed in some places. Generally speaking, the best way to write a good tag wiki is to do it yourself.

Tag wiki reviewers should generally check most suggestions via a search engine quickly to make sure they aren't plagiarized. Having been on several beta sites where this wasn't followed from the beginning, it became an enormous headache for us later to try to find the plagiarized ones. For instance, on [Anime & Manga](https://anime.stackexchange.com/tags), at one point we had quite a few users just manually check through all the tag wikis and excerpts to find plagiarized ones, spending quite a few hours in the process. It was a huge mess that could have been avoided just by catching these cases earlier and rejecting them (though there's not much you can do if the plagiarizer has over 4k rep). Hopefully we can control it here and stop it from becoming that rampant. If you find a plagiarized tag wiki, you should rewrite it.

Another thing to note is that many tags don't strictly need tag wikis, so if you are going to write them, appropriate your efforts intelligently. They're most useful when the terms are ambiguous or unclear or our use of them here is not standard. If a tag has special policies or it's unclear when to use it, definitely a tag wiki is a good idea. If it's easy to understand, a tag wiki adds more things to maintain without much benefit, so before writing it ask yourself whether it's really needed. Finally, I'll just restate the OP's statement that the tag wikis are best be written in a way that's specific to *this site* (History of Science and Math), not about the concept broadly.
As another note:

If you have 1500+ rep (which not enough users do so far, in my opinion), you can approve tag wiki edits. **I strongly recommend that all users who have passed this mark review the Suggested Edits queue to go over them.** Unlike edits to a post, where the poster can approve the edit and not need a second acceptance of the edit, there isn't a person (besides these users) who can approve these tag wiki edits (to my knowledge). If you can review these edits, please do so - and if you can review *anything*, do that, too!

Also, users with 1500+ rep may not necessarily make tag wiki edits immediately. They, too, are subject to the peer-review process.

Finally, we need to have a unified phrasing for tag wikis. Take a look at tags on other SE sites, and note that their phrasing follows a pattern.