At the moment, Mathematics SE has tag derivatives (with synonym differentiation) and tag integration. Why the lack of symmetry? Why not have tag differentiation with synonym derivatives instead?
Differentiation is about infinitesimal differences — whatever that means. Derivatives? Many things are derivative. Gasoline is a derivative of crude oil. Futures and options are (financial) derivatives.
Related:
I think it's reasonable to flip the direction of the synonym in this case for the sake of maintaining symmetry, i.e. keeping [differentiation] and [integration] as the master tags, rather than [derivatives] and [integration].
However, I disagree with the other reasons provided, namely that "derivatives" could refer to other things, i.e., "Gasoline is a derivative of crude oil. Futures and options are (financial) derivatives."
This is because there are many everyday words that are used in a technical manner in mathematics, and the purpose of the tag wiki excerpt is exactly to clarify what is the meaning and usage of that tag. Quoting the Help Center article What should a tag wiki excerpt contain?:
Guidelines for writing useful tag excerpts
The excerpt is the elevator pitch for the tag. You only have ~500 plain text characters for the excerpt, so don’t feel obligated to cover everything in it! Save that for the 30,000+ character Markdown tag wiki. The excerpt should define the shared quality of questions containing this tag — boiled down to a few short sentences.
Avoid generically defining the concept behind a tag, unless it is highly specialized. The “email” tag, for example, does not need to explain what email is. I think we can safely assume most internet users know what email is; there’s no value in a boilerplate explanation of email to anyone.
Concentrate on what a tag means to your community. For “email” on Server Fault, mention the server aspects of email including POP3, SMTP, IMAP, and server software. For “email” on Super User, mention desktop email clients and explicitly exclude webmail, as that would be more appropriate for https://webapps.stackexchange.com/.
Provide basic guidance on when to use the tag. In other words, what kinds of questions should have this tag? Tags only exist as ways of organizing questions, so if we don’t provide proper guidance on which questions need this tag, they won’t get tagged at all, rendering the tag excerpt moot. Think of it as a sales pitch: in a room full of tags screaming “pick me!”, what would convince a question asker to select your tag?
Some tags are common knowledge. Most tags require a bit of explanation in the excerpt, even if it’s only 3 or 4 words. 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.
The Stack Overflow blog post on good tagging practices goes into greater detail on this matter.
