Wikipedia:Notability (numbers)

These guidelines on the notability of numbers address notability of individual numbers, kinds of numbers and lists of numbers.

In the case of mathematical classifications of numbers, the relevant criteria are whether professional mathematicians study the classification and whether amateur mathematicians are interested by it. Therefore, the first question to ask is:


 * Have professional mathematicians published papers on this topic, or chapters in a book?

This is the question that will apply, only slightly reworded, to each of the kinds of articles about numbers we will consider. More specific questions will be added for specific article types, though there will of course be some overlap.

Notability of kinds of numbers

 * Examples Complex numbers. Transcendental numbers containing only 3s and 7s in their hexadecimal representations.

The questions to ask are:


 * 1) Have professional mathematicians published papers on this kind of number, or chapters in a book, or an entire book about this kind of number?
 * 2) Do MathWorld or PlanetMath have articles on this kind of number?
 * 3) Is there at least one commonly accepted name for this kind of number?

An affirmative answer to these three questions indicates that this kind of number is notable enough for Wikipedia to have an article about it.

In some cases, notability guidelines for sequences of numbers might be more applicable, especially when it is straightforward to put the numbers in some kind order, such as ascending order.


 * Disposition of examples There exists at least one book titled Complex Numbers, one by Walter Ledermann, and several others with titles of the form Complex Numbers and something else, such as Estermann's Complex Numbers and Functions. Both PlanetMath and MathWorld have articles on complex numbers. The name "complex number" has been almost universally accepted since mathematician Carl Friedrich Gauss coined it. Hence, complex numbers are notable enough for Wikipedia.
 * On the other hand, transcendental numbers containing only 3s and 7s in their hexadecimal representations lack a commonly accepted name, in part because the description is so long, but mainly because hardly anyone, professional or amateur, has cared to study these numbers, much less publish anything about them.

Notability of sequences of numbers

 * Examples The Mian–Chowla sequence. The sequence of numbers $n$ such that $5n^{5} + 1$ is prime.


 * 1) Have professional mathematicians published papers about this sequence, or chapters in a book, or an entire book about this sequence?
 * 2) Do MathWorld and PlanetMath have articles about this sequence?
 * 3) Is this sequence listed in the Online Encyclopedia of Integer Sequences (OEIS)?
 * 4) Is there at least one commonly accepted name for this sequence?

An affirmative answer to these four questions indicates that this sequence is notable for Wikipedia to have an article about it. Although the OEIS is restricted to integers in the values its table may hold, there are some ways around this restriction. For sequences of rational numbers, the OEIS might split off the one sequence of rational numbers into two sequences, one of numerators and another one of denominators. If the third question gets a negative response, someone arguing the notability of the sequence needs to show that there is no way the OEIS would include this sequence as a result of its rules, and not as a comment on the non-notability of the sequence.


 * Disposition of examples The mathematicians Mian and Chowla published a paper in Proc. Natl. Acad. Sci. India A14 about the sequence 1, 2, 4, 8, 13, 21, 31, 45, ... Both Mathworld and PlanetMath have articles about this sequence. The sequence is listed in the OEIS as . The modesty of the mathematicians aside, this sequence is universally known as the "Mian–Chowla sequence". Thus, the Mian–Chowla sequence is notable enough for Wikipedia.
 * The sequence of numbers n such that 5n5 + 1 is prime is in the OEIS, but it has the keyword "less". Neither PlanetMath nor MathWorld have articles about this sequence.

Integers

 * Examples 42 and 9870123.


 * 1) Are there at least three unrelated interesting mathematical properties of this integer?
 * 2) Does this number have obvious cultural significance (e.g., as a lucky or unlucky number)?
 * 3) Is it listed in a book such as David Wells's Dictionary of Curious and Interesting Numbers, or Jean-Marie De Koninck's Those Fascinating Numbers, or on Erich Friedman's "What's Special About This Number?" webpage?

In assessing how interesting the mathematical property of a particular integer might be, the essay WP:1729 could be a useful tool. A property that is shared by a large proportion of numbers, such as being a composite number, is not interesting. For the sake of completeness, however, it is accepted that every integer between −1 and 101 has its own article even if it is not as interesting as the others. This avoids having, say, a gap for 38.


 * Disposition of examples 42 is the product of the first three terms of Sylvester's sequence, it is the sum of the first eleven totients and it is a Catalan number, to name just three. As the ultimate answer in Douglas Adams's classic Hitchhiker's trilogy, the number 42 is invested with great cultural significance. 42 appears in both Wells's book and Friedman's page. Thus, 42 is notable enough for Wikipedia.
 * 9870123, on the other hand, is listed neither in Wells's book nor on Friedman's page.

Redirects to range sections
Several articles for round numbers contain a "range section". For example, 40000 (number) has a section Selected numbers, in this case for numbers in the range 40001–49999. Such sections also list integers in the given range that are not sufficiently notable to warrant their own, separate article, but nevertheless have a property that is interesting enough to mention it there. In such cases, it makes sense to make the page for the non-notable number a redirect to the article with the range section in which it is treated. For example, 40585 is a factorion, and is mentioned as such in the article 40000 (number); accordingly, the page 40585 (number) redirects to the article 40000 (number).

Irrational numbers

 * Examples The square root of 2, (sin 1)2.


 * 1) Is there a book about this irrational number, or at least a great number of papers using this number?
 * 2) Are both the decimal expansion and the continued fraction of this number listed in the OEIS?
 * 3) Is this number listed in a book such as Finch's Mathematical Constants?
 * 4) Is there at least one commonly accepted name for this irrational number?


 * Disposition of examples The square root of 2 has an entire book by David Flannery devoted to it. Its continued fraction is A040000 in the OEIS and its decimal expansion is A002193. This number is listed in Finch's book, and it is sometimes called "Pythagoras' constant," though "square root of two" is considered manageable enough. Thus, the square root of 2 is notable enough for Wikipedia.
 * (sin 1)2 is listed in the OEIS but not in Finch's book, nor is there a simpler name for it than its algebraic expression. Thus, (sin 1)2 is not notable enough for Wikipedia.

Decimal expansion redirects
Only the most famous irrational numbers merit redirects from partial decimal expansions. For example, 3.14 and 2.71828. Any others, the search engine ought to catch the number written in the appropriate page and return that as a result. To facilitate this searching, then, it is recommended that the number's decimal expansion be written out in text and not as a graphic in the page.

Notability of lists of numbers and categories
Besides the list of numbers and the list of prime numbers, any other lists are not considered to be narrowly enough construed to be useful. The creation of categories must not be taken lightly: one must be able to demonstrate that the category would be populated by a significant number of articles on notable topics.

Rationale
The subset of numbers anyone could look up in Wikipedia is very small. And if we strike out those numbers that will only be looked up only out of curiosity on whether or not Wikipedia has an article about that number, we're left with an even smaller subset. That subset, give or take a few members, is exactly the same subset WP:NUM calls for. For example, many people will look up forty-two to genuinely learn more about it, while someone would look up the "square root of 40887" only to see if Wikipedia has an article about it and nothing else. No one would be able to specifically look up an integer at some inconvenient distance between 15 googolplexes and 16 googolplexes.