Wikipedia:Articles for deletion/Degen's eight-square identity


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was Nomination withdrawn. Dougweller (talk) 18:48, 17 February 2014 (UTC)

Degen's eight-square identity

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Why is this article so interesting?? The category of natural numbers "being the sum of 8 squares" is hardly interesting because if we understand that any sum of less than 8 squares can be re-written as a sum of 8 squares by adding 0's so that the terms total 8, then there are no natural numbers less than 42.6 trillion that don't belong in this "being the sum of 8 squares" category. (Using the greedy algorithm, 42,600,227,803,223 is equal to 6526884^2 + 3612^2 + 84^2 + 12^2 + 4^2 + 2^2 + 1^2 + 1^2 + 1^2; the smallest number that takes 9 terms with this algorithm.) Does "squares" mean "non-zero squares" in this article?? Georgia guy (talk) 17:11, 16 February 2014 (UTC)


 * Comment I don't know much about the customary notability criteria for mathematical theorems, but it seems to me that this one has a good case for being notable. First of all, it has an article on mathworld:, which is subject to editorial scrutiny.  Second, this identity is discussed in some detail in an article in the The American Mathematical Monthly, available here if you have JSTOR access, and a review of which is here:  if you have MR access.  It's also been generalized in more directions than are noted in the article itself, e.g. .  I'd say it's notable, but I don't know how these things are judged.  I think the overly close paraphrasing from the Mathworld article is much more of a concern than notability.&mdash; alf laylah wa laylah (talk) 19:28, 16 February 2014 (UTC)


 * Keep. And to Georgia guy: unbelievable. There are only four normed division algebras: the real numbers, complex numbers, quaternions, and octonions, each one of which has an $$1,2,4,8$$-square bilinear identity behind it. The 8-square is behind octonion algebra, and it contains the lower dimensional ones as special cases. Perhaps you should suggest deleting the entire family: Brahmagupta-Fibonacci two-square, Euler's four-square, and Degen's eight-square, just to be consistent? Are you affiliated with the Mathematics Department of your university that you feel you are competent to delete an encyclopaedia entry on a particular instance of Pfister's Theorem? Titus III (talk) 07:20, 17 February 2014 (UTC)
 * Keep The OP should have raised a query on the talk page if they don't understand why a formula like this is of note. Or the maths reference desk as they clearly have a general problem with the idea of a formula as opposed to numbers. This particular formula is very notable. Dmcq (talk) 09:29, 17 February 2014 (UTC)
 * Keep No valid reason for deletion. It's in MathWorld as a subject and Google Books gives several hits, plus there's Christopher David Hollings, "The history of the 2-, 4- and 8-square identities", BSHM Bulletin: Journal of the British Society for the History of Mathematics, Volume 21, Issue 2, 2006 --Colapeninsula (talk) 11:39, 17 February 2014 (UTC)
 * Comment I've asked the nominator to withdraw this as it is obviously not a suitable candidate for AfD. I will note that I've seen it called the Degen-Graves-Cayley Eight-Square Identity and the Degen-Graves Eight-Square Identity. Dougweller (talk) 17:07, 17 February 2014 (UTC)
 * Keep Notability in mathematics is slippery enough that we should err on the side of caution in deletion. (John Ohno) 17:38, 17 February 2014 (UTC)


 * Comment I vote keep and expand by explaining more completely its connections to complex numbers, quaternions, and octonions, thus explaining why the article should be considered interesting. ([User: Kermit Rose.    February 17 2014 )  — Preceding unsigned comment added by Kermit1941 (talk • contribs) 17:51, 17 February 2014 (UTC)
 * Withdraw. Per my understanding of the above votes to keep, sometimes number categories that aren't interesting as sub-categories of natural numbers (e.g. numbers that are the sum of 8 squares) might be interesting for some purposes. Georgia guy (talk) 18:45, 17 February 2014 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.