Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Importance

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Assessing the priority or importance level of mathematics articles is not straightforward for at least the following reasons:

  1. it is difficult to define clearly what the importance levels mean, both in general, and for mathematics articles in particular;
  2. there are varying opinions on what should be the context within which importance should be assessed;
  3. there is an ambiguity as to whether the importance level refers to the subject or the article.

This page is intended to provide guidance on these issues specific to mathematics articles. Importance ratings are inherently subjective, and fluctuations are inevitable, but this guidance is intended to keep subjectivity and fluctuation to a minimum, by discussing the above issues, providing detailed descriptors for the four importance levels, and explaining what importance ratings are for.

What are importance levels for?[edit]

The first point to make is that the whole maths rating scheme is for editors, not for readers: this is why it is placed on the talk page, and none of its content appears in the article (the only exceptions are the Good and Featured Article symbols, but this is because the overlapping GA/FA scheme is for readers as well as editors). The primary purpose of these ratings is to help editors improve articles and to help the project track its progress. The ratings are also used to decide which articles to include in fixed versions of Wikipedia such as Wikipedia 0.5, 0.7, and the 1.0 release.

The importance level or priority of an article is intended to indicate how important it is that Wikipedia should have a high quality article on the subject.

Article or subject?[edit]

It would seem to follow from this that importance primarily rates the priority of the article, not the subject. However, it does not assess the importance of the article as it is currently written, but the potential value of having a high quality article on the topic. This is usually closely tied to how important the subject is, and consequently, importance levels are often described in terms of the importance of the subject rather than the article.

Mathematicians: article or person?[edit]

Assessing importance/priority for articles on mathematicians can be particularly difficult. In the past, the project has followed WikiProject Biography guidelines, which refer to the importance and impact of the person, rather than the need for the article.[1] Although (as with general articles) these two metrics are closely related, there are examples (Srinivasa Ramanujan being one such case) where the importance of the article goes beyond the impact of the individual on mathematics. The project no longer recommends using the Biography guidelines. In particular, criteria such as impact across generations may inform, but should not determine, importance levels, and are inappropriate for articles on contemporary mathematicians.

Scope and goals[edit]

When assessing importance/priority of articles, it may be useful to bear in mind the scope of the project as a whole. There are currently over 25000 subject articles in the List of mathematics articles and over 3000 articles on people in the List of mathematicians.

Early experience assessing subject articles suggested that approximate half of these articles are sufficiently important and relevant to the Mathematics WikiProject to be worth rating. It was also generally agreed that the lower priority categories should be more populated than the higher ones, and in particular, that the Top importance category should only contain a few hundred articles. In the last few years, the number of Top priority articles has remained fairly static at 200–250, while High priority has grown from c. 400 to c. 700. It could be argued that the proportion of High to Top priority articles should be closer to 2:1, with more articles given Top priority than at present, but the current ratio is more than 3:1.

In 2007/8 the numbers of Mid and Low priority articles were approximately equal, at around 1000–1500. This may have been due to a tendency for more important articles to be assessed sooner, but there may also have been some over-rating when the guidelines were less detailed and the low importance description was unnecessarily dismissive. The ratio is now more than 2:1, with c. 2500 Mid priority articles and over 5000 Low priority articles.

The Top:High:Mid:Low ratio, where the aim in 2007/8 was 1:2:4:6+, is expanding: a ratio of 1:3:10:25 may be reasonable (for example, 300 Top-Priority, 900 High-Priority, 3000 Mid-Priority and 7500 Low-Priority).

Defining importance[edit]


In the Wikipedia 1.0 Assessment Scheme, of which this is a part, it is emphasised that importance/priority is a relative term, i.e., an article which is Top-Priority in one context, may only be Mid-Priority in a wider context (see below). In other words, importance levels are not assessed across Wikipedia as a whole, but in context. In order to understand this, it may be helpful to think of Wikipedia not as one monolithic encyclopedia, but as a family of nested, overlapping encyclopedias.

However, this immediately raises the question: how to determine the context? There does not appear to be clear consensus on how to do this. One approach is to declare that the context is mathematics. However, this has a couple of disadvantages:

  • it is difficult to compare the importance of articles in different fields (indeed, this can be tricky even within a branch of mathematics);
  • it may not be easy to ensure the higher priority levels are sufficiently well populated, nor that there is enough discrimination between lower importance articles.

This suggests that context should be more finely grained. There are (at least) two methods to do this:

  1. use the field parameter in the maths rating template to determine context;
  2. use the category hierarchy to determine context.

The first of these is simpler, although currently the fields are rather broad, and so this methods shares some of the difficulties with using "mathematics" as the context, albeit to a lesser extent. The second method, on the other hand, has problems of subjectivity: in more detail, the context for an article might be the smallest substantial category to which it belongs (either directly, or via a subcategory), but substantial is a rather subjective term.

However, the difficulty in determining context can at least partially be ameliorated by the following principle:

the finer or more specialized the context, the more conservative one should be in assigning higher importance levels to articles.

In other words, one can take advantage of the fact that the characterization of the importance levels discussed below is also subjective.

Finally, it may be helpful to keep in mind the suggested ratios between the numbers of articles in each importance level.

Describing importance[edit]

Three different ways of expressing the priority of articles are currently used.

  1. The importance, significance and depth of the topic within its particular field or subject.
  2. The extent of the topic's impact, usually in the sense of "impact beyond its particular field", but it is also used to express global impact, and impact through history.
  3. The bottom line: how important is it for an encyclopedia to have an article on the given topic?

These are often different ways of saying the same thing, but the current WP 1.0 summary table mixes the three approaches: Top priority is described using method 3, High and Mid priority using method 1, and Low priority using method 2.

The following table of possible priority or importance levels lists these distinct approaches in separate columns, and provides more detail on the meaning of the individual levels, as well as examples.

Article importance/priority rating scheme
Priority Importance within field Impact Need for encyclopedia Examples
Top Article/subject is extremely important, even crucial, to its field Widespread and very significant An absolute "must-have" for any reasonable mathematical encyclopedia Trigonometric function, Manifold, Special relativity
High Article/subject contributes a substantial depth of knowledge Significant impact in other fields Very much needed, even vital 3-manifold, Linear combination, Poisson distribution
Mid Article/subject adds important further details within its field Some impact beyond field Adds further depth, but not vital to encyclopedia Homotopy groups of spheres, Second order logic, Generalized hypergeometric function
Low Article/subject contributes more specific or less significant details Mainly of specialist interest Not at all essential, or can be covered adequately by other articles Area of a disk, Abel transform, Companion matrix
(None) Article/subject may be peripheral May be too highly specialized May not be relevant or may be too trivial in content to be needed Comment: such articles are not relevant enough to the mathematics project to need a maths rating.

The last row is not an importance level per se, but is intended to provide guidance on adding (and perhaps sometimes even removing) maths ratings. In addition there is a Category:Unassessed importance mathematics articles for articles which have a maths rating, but no importance level: editors should feel free either to assign an importance level (Low-Priority or higher) or remove the maths rating from these articles.

Some editors may wish to add the maths rating template to pages which are not articles, but disambiguation pages, categories, templates or images, simply to indicate that these pages are within the scope of the Mathematics WikiProject. Such pages do not need an importance rating, and the tag "importance=NA" (for non-article or not applicable) should be used in the maths rating template.

Prescribing importance[edit]

While importance is hard to describe, it may be easier to prescribe how to assign importance ratings. A few suggestions follow.

  • Compare the article to similar articles.
  • Bear in mind the approximate ratios Top:High:Mid:Low. These ratios should approximately hold within any given context.
  • Importance is not set in stone, it is dynamic. An article can change in importance as other articles are created, or articles are merged.
  • If in doubt, underrate, particularly when adding a new maths rating: adding a maths rating with "importance=X" means "this article matters to the Mathematics WikiProject, and it is at least X-Priority". Other editors will uprate the importance if necessary. Downrating importance tends to provoke more controversy, so be conservative!

Wikipedia 1.0 definitions[edit]

This section is based closely on the discussion of importance at Wikipedia 1.0.

Need: The article's priority or importance, regardless of its quality

Top Subject is a must-have for a good encyclopedia
High Subject contributes a depth of knowledge
Mid Subject fills in more minor details
Low Subject is mainly of specialist interest.

Importance or Priority must be regarded as a relative term. If importance values are applied within this project, these only reflect the perceived importance to this project. An article judged to be "Top-Priority" in one context may be only "Mid-Priority" in another.

By "priority" or "importance" of topics for a static version of the encyclopedia, we generally mean to indicate the level of expectation or desire that the topic would be covered in a traditional encyclopedia.

A more detailed cross-Wikipedia importance scheme has been proposed at Template:Importance Scheme, but is not widely accepted, and may be inappropriate for mathematics because it emphasises a local/continental/international dimension which is largely irrelevant.

Inclusion in Wikipedia 0.5, 0.7 and 1.0[edit]

Consider a hierarchy such as

Algebra -> Abstract algebra -> Ring theory -> Ideals.

An article rated as "Top-Priority" in Abstract algebra would probably warrant inclusion in v0.5, v0.7, v1.0 and other releases. A "Top-Priority" article in Ring theory would be a reasonable candidate for inclusion, but most "Top-Priority" articles in Ideals would probably not be included in early releases. Nevertheless such ranking within a subject area is very helpful in deciding which articles are included first as the scope of the Wikipedia 1.0 project expands. Quality articles which are not considered to be on topics important enough for inclusion on v0.5 will be held in a held nominations page, ready for inclusion as the scope expands.


  1. ^ Wikipedia:WikiProject Biography/Assessment#Priority scale has the following scheme:
    Top - Must have had a large impact outside of their main discipline, across several generations, and in the majority of the world. For instance, Einstein, brilliant physicist, but his theories have affected people outside of physics and in many other countries besides his nation of origin and several generations. His ideas have changed the way people think.
    High - Must have had a large impact in their main discipline, across a couple of generations. Had some impact outside their country of origin.
    Mid - Important in their discipline.
    Low - Subject is notable in their main discipline.
    Some of these criteria, such as impact across generations, and impact beyond country of origin, are not particularly useful for rating the importance of articles on mathematicians. The generational criteria are also problematic when rating articles on living people.