In short:
- This is not a normal category, but a longlist, like an index list at the end of a book on Mathematics.
- Purpose: to have quick access to subcategories deep down in the category tree.
- Overcategorisation is allowed here.
More information (for editors):
This category contains an index of concepts within the context of Mathematics which are represented by Commons categories and should have an essentially flat organization (as opposed to the main topical category tree. This category can be seen as a long index list like you can find at the end of a book on Mathematics.
- Guidelines for readers seeking details on facets of the main topic:
- Users can find and quickly access categories for each facet of the main topic directly from this category.
- For more information about a given term or facet listed here, select the category and see the interwiki links (listed in the bottom left column).
- Guidelines for editing this category and deciding which contents should be added here:
- Overcategorisation is allowed here.
- Assigned subcategories:
- should be topic categories (so for instance have not 'by' in the category name or is about a medium) with few exceptions
- may be from any level down under the main topic
- should be directly relevant to the main topic (though aircraft is a vehicle and so a product and thus part of economics, it does not make sense to have aircraft in the Category:Economics by topic).
- Category:Mathematics by topic should never be the only parent category of any subcategory here. All these subcategories should have other proper parent topical categories, so that they also can be found via the regular category structure of Category:Mathematics.
- Keep overall contents limited to relevant facets of the main topic. Ideally, an upper bound of 200 categories is ideal to permit easy use of Ctrl-F to find contents. If there are more: first remove categories with similar category names (see below), when that is not enough: split it into important sub-areas.
- When categories here have similar names (like Category:Industry and Category:Industrial architecture) only the most directly connected to the main topic needs to be retained here, as others can be found through that primary sub-category.
- For larger indices, consider adding table of contents and other content access features.
- Guidelines for improving sub-categories:
- Add a useful and concise description in each language you can accurately contribute. This should be done in the Wikidata item if it is present, or directly in the header of the subcategory.
- Consider adding Wikidata items and information for categories lacking them. Use {{Wikidata Infobox}} to link existing Wikidata items.
- Ensure proper topical parent categories are added to each sub-category, both within the main topic tree and to other relevant topics.
More information: Commons:Categories_for_discussion/2023/12/Category:Estonia_by_topic and Commons:Categories for discussion/2023/10/Category:Terminology. | 
