a repository of mathematical know-how



I would like to encourage people to think about how to categorize articles in such a way that they are likely to be found by those who need them. A good way of starting to think about this is to click on "Top level" (in grey at the top of any of the mathematical articles) and then on "Uncategorized" to see a list of currently uncategorized articles. How should they fit into the structure of the Tricki? Often there will be two answers, one based on subject matter and one on the kind of problem that a technique is useful for. But sometimes a technique is too general to have a neat subject-matter categorization, and then categorizing it becomes a challenge.

If an article is already categorized by subject matter (which you can tell by looking at its parent articles) then there may still be important work to be done: ideally we want all articles to be categorized by the type of problems they help you solve. If you can think of some general descriptions of types of problems that have not yet been explicitly mentioned on the Tricki, then we'd like to know about them.

But for the purposes of this forum topic, I go back to my previous question: what should we do about the currently uncategorized articles. The answers are sufficiently non-obvious to me that I would like to have some discussion about it before making any decisions.

I'm very interested on this issue. I would like to know which are exactly "the Tricki structure" and the categorization mechanisms (categories and rules to make them up) implemented on it just now. Is there a good explanation/discussion page for them?

As you know, I already suggested several ways to categorize, trying to be creative... but I can suggest yet another, simpler one. We could design a "Standard Hierarchy" with, say, 20 levels of increasing abstraction bottom-up. It won't be a really natural hierarchy, but an artificial one. What I have in mind is to break with the "intuitive categorization", because intuition can be different from person to person. Instead of letting people imagine what the categories are and which are its levels of abstraction, we create those as fixed, stationary elements understanable by their definitions and let people get accustomed to our Standard Hierarchy. Just like they do in (biological) Taxonomy with taxa like Kingdom, Phylum, Class, Order, Family, Genus, Species, etc. Some categories will feel more logical, some of them less, but all should be meaningful enough to let people get a good grasp of them with its continued use.

It may seem that with a Standard Hierarchy we would lose flexibility, but we will still have it if we allow a sufficient number of levels on it. Moreover, we can have a "Taxonomy Comission", a group of people (permanent or dynamic) in charge of changing the number of levels, its definitions or even evolving the Hierarchy rules if found necessary.