Wikipedia talk:WikiProject Mathematics/Wikipedia 1.0/Importance

This page is part of a response to a discussion of importance rating at the Mathematics WikiProject. It is intended to develop mathematics-specific guidelines on assessing importance of mathematics articles. The page has been seeded with material from elsewhere in the Wikipedia 1.0 topic, together with some comments as to why the existing guidelines need refinement in the mathematical context. Please comment further here, or simply edit the article to improve it. Geometry guy 13:52, 25 May 2007 (UTC)

Ideas from coverage or scope

At WT:WPM, Salix alba suggested the following hierarchy.

...loosely we could have coverage or scope

• Of high importance across all numerate discipline - everyone should know this
• Of high importance throughout mathematics - all mathematicians should know this
• Of high importance in a major field of mathematics - all those working in the field should know this
• Of importance within one field (high importance in a sub-field) - most working in the field would know this
• Mainly limited to a sub-field
• Specialist, mainly work of one researcher.

Even if coverage or scope is not implemented, these descriptors suggest improvements to the importance rating scheme. Geometry guy 20:38, 29 May 2007 (UTC)

Multiple ways of describing importance

One of the issues with the current importance scheme is that there are several different ways importance can be described.

1. The importance of the topic within its field.
2. The impact of the topic beyond its specialty.
3. How important it is that Wikipedia has an article on the subject.

One of the problems with the current template is that it mixes these different approaches (Top is described by method 3, High and Mid by method 1, and Low by method 2). Geometry guy 11:14, 2 June 2007 (UTC)

I agree! This suggests to me that the importance scheme should be split into columns. Geometry guy 11:16, 2 June 2007 (UTC)

Descriptive or prescriptive?

Unresolved

Initially a comment from User:Silly rabbit to User:Geometry guy

I am examining with great interest and optimism your progress on this page. Another way to describe importance, which you seem to have overlooked, is as a family resemblance concept (as Ludwig Wittgenstein would put it). As mathematicians, we like to pin things down precisely; perhaps too precisely for something as contentious as a nebulous idea of importance. That's why I linked Top, High, Mid, and Low to their respective categories in the table on the page. It seems that one very effective way to determine the importance of an article is to examine it in relation to other articles which are of potentially equal importance, and such an approach is likely to appeal to naive editors (such as myself).

I am a big fan of wikilinking entries in tables, so thanks for doing this! I agree that the best way to determine importance of an article is to relate it to other articles. However, I think the other articles should be comparable, which is the main reason I think importance needs to be handled within some sort of context. It isn't much help to compare degrees of freedom (statistics) with deformation theory, whereas it is helpful to compare group (mathematics) and ring (mathematics). Geometry guy 21:47, 2 June 2007 (UTC)

However, this method is not without its pitfalls, as I just discovered in my disastrous recent debut into the math ratings community. For instance, if group (mathematics) and commutative ring are both Top, then clearly ring (mathematics) must also be Top. It's a slippery slope from then on, though. (Kernel and image to High, for instance, etc.) Reflecting on my reasons for upgrading some of these "fundamental ideas" in the light of your descriptive classification of importance, I still see no reason that group/ring/commutative ring should be categorized as any less than Top. So, given the opportunity, I would likely make the same errors in judgement all over again.

I actually think that the judgement to rate the key groups and rings articles as Top was correct. One of the more interesting cases is group representation theory. This is effectively the lead article in the whole representation theory category. To my mind, this makes it top importance, because the subject is very significant and has many ramifications. However, this is very much a rating within context: a good article on group theory might also mention group representations, making the latter subject less important as an independent article. I still think it is top importance.

Some other users (and I guess I am thinking of User:Arcfrk but I don't want to put words in his mouth) have what might be called a depth criterion for importance: for instance, kernel and image do not add much depth once one has the key notion of a homomorphism. I am not convinced by this, since the rating is meant to reflect the importance/priority of having an article on the subject. A mathematical encyclopedia without an article on the importance and ramifications of "kernel" (in group theory, linear algebra, linear differential equations etc.) would be very poor indeed! On the other hand, image, in this context, is actually not as important, even though logically it has much in common with the concept of kernel! Geometry guy 21:47, 2 June 2007 (UTC)

I propose that instead of attempting to describe the categories of the importance scale in detail, that we should be attempting to create a prescription for how importance is assigned. Silly rabbit 19:43, 2 June 2007 (UTC)

The importance ratings can be roughly described as follows:

1. Top

• Description. The major fields of mathematics, and ideas of mathematics without which mathematics would fail to exist as we know it today.

• Prescription. If you could save just ten books from the burning library of Alexandria, what would they be? Be sure to check that no other editor has saved a book treating the same or similar subject.

• Examples. Calculus, mathematical analysis, abstract algebra, Fundamental theorem of calculus, function (mathematics), addition, multiplication, etc.

Bad examples. probability density function, probability space — since someone else already saved the book on probability and probability theory. fraction (mathematics) — superceded by arithmetic.

2. High

• Description. The most significant ideas and most sweeping theorems of mathematics.

• Prescription. If you could only save one hundred mathematical concepts, which ones would they be? Again, be sure to check that someone else hasn't saved a concept which supercedes one of your choices!

• Examples. isomorphism theorem, Lie group, homomorphism, integral

3. Mid

• Description. The more significant components of a particular mathematical field.

There is a lot to be said in favour of this approach, but the question I would ask is who is "you". For example, there may be information on probability density functions that some people might find vital, which are not covered by a general article on probability theory. I think there is a difficult compromise to made between rating importance within mathematics as a whole and importance within context. Geometry guy 21:47, 2 June 2007 (UTC)

Priority: None

For priority None we read: "A maths rating is not necessary for these articles". Unless someone goes through the effort of doing the maths rating for these articles, how do we know the priority is None? If the article is in the purview of WikiProject Mathematics, we should, eventually, in any case assign a quality rating. Isn't Low low enough for the importance rating? In any case, we should not put None in the table unless we recognize it as one more importance rating level below Low. Template {{Math rating}} does not mention None, but it does mention importance=NA for non-articles.  --Lambiam^Talk 14:00, 3 June 2007 (UTC)

I was trying to express the idea that priority None means that the article is, in some sense, not in the purview of WikiProject Mathematics, at least not from the point of view of maths ratings. This is partly because the List of mathematics articles contains a very large number of articles which are not really mathematics, but happen to have a secondary mathematics category assigned to them. It is also partly a matter of pragmatism: adding maths ratings to all 15000 articles is impractical.

The coverage of the maths ratings process is always going to be incomplete. Any editor, on finding a maths article without a rating, can make a judgement for themselves about whether to add one: if they do, the priority should be low or higher. This seems to be the current practice, although I'm not sure how to express it most clearly. Would it help if the None were removed from that column? Geometry guy 15:03, 3 June 2007 (UTC)

The revised formulation is an improvement, but I think the purpose is better served by not having a row with a pseudo rating None followed by a clarifying sentence in running text, but instead just a small paragraph preceding the table, such as:::On the other hand, NA should be added to that list of ratings.  --Lambiam^Talk 08:51, 4 June 2007 (UTC)

High vs Top importance

At WT:WPM it was generally agreed that there should not be too many Top-Priority mathematics articles (a few hundred). However, looking at the figures, it seems to me that the main issue currently is that there are too many High-Priority maths articles. Some of these may only be Mid-Priority, but I think it would be helpful to identify a handful of the most important among them, and raise their priority level to Top, in order to help editors find them, particularly as there are now not many Top-Priority articles of Start class or lower. Comments? Geometry guy 15:09, 3 June 2007 (UTC)

Hi Geomety guy! In response to your comment, I've uprated about 40 articles from High to Top (I also downrated a couple). I was fairly conservative about which articles I uprated, so there is still room for other users to uprate a few more. Geometry guy 20:59, 3 June 2007 (UTC)

Scope and goals

With almost 26,000 articles plus over 3,000 Mathematician articles it would appear that the ratios need to be scaled enough to be inclusive of growth over the next few years. Mathematics articles are almost certainly increasing by 5% a year—over a thousand articles per year. The fill of each Importance level should not exceed 75-85% of the projected quantities based on the ratios adopted. Using 30,000 as a rough total of articles, a 75-85% fill would suggest the ratio plan should aim for 35,000-40,000 total articles. I believe the 300-400 Top Importance articles is consistent with other projects. A ratio of 4.5:1 for each level would produce a 35,000 total for 300 Top articles; almost 41,000 for 350 Top; over 46,000 for 400 Top.

When some consensus is reached, the current section should be rewritten to simply discuss the expected scope and goals. The historical ratios and numbers should be clearly relegated to a history discussion.98.211.41.239 (talk) 01:45, 24 May 2011 (UTC)